Sennur Ulukus

Age-Based Scheduling for a Memory-Constrained Quantum Switch

In a time-slotted system, we study the problem of scheduling multipartite entanglement requests in a quantum switch with a finite number of quantum memory registers. Specifically, we consider probabilistic link-level entanglement (LLE) generation for each user, probabilistic entanglement swapping, and one-slot decoherence. To evaluate the performance of the proposed scheduling policies, we introduce a novel age-based metric, coined age of entanglement establishment (AoEE). We consider two families of low-complexity policies for which we obtain closed-form expressions for their corresponding AoEE performance. Optimizing over each family, we obtain two policies. Further, we propose one more low-complexity policy and provide its performance guarantee. Finally, we numerically compare the performance of the proposed policies.

An Incentive-Compatible Semi-Parallel Proof-of-Work Protocol

Parallel Proof-of-Work (PoW) protocols have been suggested in the literature to improve the safety guarantees, transaction throughput and confirmation latencies of Nakamoto consensus. In this work, we first consider the existing parallel PoW protocols and develop hard-coded incentive attack structures. Our theoretical results and simulations show that the existing parallel PoW protocols are more vulnerable to incentive attacks than the Nakamoto consensus, e.g., attacks have smaller profitability threshold and they result in higher relative rewards. Next, we introduce a voting-based semi-parallel PoW protocol that outperforms both Nakamoto consensus and the existing parallel PoW protocols from most practical perspectives such as communication overheads, throughput, transaction conflicts, incentive compatibility of the protocol as well as a fair distribution of transaction fees among the voters and the leaders. We use state-of-the-art analysis to evaluate the consistency of the protocol and consider Markov decision process (MDP) models to substantiate our claims about the resilience of our protocol against incentive attacks.

Breaking the Storage-Bandwidth Tradeoff in Distributed Storage with Quantum Entanglement

This work investigates the use of quantum resources in distributed storage systems. Consider an $(n,k,d)$ distributed storage system in which a file is stored across $n$ nodes such that any $k$ nodes suffice to reconstruct the file. When a node fails, any $d$ helper nodes transmit information to a newcomer to rebuild the system. In contrast to the classical repair, where helper nodes transmit classical bits, we allow them to send classical information over quantum channels to the newcomer. The newcomer then generates its storage by performing appropriate measurements on the received quantum states. In this setting, we fully characterize the fundamental tradeoff between storage and repair bandwidth (total communication cost). Compared to classical systems, the optimal storage--bandwidth tradeoff can be significantly improved with the enhancement of quantum entanglement shared only among the surviving nodes, particularly at the minimum-storage regenerating point. Remarkably, we show that when $d \geq 2k-2$ , there exists an operating point at which \textit{both storage and repair bandwidth are simultaneously minimized}. This phenomenon breaks the tradeoff in the classical setting and reveals a fundamentally new regime enabled by quantum communication.

Convergence Properties of Good Quantum Codes for Classical Communication

An important part of the information theory folklore had been about the output statistics of codes that achieve the capacity and how the empirical distributions compare to the output distributions induced by the optimal input in the channel capacity problem. Results for a variety of such empirical output distributions of good codes have been known in the literature, such as the comparison of the output distribution of the code to the optimal output distribution in vanishing and non-vanishing error probability cases. Motivated by these, we aim to achieve similar results for the quantum codes that are used for classical communication, that is the setting in which the classical messages are communicated through quantum codewords that pass through a noisy quantum channel. We first show the uniqueness of the optimal output distribution, to be able to talk more concretely about the optimal output distribution. Then, we extend the vanishing error probability results to the quantum case, by using techniques that are close in spirit to the classical case. We also extend non-vanishing error probability results to the quantum case on block codes, by using the second-order converses for such codes based on hypercontractivity results for the quantum generalized depolarizing semi-groups.

On the Capacity Region of Individual Key Rates in Vector Linear Secure Aggregation

We provide new insights into an open problem recently posed by Yuan-Sun [ISIT 2025], concerning the minimum individual key rate required in the vector linear secure aggregation problem. Consider a distributed system with $K$ users, where each user $k\in [K]$ holds a data stream $W_k$ and an individual key $Z_k$ . A server aims to compute a linear function $\mathbf{F}[W_1;\ldots;W_K]$ without learning any information about another linear function $\mathbf{G}[W_1;\ldots;W_K]$ , where $[W_1;\ldots;W_K]$ denotes the row stack of $W_1,\ldots,W_K$ . The open problem is to determine the minimum required length of $Z_k$ , denoted as $R_k$ , $k\in [K]$ . In this paper, we characterize a new achievable region for the rate tuple $(R_1,\ldots,R_K)$ . The region is polyhedral, with vertices characterized by a binary rate assignment $(R_1,\ldots,R_K) = (\mathbf{1}(1 \in \mathcal{I}),\ldots,\mathbf{1}(K\in \mathcal{I}))$ , where $\mathcal{I}\subseteq [K]$ satisfies the \textit{rank-increment condition}: $\mathrm{rank}\left(\bigl[\mathbf{F}_{\mathcal{I}};\mathbf{G}_{\mathcal{I}}\bigr]\right) =\mathrm{rank}\bigl(\mathbf{F}_{\mathcal{I}}\bigr)+N$ . Here, $\mathbf{F}_\mathcal{I}$ and $\mathbf{G}_\mathcal{I}$ are the submatrices formed by the columns indexed by $\mathcal{I}$ . Our results uncover the novel fact that it is not necessary for every user to hold a key, thereby strictly enlarging the best-known achievable region in the literature. Furthermore, we provide a converse analysis to demonstrate its optimality when minimizing the number of users that hold keys.

RunAgent: Interpreting Natural-Language Plans with Constraint-Guided Execution

Humans solve problems by executing targeted plans, yet large language models (LLMs) remain unreliable for structured workflow execution. We propose RunAgent, a multi-agent plan execution platform that interprets natural-language plans while enforcing stepwise execution through constraints and rubrics. RunAgent bridges the expressiveness of natural language with the determinism of programming via an agentic language with explicit control constructs (e.g., \texttt{IF}, \texttt{GOTO}, \texttt{FORALL}). Beyond verifying syntactic and semantic verification of the step output, which is performed based on the specific instruction of each step, RunAgent autonomously derives and validates constraints based on the description of the task and its instance at each step. RunAgent also dynamically selects among LLM-based reasoning, tool usage, and code generation and execution (e.g., in Python), and incorporates error correction mechanisms to ensure correctness. Finally, RunAgent filters the context history by retaining only relevant information during the execution of each step. Evaluations on Natural-plan and SciBench Datasets demonstrate that RunAgent outperforms baseline LLMs and state-of-the-art PlanGEN methods.

preprint2025arXiv

Privacy-Preserving Semantic Communications via Multi-Task Learning and Adversarial Perturbations

Semantic communications conveys task-relevant meaning rather than focusing solely on message reconstruction, improving bandwidth efficiency and robustness for next-generation wireless systems. However, learned semantic representations can still leak sensitive information to unintended receivers (eavesdroppers). This paper presents a deep learning-based semantic communication framework that jointly supports multiple receiver tasks while explicitly limiting semantic leakage to an eavesdropper. The legitimate link employs a learned encoder at the transmitter, while the receiver trains decoders for semantic inference and data reconstruction. The security problem is formulated via an iterative min-max optimization in which an eavesdropper is trained to improve its semantic inference, while the legitimate transmitter-receiver pair is trained to preserve task performance while reducing the eavesdropper's success. We also introduce an auxiliary layer that superimposes a cooperative, adversarially crafted perturbation on the transmitted waveform to degrade semantic leakage to an eavesdropper. Performance is evaluated over Rayleigh fading channels with additive white Gaussian noise using MNIST and CIFAR-10 datasets. Semantic accuracy and reconstruction quality improve with increasing latent dimension, while the min-max mechanism reduces the eavesdropper's inference performance significantly without degrading the legitimate receiver. The perturbation layer is successful in reducing semantic leakage even when the legitimate link is trained only for its own task. This comprehensive framework motivates semantic communication designs with tunable, end-to-end privacy against adaptive adversaries in realistic wireless settings.

preprint2024arXiv

Will 6G be Semantic Communications? Opportunities and Challenges from Task Oriented and Secure Communications to Integrated Sensing

This paper explores opportunities and challenges of task (goal)-oriented and semantic communications for next-generation (NextG) communication networks through the integration of multi-task learning. This approach employs deep neural networks representing a dedicated encoder at the transmitter and multiple task-specific decoders at the receiver, collectively trained to handle diverse tasks including semantic information preservation, source input reconstruction, and integrated sensing and communications. To extend the applicability from point-to-point links to multi-receiver settings, we envision the deployment of decoders at various receivers, where decentralized learning addresses the challenges of communication load and privacy concerns, leveraging federated learning techniques that distribute model updates across decentralized nodes. However, the efficacy of this approach is contingent on the robustness of the employed deep learning models. We scrutinize potential vulnerabilities stemming from adversarial attacks during both training and testing phases. These attacks aim to manipulate both the inputs at the encoder at the transmitter and the signals received over the air on the receiver side, highlighting the importance of fortifying semantic communications against potential multi-domain exploits. Overall, the joint and robust design of task-oriented communications, semantic communications, and integrated sensing and communications in a multi-task learning framework emerges as the key enabler for context-aware, resource-efficient, and secure communications ultimately needed in NextG network systems.

preprint2023arXiv

Age of Information of a Power Constrained Scheduler in the Presence of a Power Constrained Adversary

We consider a time slotted communication network consisting of a base station (BS), an adversary, $N$ users and $N_s$ communication channels. Both the BS and the adversary have average power constraints and the probability of successful transmission of an update packet depends on the transmission power of the BS and the blocking power of the adversary. We provide a universal lower bound for the average age for this communication network. We prove that the uniform scheduling algorithm with any feasible transmission power choosing policy is $4$ optimal; and the max-age user choosing policy is $2$ optimal. In the second part of the paper, we consider the setting where the BS chooses a transmission policy and the adversary chooses a blocking policy from the set of randomized stationary policies. We show that the Nash equilibrium point may or may not exist for this communication network. We find special cases where the Nash equilibrium always exists.

preprint2023arXiv

Minimizing the Age of Information Over an Erasure Channel for Random Packet Arrivals With a Storage Option at the Transmitter

We consider a time slotted communication system consisting of a base station (BS) and a user. At each time slot an update packet arrives at the BS with probability $p$ , and the BS successfully transmits the update packet with probability $q$ over an erasure channel. We assume that the BS has a unit size buffer where it can store an update packet upon paying a storage cost $c$ . There is a trade-off between the age of information and the storage cost. We formulate this trade-off as a Markov decision process and find an optimal switching type storage policy.

preprint2023arXiv

Private Federated Submodel Learning via Private Set Union

We consider the federated submodel learning (FSL) problem and propose an approach where clients are able to update the central model information theoretically privately. Our approach is based on private set union (PSU), which is further based on multi-message symmetric private information retrieval (MM-SPIR). The server has two non-colluding databases which keep the model in a replicated manner. With our scheme, the server does not get to learn anything further than the subset of submodels updated by the clients: the server does not get to know which client updated which submodel(s), or anything about the local client data. In comparison to the state-of-the-art private FSL schemes of Jia-Jafar and Vithana-Ulukus, our scheme does not require noisy storage of the model at the databases; and in comparison to the secure aggregation scheme of Zhao-Sun, our scheme does not require pre-distribution of client-side common randomness, instead, our scheme creates the required client-side common randomness via random SPIR and one-time pads. The protocol starts with a common randomness generation (CRG) phase where the two databases establish common randomness at the client-side using RSPIR and one-time pads (this phase is called FSL-CRG). Next, the clients utilize the established client-side common randomness to have the server determine privately the union of indices of submodels to be updated collectively by the clients (this phase is called FSL-PSU). Then, the two databases broadcast the current versions of the submodels in the set union to clients. The clients update the submodels based on their local training data. Finally, the clients use a variation of FSL-PSU to write the updates back to the databases privately (this phase is called FSL-write). Our proposed private FSL scheme is robust against client drop-outs, client late-arrivals, and database drop-outs.

Age of Gossip in Ring Networks in the Presence of Jamming Attacks

We consider a system with a source which maintains the most current version of a file, and a ring network of $n$ user nodes that wish to acquire the latest version of the file. The source gets updated with newer file versions as a point process, and forwards them to the user nodes, which further forward them to their neighbors using a memoryless gossip protocol. We study the average version age of this network in the presence of $\tilde{n}$ jammers that disrupt inter-node communications. To this purpose, we construct an alternate system model of mini-rings and prove that the version age of the original model can be sandwiched between constant multiples of the version age of the alternate model. We show that when the number of jammers scales as a fractional power of the network size, i.e., $\tilde n= cn^α$ , the version age scales as $\sqrt{n}$ when $α< \frac{1}{2}$ , and as $n^α$ when $α\geq \frac{1}{2}$ . As the version age of a ring network without any jammers scales as $\sqrt{n}$ , our result implies that the version age with gossiping is robust against up to $\sqrt{n}$ jammers in a ring network.

Age of Information in the Presence of an Adversary

We consider a communication system where a base station serves $N$ users, one user at a time, over a wireless channel. We consider the timeliness of the communication of each user via the age of information metric. A constrained adversary can block at most a given fraction, $α$ , of the time slots over a horizon of $T$ slots, i.e., it can block at most $αT$ slots. We show that an optimum adversary blocks $αT$ consecutive time slots of a randomly selected user. The interesting consecutive property of the blocked time slots is due to the cumulative nature of the age metric.

ASUMAN: Age Sense Updating Multiple Access in Networks

We consider a fully-connected wireless gossip network which consists of a source and $n$ receiver nodes. The source updates itself with a Poisson process and also sends updates to the nodes as Poisson arrivals. Upon receiving the updates, the nodes update their knowledge about the source. The nodes gossip the data among themselves in the form of Poisson arrivals to disperse their knowledge about the source. The total gossiping rate is bounded by a constraint. The goal of the network is to be as timely as possible with the source. In this work, we propose ASUMAN, a distributed opportunistic gossiping scheme, where after each time the source updates itself, each node waits for a time proportional to its current age and broadcasts a signal to the other nodes of the network. This allows the nodes in the network which have higher age to remain silent and only the low-age nodes to gossip, thus utilizing a significant portion of the constrained total gossip rate. We calculate the average age for a typical node in such a network with symmetric settings and show that the theoretical upper bound on the age scales as $O(1)$ . ASUMAN, with an average age of $O(1)$ , offers significant gains compared to a system where the nodes just gossip blindly with a fixed update rate in which case the age scales as $O(\log n)$ .

Communication Cost of Two-Database Symmetric Private Information Retrieval: A Conditional Disclosure of Multiple Secrets Perspective

We consider the total (upload plus download) communication cost of two-database symmetric private information retrieval (SPIR) through its relationship to conditional disclosure of secrets (CDS). In SPIR, a user wishes to retrieve a message out of $K$ messages from $N$ non-colluding and replicated databases without learning anything beyond the retrieved message, while no individual database learns the retrieved message index. In CDS, two parties each holding an individual input and sharing a common secret wish to disclose this secret to an external party in an efficient manner if and only if their inputs satisfy a public deterministic function. As a natural extension of CDS, we introduce conditional disclosure of multiple secrets (CDMS) where two parties share multiple i.i.d.~common secrets rather than a single common secret as in CDS. We show that a special configuration of CDMS is equivalent to two-database SPIR. Inspired by this equivalence, we design download cost efficient SPIR schemes using bipartite graph representation of CDS and CDMS, and determine the exact minimum total communication cost of $N=2$ database SPIR for $K=3$ messages.

Digital Blind Box: Random Symmetric Private Information Retrieval

We introduce the problem of random symmetric private information retrieval (RSPIR). In canonical PIR, a user downloads a message out of $K$ messages from $N$ non-colluding and replicated databases in such a way that no database can know which message the user has downloaded (user privacy). In SPIR, the privacy is symmetric, in that, not only that the databases cannot know which message the user has downloaded, the user itself cannot learn anything further than the particular message it has downloaded (database privacy). In RSPIR, different from SPIR, the user does not have an input to the databases, i.e., the user does not pick a specific message to download, instead is content with any one of the messages. In RSPIR, the databases need to send symbols to the user in such a way that the user is guaranteed to download a message correctly (random reliability), the databases do not know which message the user has received (user privacy), and the user does not learn anything further than the one message it has received (database privacy). This is the digital version of a blind box, also known as gachapon, which implements the above specified setting with physical objects for entertainment. This is also the blind version of $1$ -out-of- $K$ oblivious transfer (OT), an important cryptographic primitive. We study the information-theoretic capacity of RSPIR for the case of $N=2$ databases. We determine its exact capacity for the cases of $K = 2, 3, 4$ messages. While we provide a general achievable scheme that is applicable to any number of messages, the capacity for $K\geq 5$ remains open.

Dynamic Infection Spread Model Based Group Testing

We study a dynamic infection spread model, inspired by the discrete time SIR model, where infections are spread via non-isolated infected individuals. While infection keeps spreading over time, a limited capacity testing is performed at each time instance as well. In contrast to the classical, static, group testing problem, the objective in our setup is not to find the minimum number of required tests to identify the infection status of every individual in the population, but to control the infection spread by detecting and isolating the infections over time by using the given, limited number of tests. In order to analyze the performance of the proposed algorithms, we focus on the mean-sense analysis of the number of individuals that remain non-infected throughout the process of controlling the infection. We propose two dynamic algorithms that both use given limited number of tests to identify and isolate the infections over time, while the infection spreads. While the first algorithm is a dynamic randomized individual testing algorithm, in the second algorithm we employ the group testing approach similar to the original work of Dorfman. By considering weak versions of our algorithms, we obtain lower bounds for the performance of our algorithms. Finally, we implement our algorithms and run simulations to gather numerical results and compare our algorithms and theoretical approximation results under different sets of system parameters.

Dynamic SAFFRON: Disease Control Over Time Via Group Testing

We consider the dynamic infection spread model that is based on the discrete SIR model which assumes infections to be spread over time via infected and non-isolated individuals. In our system, the main objective is not to minimize the number of required tests to identify every infection, but instead, to utilize the available, given testing capacity $T$ at each time instance to efficiently control the infection spread. We introduce and study a novel performance metric, which we coin as $ε$ -disease control time. This metric can be used to measure how fast a given algorithm can control the spread of a disease. We characterize the performance of dynamic individual testing algorithm and introduce a novel dynamic SAFFRON based group testing algorithm. We present theoretical results and implement the proposed algorithms to compare their performances.

Dynamical Dorfman Testing with Quarantine

We consider dynamical group testing problem with a community structure. With a discrete-time SIR (susceptible, infectious, recovered) model, we use Dorfman's two-step group testing approach to identify infections, and step in whenever necessary to inhibit infection spread via quarantines. We analyze the trade-off between quarantine and test costs as well as disease spread. For the special dynamical i.i.d. model, we show that the optimal first stage Dorfman group size differs in dynamic and static cases. We compare the performance of the proposed dynamic two-stage Dorfman testing with state-of-the-art non-adaptive group testing method in dynamic settings.

FedGradNorm: Personalized Federated Gradient-Normalized Multi-Task Learning

Multi-task learning (MTL) is a novel framework to learn several tasks simultaneously with a single shared network where each task has its distinct personalized header network for fine-tuning. MTL can be implemented in federated learning settings as well, in which tasks are distributed across clients. In federated settings, the statistical heterogeneity due to different task complexities and data heterogeneity due to non-iid nature of local datasets can both degrade the learning performance of the system. In addition, tasks can negatively affect each other's learning performance due to negative transference effects. To cope with these challenges, we propose FedGradNorm which uses a dynamic-weighting method to normalize gradient norms in order to balance learning speeds among different tasks. FedGradNorm improves the overall learning performance in a personalized federated learning setting. We provide convergence analysis for FedGradNorm by showing that it has an exponential convergence rate. We also conduct experiments on multi-task facial landmark (MTFL) and wireless communication system dataset (RadComDynamic). The experimental results show that our framework can achieve faster training performance compared to equal-weighting strategy. In addition to improving training speed, FedGradNorm also compensates for the imbalanced datasets among clients.

Game Theoretic Analysis of an Adversarial Status Updating System

We investigate the game theoretic equilibrium points of a status updating system with an adversary that jams the updates in the downlink. We consider the system models with and without diversity. The adversary can jam up to $α$ proportion of the entire communication window. In the model without diversity, in each time slot, the base station schedules a user from $N$ users according to a stationary distribution. The adversary blocks (jams) $αT$ time slots of its choosing out of the total $T$ time slots. For this system, we show that a Nash equilibrium does not exist, however, a Stackelberg equilibrium exists when the scheduling algorithm of the base station acts as the leader and the adversary acts as the follower. In the model with diversity, in each time slot, the base station schedules a user from $N$ users and chooses a sub-carrier from $N_{sub}$ sub-carriers to transmit update packets to the scheduled user according to a stationary distribution. The adversary blocks $αT$ time slots of its choosing out of $T$ time slots at the sub-carriers of its choosing. For this system, we show that a Nash equilibrium exists and identify the Nash equilibrium.

Group Testing with a Graph Infection Spread Model

We propose a novel infection spread model based on a random connection graph which represents connections between $n$ individuals. Infection spreads via connections between individuals and this results in a probabilistic cluster formation structure as well as a non-i.i.d. (correlated) infection status for individuals. We propose a class of two-step sampled group testing algorithms where we exploit the known probabilistic infection spread model. We investigate the metrics associated with two-step sampled group testing algorithms. To demonstrate our results, for analytically tractable exponentially split cluster formation trees, we calculate the required number of tests and the expected number of false classifications in terms of the system parameters, and identify the trade-off between them. For such exponentially split cluster formation trees, for zero-error construction, we prove that the required number of tests is $O(\log_2n)$ . Thus, for such cluster formation trees, our algorithm outperforms any zero-error non-adaptive group test, binary splitting algorithm, and Hwang's generalized binary splitting algorithm. Our results imply that, by exploiting probabilistic information on the connections of individuals, group testing can be used to reduce the number of required tests significantly even when infection rate is high, contrasting the prevalent belief that group testing is useful only when infection rate is low.

Private Federated Submodel Learning with Sparsification

We investigate the problem of private read update write (PRUW) in federated submodel learning (FSL) with sparsification. In FSL, a machine learning model is divided into multiple submodels, where each user updates only the submodel that is relevant to the user's local data. PRUW is the process of privately performing FSL by reading from and writing to the required submodel without revealing the submodel index, or the values of updates to the databases. Sparsification is a widely used concept in learning, where the users update only a small fraction of parameters to reduce the communication cost. Revealing the coordinates of these selected (sparse) updates leaks privacy of the user. We show how PRUW in FSL can be performed with sparsification. We propose a novel scheme which privately reads from and writes to arbitrary parameters of any given submodel, without revealing the submodel index, values of updates, or the coordinates of the sparse updates, to databases. The proposed scheme achieves significantly lower reading and writing costs compared to what is achieved without sparsification.

Private Read Update Write (PRUW) in Federated Submodel Learning (FSL): Communication Efficient Schemes With and Without Sparsification

We investigate the problem of private read update write (PRUW) in relation to private federated submodel learning (FSL), where a machine learning model is divided into multiple submodels based on the different types of data used to train the model. In PRUW, each user downloads the required submodel without revealing its index in the reading phase, and uploads the updates of the submodel without revealing the submodel index or the values of the updates in the writing phase. In this work, we first provide a basic communication efficient PRUW scheme, and study further means of reducing the communication cost via sparsification. Gradient sparsification is a widely used concept in learning applications, where only a selected set of parameters is downloaded and updated, which significantly reduces the communication cost. In this paper, we study how the concept of sparsification can be incorporated in private FSL with the goal of reducing the communication cost, while guaranteeing information theoretic privacy of the updated submodel index as well as the values of the updates. To this end, we introduce two schemes: PRUW with top $r$ sparsification and PRUW with random sparsification. The former communicates only the most significant parameters/updates among the servers and the users, while the latter communicates a randomly selected set of parameters/updates. The two proposed schemes introduce novel techniques such as parameter/update (noisy) permutations to handle the additional sources of information leakage in PRUW caused by sparsification. Both schemes result in significantly reduced communication costs compared to that of the basic (non-sparse) PRUW scheme.

Private Read Update Write (PRUW) with Storage Constrained Databases

We investigate the problem of private read update write (PRUW) in relation to federated submodel learning (FSL) with storage constrained databases. In PRUW, a user privately reads a submodel from a system of $N$ databases containing $M$ submodels, updates it locally, and writes the update back to the databases without revealing the submodel index or the value of the update. The databases considered in this problem are only allowed to store a given amount of information specified by an arbitrary storage constraint. We provide a storage mechanism that determines the contents of each database prior to the application of the PRUW scheme, such that the total communication cost is minimized. We show that the proposed storage scheme achieves a lower total cost compared to what is achieved by using \emph{coded storage} or \emph{divided storage} to meet the given storage constraint.

Rate Distortion Tradeoff in Private Read Update Write in Federated Submodel Learning

We investigate the rate distortion tradeoff in private read update write (PRUW) in relation to federated submodel learning (FSL). In FSL a machine learning (ML) model is divided into multiple submodels based on different types of data used for training. Each user only downloads and updates the submodel relevant to its local data. The process of downloading and updating the required submodel while guaranteeing privacy of the submodel index and the values of updates is known as PRUW. In this work, we study how the communication cost of PRUW can be reduced when a pre-determined amount of distortion is allowed in the reading (download) and writing (upload) phases. We characterize the rate distortion tradeoff in PRUW along with a scheme that achieves the lowest communication cost while working under a given distortion budget.

State Amplification and Masking While Timely Updating

In status update systems, multiple features carried by the status updating process require pursuit of objectives beyond timeliness measured by the age of information of updates. We consider such a problem where the transmitter sends status update messages through a noiseless binary energy harvesting channel that is equivalent to a timing channel. The transmitter aims to amplify or mask the energy state information that is carried in the updating process. The receiver extracts encoded information, infers the energy state sequence while maintaining timeliness of status updates. Consequently, the timings of the updates must be designed to control the message rate, the energy state uncertainty, and the age of information. We investigate this three-way trade-off between the achievable rate, the reduction in energy arrival state uncertainty, and the age of information, for zero and infinite battery cases.

Susceptibility of Age of Gossip to Timestomping

We consider a fully connected network consisting of a source that maintains the current version of a file, $n$ nodes that use asynchronous gossip mechanisms to disseminate fresh information in the network, and an adversary who infects the packets at a target node through data timestamp manipulation, with the intent to replace circulation of fresh packets with outdated packets in the network. We show that a single infected node increases the expected age of a fully connected network from $O(\log n)$ to $O(n)$ . Further, we show that the optimal behavior for an adversary is to reset the timestamps of all outgoing packets to the current time and of all incoming packets to an outdated time. Additionally, if the adversary allows the infected node to accept a small fraction of incoming packets from the network, then a large network can manage to curb the spread of stale files coming from the infected node and pull the network age back to $O(\log n)$ . Lastly, we show that if an infected node contacts only a single node instead of all nodes of the network, the system age can still be degraded to $O(n)$ . These show that fully connected nature of a network can be both a benefit and a detriment for information freshness; full connectivity, while enabling fast dissemination of information, also enables fast dissipation of adversarial inputs.

Timely Gossiping with File Slicing and Network Coding

We consider a system consisting of a large network of $n$ users and a library of files, wherein inter-user communication is established based upon gossip mechanisms. Each file is initially present at exactly one node, which is designated as the file \emph{source}. The source gets updated with newer versions of the file according to an arbitrary distribution in real time, and the other users in the network wish to acquire the latest possible version of the file. We present a class of gossip protocols that achieve $O(1)$ age at a typical node in a single-file system and $O(n)$ age at a typical node for a given file in an $n$ -file system. We show that file slicing and network coding based protocols fall under the presented class of protocols. Numerical evaluation results are presented to confirm the aforementioned bounds.

Timestomping Vulnerability of Age-Sensitive Gossip Networks

We consider gossip networks consisting of a source that maintains the current version of a file, $n$ nodes that use asynchronous gossip mechanisms to disseminate fresh information in the network, and an oblivious adversary who infects the packets at a target node through data timestamp manipulation, with the intent to replace circulation of fresh packets with outdated packets in the network. We demonstrate how network topology capacitates an adversary to influence age scaling in a network. We show that in a fully connected network, a single infected node increases the expected age from $O(\log n)$ to $O(n)$ . Further, we show that the optimal behavior for an adversary is to reset the timestamps of all outgoing packets to the current time and of all incoming packets to an outdated time for the infected node; thereby preventing any fresh information to go into the infected node, and facilitating acceptance of stale information out of the infected node into other network nodes. Lastly for fully connected network, we show that if an infected node contacts only a single node instead of all nodes of the network, the system age can still be degraded to $O(n)$ . These show that fully connected nature of a network can be both a benefit and a detriment for information freshness; full connectivity, while enabling fast dissemination of information, also enables fast dissipation of adversarial inputs. We then analyze the unidirectional ring network, the other end of the network connectivity spectrum, where we show that the adversarial effect on age scaling of a node is limited by its distance from the adversary, and the age scaling for a large fraction of the network continues to be $O(\sqrt{n})$ , unchanged from the case with no adversary. We finally support our findings with simulations.

Using Timeliness in Tracking Infections

We consider real-time timely tracking of infection status (e.g., covid-19) of individuals in a population. In this work, a health care provider wants to detect infected people as well as people who have recovered from the disease as quickly as possible. In order to measure the timeliness of the tracking process, we use the long-term average difference between the actual infection status of the people and their real-time estimate by the health care provider based on the most recent test results. We first find an analytical expression for this average difference for given test rates, infection rates and recovery rates of people. Next, we propose an alternating minimization based algorithm to find the test rates that minimize the average difference. We observe that if the total test rate is limited, instead of testing all members of the population equally, only a portion of the population may be tested in unequal rates calculated based on their infection and recovery rates. Next, we characterize the average difference when the test measurements are erroneous (i.e., noisy). Further, we consider the case where the infection status of individuals may be dependent, which happens when an infected person spreads the disease to another person if they are not detected and isolated by the health care provider. Then, we consider an age of incorrect information based error metric where the staleness metric increases linearly over time as long as the health care provider does not detect the changes in the infection status of the people. In numerical results, we observe that an increased population size increases diversity of people with different infection and recovery rates which may be exploited to spend testing capacity more efficiently. Depending on the health care provider's preferences, test rate allocation can be adjusted to detect either the infected people or the recovered people more quickly.

preprint2021arXiv

Channel Effects on Surrogate Models of Adversarial Attacks against Wireless Signal Classifiers

We consider a wireless communication system that consists of a background emitter, a transmitter, and an adversary. The transmitter is equipped with a deep neural network (DNN) classifier for detecting the ongoing transmissions from the background emitter and transmits a signal if the spectrum is idle. Concurrently, the adversary trains its own DNN classifier as the surrogate model by observing the spectrum to detect the ongoing transmissions of the background emitter and generate adversarial attacks to fool the transmitter into misclassifying the channel as idle. This surrogate model may differ from the transmitter's classifier significantly because the adversary and the transmitter experience different channels from the background emitter and therefore their classifiers are trained with different distributions of inputs. This system model may represent a setting where the background emitter is a primary user, the transmitter is a secondary user, and the adversary is trying to fool the secondary user to transmit even though the channel is occupied by the primary user. We consider different topologies to investigate how different surrogate models that are trained by the adversary (depending on the differences in channel effects experienced by the adversary) affect the performance of the adversarial attack. The simulation results show that the surrogate models that are trained with different distributions of channel-induced inputs severely limit the attack performance and indicate that the transferability of adversarial attacks is neither readily available nor straightforward to achieve since surrogate models for wireless applications may significantly differ from the target model depending on channel effects.

preprint2021arXiv

Gradient Coding with Dynamic Clustering for Straggler-Tolerant Distributed Learning

Distributed implementations are crucial in speeding up large scale machine learning applications. Distributed gradient descent (GD) is widely employed to parallelize the learning task by distributing the dataset across multiple workers. A significant performance bottleneck for the per-iteration completion time in distributed synchronous GD is $straggling$ workers. Coded distributed computation techniques have been introduced recently to mitigate stragglers and to speed up GD iterations by assigning redundant computations to workers. In this paper, we consider gradient coding (GC), and propose a novel dynamic GC scheme, which assigns redundant data to workers to acquire the flexibility to dynamically choose from among a set of possible codes depending on the past straggling behavior. In particular, we consider GC with clustering, and regulate the number of stragglers in each cluster by dynamically forming the clusters at each iteration; hence, the proposed scheme is called $GC$ $with$ $dynamic$ $clustering$ (GC-DC). Under a time-correlated straggling behavior, GC-DC gains from adapting to the straggling behavior over time such that, at each iteration, GC-DC aims at distributing the stragglers across clusters as uniformly as possible based on the past straggler behavior. For both homogeneous and heterogeneous worker models, we numerically show that GC-DC provides significant improvements in the average per-iteration completion time without an increase in the communication load compared to the original GC scheme.

preprint2021arXiv

Wireless Power Transfer for Future Networks: Signal Processing, Machine Learning, Computing, and Sensing

Wireless power transfer (WPT) is an emerging paradigm that will enable using wireless to its full potential in future networks, not only to convey information but also to deliver energy. Such networks will enable trillions of future low-power devices to sense, compute, connect, and energize anywhere, anytime, and on the move. The design of such future networks brings new challenges and opportunities for signal processing, machine learning, sensing, and computing so as to make the best use of the RF radiations, spectrum, and network infrastructure in providing cost-effective and real-time power supplies to wireless devices and enable wireless-powered applications. In this paper, we first review recent signal processing techniques to make WPT and wireless information and power transfer as efficient as possible. Topics include power amplifier and energy harvester nonlinearities, active and passive beamforming, intelligent reflecting surfaces, receive combining with multi-antenna harvester, modulation, coding, waveform, massive MIMO, channel acquisition, transmit diversity, multi-user power region characterization, coordinated multipoint, and distributed antenna systems. Then, we overview two different design methodologies: the model and optimize approach relying on analytical system models, modern convex optimization, and communication theory, and the learning approach based on data-driven end-to-end learning and physics-based learning. We discuss the pros and cons of each approach, especially when accounting for various nonlinearities in wireless-powered networks, and identify interesting emerging opportunities for the approaches to complement each other. Finally, we identify new emerging wireless technologies where WPT may play a key role -- wireless-powered mobile edge computing and wireless-powered sensing -- arguing WPT, communication, computation, and sensing must be jointly designed.

Adversarial Attacks with Multiple Antennas Against Deep Learning-Based Modulation Classifiers

We consider a wireless communication system, where a transmitter sends signals to a receiver with different modulation types while the receiver classifies the modulation types of the received signals using its deep learning-based classifier. Concurrently, an adversary transmits adversarial perturbations using its multiple antennas to fool the classifier into misclassifying the received signals. From the adversarial machine learning perspective, we show how to utilize multiple antennas at the adversary to improve the adversarial (evasion) attack performance. Two main points are considered while exploiting the multiple antennas at the adversary, namely the power allocation among antennas and the utilization of channel diversity. First, we show that multiple independent adversaries, each with a single antenna cannot improve the attack performance compared to a single adversary with multiple antennas using the same total power. Then, we consider various ways to allocate power among multiple antennas at a single adversary such as allocating power to only one antenna, and proportional or inversely proportional to the channel gain. By utilizing channel diversity, we introduce an attack to transmit the adversarial perturbation through the channel with the largest channel gain at the symbol level. We show that this attack reduces the classifier accuracy significantly compared to other attacks under different channel conditions in terms of channel variance and channel correlation across antennas. Also, we show that the attack success improves significantly as the number of antennas increases at the adversary that can better utilize channel diversity to craft adversarial attacks.

Age of Information for Updates with Distortion: Constant and Age-Dependent Distortion Constraints

We consider an information update system where an information receiver requests updates from an information provider in order to minimize its age of information. The updates are generated at the information provider (transmitter) as a result of completing a set of tasks such as collecting data and performing computations. We refer to this as the update generation process. We model the $quality$ of an update as an increasing function of the processing time spent while generating the update at the transmitter. In particular, we use $distortion$ as a proxy for $quality$ , and model distortion as a decreasing function of processing time. Processing longer at the transmitter results in a better quality (lower distortion) update, but it causes the update to age. We determine the age-optimal policies for the update request times at the receiver and the update processing times at the transmitter subject to a minimum required quality (maximum allowed distortion) constraint on the updates. For the required quality constraint, we consider the cases of constant maximum allowed distortion constraints, as well as age-dependent maximum allowed distortion constraints.

Age of Information with Gilbert-Elliot Servers and Samplers

We study age of information in a status updating system that consists of a single sampler, i.e., source node, that sends time-sensitive status updates to a single monitor node through a server node. We first consider a Gilbert-Elliot service profile at the server node. In this model, service times at the server node follow a finite state Markov chain with two states: ${bad}$ state $b$ and ${good}$ state $g$ where the server is faster in state $g$ . We determine the time average age experienced by the monitor node and characterize the age-optimal state transition matrix $P$ with and without an average cost constraint on the service operation. Next, we consider a Gilbert-Elliot sampling profile at the source. In this model, the interarrival times follow a finite state Markov chain with two states: ${bad}$ state $b$ and ${good}$ state $g$ where samples are more frequent in state $g$ . We find the time average age experienced by the monitor node and characterize the age-optimal state transition matrix $P$ .

Age of Information: An Introduction and Survey

We summarize recent contributions in the broad area of age of information (AoI). In particular, we describe the current state of the art in the design and optimization of low-latency cyberphysical systems and applications in which sources send time-stamped status updates to interested recipients. These applications desire status updates at the recipients to be as timely as possible; however, this is typically constrained by limited system resources. We describe AoI timeliness metrics and present general methods of AoI evaluation analysis that are applicable to a wide variety of sources and systems. Starting from elementary single-server queues, we apply these AoI methods to a range of increasingly complex systems, including energy harvesting sensors transmitting over noisy channels, parallel server systems, queueing networks, and various single-hop and multi-hop wireless networks. We also explore how update age is related to MMSE methods of sampling, estimation and control of stochastic processes. The paper concludes with a review of efforts to employ age optimization in cyberphysical applications.

Age-Based Coded Computation for Bias Reduction in Distributed Learning

Coded computation can be used to speed up distributed learning in the presence of straggling workers. Partial recovery of the gradient vector can further reduce the computation time at each iteration; however, this can result in biased estimators, which may slow down convergence, or even cause divergence. Estimator bias will be particularly prevalent when the straggling behavior is correlated over time, which results in the gradient estimators being dominated by a few fast servers. To mitigate biased estimators, we design a $timely$ dynamic encoding framework for partial recovery that includes an ordering operator that changes the codewords and computation orders at workers over time. To regulate the recovery frequencies, we adopt an $age$ metric in the design of the dynamic encoding scheme. We show through numerical results that the proposed dynamic encoding strategy increases the timeliness of the recovered computations, which as a result, reduces the bias in model updates, and accelerates the convergence compared to the conventional static partial recovery schemes.

How to Make 5G Communications "Invisible": Adversarial Machine Learning for Wireless Privacy

We consider the problem of hiding wireless communications from an eavesdropper that employs a deep learning (DL) classifier to detect whether any transmission of interest is present or not. There exists one transmitter that transmits to its receiver in the presence of an eavesdropper, while a cooperative jammer (CJ) transmits carefully crafted adversarial perturbations over the air to fool the eavesdropper into classifying the received superposition of signals as noise. The CJ puts an upper bound on the strength of perturbation signal to limit its impact on the bit error rate (BER) at the receiver. We show that this adversarial perturbation causes the eavesdropper to misclassify the received signals as noise with high probability while increasing the BER only slightly. On the other hand, the CJ cannot fool the eavesdropper by simply transmitting Gaussian noise as in conventional jamming and instead needs to craft perturbation signals built by adversarial machine learning to enable covert communications. Our results show that signals with different modulation types and eventually 5G communications can be effectively hidden from an eavesdropper even if it is equipped with a DL classifier to detect transmissions.

Multi-Party Private Set Intersection: An Information-Theoretic Approach

We investigate the problem of multi-party private set intersection (MP-PSI). In MP-PSI, there are $M$ parties, each storing a data set $\mathcal{p}_i$ over $N_i$ replicated and non-colluding databases, and we want to calculate the intersection of the data sets $\cap_{i=1}^M \mathcal{p}_i$ without leaking any information beyond the set intersection to any of the parties. We consider a specific communication protocol where one of the parties, called the leader party, initiates the MP-PSI protocol by sending queries to the remaining parties which are called client parties. The client parties are not allowed to communicate with each other. We propose an information-theoretic scheme that privately calculates the intersection $\cap_{i=1}^M \mathcal{p}_i$ with a download cost of $D = \min_{t \in \{1, \cdots, M\}} \sum_{i \in \{1, \cdots M\}\setminus {t}} \left\lceil \frac{|\mathcal{p}_t|N_i}{N_i-1}\right\rceil$ . Similar to the 2-party PSI problem, our scheme builds on the connection between the PSI problem and the multi-message symmetric private information retrieval (MM-SPIR) problem. Our scheme is a non-trivial generalization of the 2-party PSI scheme as it needs an intricate design of the shared common randomness. Interestingly, in terms of the download cost, our scheme does not incur any penalty due to the more stringent privacy constraints in the MP-PSI problem compared to the 2-party PSI problem.

Optimal Selective Encoding for Timely Updates

We consider a system in which an information source generates independent and identically distributed status update packets from an observed phenomenon that takes $n$ possible values based on a given pmf. These update packets are encoded at the transmitter node to be sent to the receiver node. Instead of encoding all $n$ possible realizations, the transmitter node only encodes the most probable $k$ realizations and disregards whenever a realization from the remaining $n-k$ values occurs. We find the average age and determine the age-optimal real codeword lengths such that the average age at the receiver node is minimized. Through numerical evaluations for arbitrary pmfs, we show that this selective encoding policy results in a lower average age than encoding every realization and find the age-optimal $k$ . We also analyze a randomized selective encoding policy in which the remaining $n-k$ realizations are encoded and sent with a certain probability to further inform the receiver at the expense of longer codewords for the selected $k$ realizations.

Over-the-Air Adversarial Attacks on Deep Learning Based Modulation Classifier over Wireless Channels

We consider a wireless communication system that consists of a transmitter, a receiver, and an adversary. The transmitter transmits signals with different modulation types, while the receiver classifies its received signals to modulation types using a deep learning-based classifier. In the meantime, the adversary makes over-the-air transmissions that are received as superimposed with the transmitter's signals to fool the classifier at the receiver into making errors. While this evasion attack has received growing interest recently, the channel effects from the adversary to the receiver have been ignored so far such that the previous attack mechanisms cannot be applied under realistic channel effects. In this paper, we present how to launch a realistic evasion attack by considering channels from the adversary to the receiver. Our results show that modulation classification is vulnerable to an adversarial attack over a wireless channel that is modeled as Rayleigh fading with path loss and shadowing. We present various adversarial attacks with respect to availability of information about channel, transmitter input, and classifier architecture. First, we present two types of adversarial attacks, namely a targeted attack (with minimum power) and non-targeted attack that aims to change the classification to a target label or to any other label other than the true label, respectively. Both are white-box attacks that are transmitter input-specific and use channel information. Then we introduce an algorithm to generate adversarial attacks using limited channel information where the adversary only knows the channel distribution. Finally, we present a black-box universal adversarial perturbation (UAP) attack where the adversary has limited knowledge about both channel and transmitter input.

Partial Updates: Losing Information for Freshness

We consider an information updating system where a source produces updates as requested by a transmitter. The transmitter further processes these updates in order to generate $partial$ $updates$ , which have smaller information compared to the original updates, to be sent to a receiver. We study the problem of generating partial updates, and finding their corresponding real-valued codeword lengths, in order to minimize the average age experienced by the receiver, while maintaining a desired level of mutual information between the original and partial updates. This problem is NP hard. We relax the problem and develop an alternating minimization based iterative algorithm that generates a pmf for the partial updates, and the corresponding age-optimal real-valued codeword length for each update. We observe that there is a tradeoff between the attained average age and the mutual information between the original and partial updates.

Selective Encoding Policies for Maximizing Information Freshness

An information source generates independent and identically distributed status update messages from an observed random phenomenon which takes $n$ distinct values based on a given pmf. These update packets are encoded at the transmitter node to be sent to a receiver node which wants to track the observed random variable with as little age as possible. The transmitter node implements a selective $k$ encoding policy such that rather than encoding all possible $n$ realizations, the transmitter node encodes the most probable $k$ realizations. We consider three different policies regarding the remaining $n-k$ less probable realizations: $highest$ $k$ $selective$ $encoding$ which disregards whenever a realization from the remaining $n-k$ values occurs; $randomized$ $selective$ $encoding$ which encodes and sends the remaining $n-k$ realizations with a certain probability to further inform the receiver node at the expense of longer codewords for the selected $k$ realizations; and $highest$ $k$ $selective$ $encoding$ $with$ $an$ $empty$ $symbol$ which sends a designated empty symbol when one of the remaining $n-k$ realizations occurs. For all of these three encoding schemes, we find the average age and determine the age-optimal real codeword lengths, including the codeword length for the empty symbol in the case of the latter scheme, such that the average age at the receiver node is minimized. Through numerical evaluations for arbitrary pmfs, we show that these selective encoding policies result in a lower average age than encoding every realization, and find the corresponding age-optimal $k$ values.

Semantic Private Information Retrieval

We investigate the problem of semantic private information retrieval (semantic PIR). In semantic PIR, a user retrieves a message out of $K$ independent messages stored in $N$ replicated and non-colluding databases without revealing the identity of the desired message to any individual database. The messages come with \emph{different semantics}, i.e., the messages are allowed to have \emph{non-uniform a priori probabilities} denoted by $(p_i>0,\: i \in [K])$ , which are a proxy for their respective popularity of retrieval, and \emph{arbitrary message sizes} $(L_i,\: i \in [K])$ . This is a generalization of the classical private information retrieval (PIR) problem, where messages are assumed to have equal a priori probabilities and equal message sizes. We derive the semantic PIR capacity for general $K$ , $N$ . The results show that the semantic PIR capacity depends on the number of databases $N$ , the number of messages $K$ , the a priori probability distribution of messages $p_i$ , and the message sizes $L_i$ . We present two achievable semantic PIR schemes: The first one is a deterministic scheme which is based on message asymmetry. This scheme employs non-uniform subpacketization. The second scheme is probabilistic and is based on choosing one query set out of multiple options at random to retrieve the required message without the need for exponential subpacketization. We derive necessary and sufficient conditions for the semantic PIR capacity to exceed the classical PIR capacity with equal priors and sizes. Our results show that the semantic PIR capacity can be larger than the classical PIR capacity when longer messages have higher popularities. However, when messages are equal-length, the non-uniform priors cannot be exploited to improve the retrieval rate over the classical PIR capacity.

Straggler-aware Distributed Learning: Communication Computation Latency Trade-off

When gradient descent (GD) is scaled to many parallel workers for large scale machine learning problems, its per-iteration computation time is limited by the straggling workers. Straggling workers can be tolerated by assigning redundant computations and coding across data and computations, but in most existing schemes, each non-straggling worker transmits one message per iteration to the parameter server (PS) after completing all its computations. Imposing such a limitation results in two main drawbacks; over-computation due to inaccurate prediction of the straggling behaviour, and under-utilization due to treating workers as straggler/non-straggler and discarding partial computations carried out by stragglers. In this paper, to overcome these drawbacks, we consider multi-message communication (MMC) by allowing multiple computations to be conveyed from each worker per iteration, and design straggler avoidance techniques accordingly. Then, we analyze how the proposed designs can be employed efficiently to seek a balance between the computation and communication latency to minimize the overall latency. Furthermore, through extensive simulations, both model-based and real implementation on Amazon EC2 servers, we identify the advantages and disadvantages of these designs in different settings, and demonstrate that MMC can help improve upon existing straggler avoidance schemes.

Who Should Google Scholar Update More Often?

We consider a resource-constrained updater, such as Google Scholar, which wishes to update the citation records of a group of researchers, who have different mean citation rates (and optionally, different importance coefficients), in such a way to keep the overall citation index as up to date as possible. The updater is resource-constrained and cannot update citations of all researchers all the time. In particular, it is subject to a total update rate constraint that it needs to distribute among individual researchers. We use a metric similar to the age of information: the long-term average difference between the actual citation numbers and the citation numbers according to the latest updates. We show that, in order to minimize this difference metric, the updater should allocate its total update capacity to researchers proportional to the $square$ $roots$ of their mean citation rates. That is, more prolific researchers should be updated more often, but there are diminishing returns due to the concavity of the square root function. More generally, our paper addresses the problem of optimal operation of a resource-constrained sampler that wishes to track multiple independent counting processes in a way that is as up to date as possible.

Covert Bits Through Queues

We consider covert communication using a queuing timing channel in the presence of a warden. The covert message is encoded using the inter-arrival times of the packets, and the legitimate receiver and the warden observe the inter-departure times of the packets from their respective queues. The transmitter and the legitimate receiver also share a secret key to facilitate covert communication. We propose achievable schemes that obtain non-zero covert rate for both exponential and general queues when a sufficiently high rate secret key is available. This is in contrast to other channel models such as the Gaussian channel or the discrete memoryless channel where only $\mathcal{O}(\sqrt{n})$ covert bits can be sent over $n$ channel uses, yielding a zero covert rate.

MIMO Wiretap Channel under Receiver Side Power Constraints with Applications to Wireless Power Transfer and Cognitive Radio

We consider the multiple-input multiple-output (MIMO) wiretap channel under a minimum receiver-side power constraint in addition to the usual maximum transmitter-side power constraint. This problem is motivated by energy harvesting communications with wireless energy transfer, where an added goal is to deliver a minimum amount of energy to a receiver in addition to delivering secure data to another receiver. In this paper, we characterize the exact secrecy capacity of the MIMO wiretap channel under transmitter and receiver-side power constraints. We first show that solving this problem is equivalent to solving the secrecy capacity of the wiretap channel under a double-sided correlation matrix constraint on the channel input. We show the converse by extending the channel enhancement technique to our case. We present two achievable schemes that achieve the secrecy capacity: the first achievable scheme uses a Gaussian codebook with a fixed mean, and the second achievable scheme uses artificial noise (or cooperative jamming) together with a Gaussian codebook. The role of the mean or the artificial noise is to enable energy transfer without sacrificing from the secure rate. This is the first instance of a channel model where either the use of a mean signal or the use of channel prefixing via artificial noise is strictly necessary for the MIMO wiretap channel. We then extend our work to consider a maximum receiver-side power constraint. This problem is motivated by cognitive radio applications, where an added goal is to decrease the received signal energy (interference temperature) at a receiver. We further extend our results to: requiring receiver-side power constraints at both receivers; considering secrecy constraints at both receivers to study broadcast channels with confidential messages; and removing the secrecy constraints to study the classical broadcast channel.

Partial Strong Converse for the Non-Degraded Wiretap Channel

We prove the partial strong converse property for the discrete memoryless \emph{non-degraded} wiretap channel, for which we require the leakage to the eavesdropper to vanish but allow an asymptotic error probability $ε\in [0,1)$ to the legitimate receiver. We show that when the transmission rate is above the secrecy capacity, the probability of correct decoding at the legitimate receiver decays to zero exponentially. Therefore, the maximum transmission rate is the same for $ε\in [0,1)$ , and the partial strong converse property holds. Our work is inspired by a recently developed technique based on information spectrum method and Chernoff-Cramer bound for evaluating the exponent of the probability of correct decoding.

Secrecy in MIMO Networks with No Eavesdropper CSIT

We consider two fundamental multi-user channel models: the multiple-input multiple-output (MIMO) wiretap channel with one helper (WTH) and the MIMO multiple access wiretap channel (MAC-WT). In each case, the eavesdropper has $K$ antennas while the remaining terminals have $N$ antennas each. We consider a fast fading channel where the channel state information (CSI) of the legitimate receiver is available at the transmitters but no channel state information at the transmitters (CSIT) is available for the eavesdropper's channel. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for each channel model for the regime $K\leq N$ , and show that in this regime, the MAC-WT channel reduces to the WTH in the absence of eavesdropper CSIT. For the regime $N\leq K\leq 2N$ , we obtain the optimal linear s.d.o.f., and show that the MAC-WT channel and the WTH have the same optimal s.d.o.f. when restricted to linear encoding strategies. In the absence of any such restrictions, we provide an upper bound for the sum s.d.o.f. of the MAC-WT chanel in the regime $N\leq K\leq 2N$ . Our results show that unlike in the single-input single-output (SISO) case, there is loss of s.d.o.f. for even the WTH due to lack of eavesdropper CSIT when $K\geq N$ .

Secure Degrees of Freedom of the Multiple Access Wiretap Channel with Multiple Antennas

We consider a two-user multiple-input multiple-output (MIMO) multiple access wiretap channel with $N$ antennas at each transmitter, $N$ antennas at the legitimate receiver, and $K$ antennas at the eavesdropper. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for this model for all values of $N$ and $K$ . We subdivide our problem into several regimes based on the values of $N$ and $K$ , and provide achievable schemes based on real and vector space alignment techniques for fixed and fading channel gains, respectively. To prove the optimality of the achievable schemes, we provide matching converses for each regime. Our results show how the number of eavesdropper antennas affects the optimal sum s.d.o.f. of the multiple access wiretap channel.

The Capacity of Private Information Retrieval from Coded Databases

We consider the problem of private information retrieval (PIR) over a distributed storage system. The storage system consists of $N$ non-colluding databases, each storing a coded version of $M$ messages. In the PIR problem, the user wishes to retrieve one of the available messages without revealing the message identity to any individual database. We derive the information-theoretic capacity of this problem, which is defined as the maximum number of bits of the desired message that can be privately retrieved per one bit of downloaded information. We show that the PIR capacity in this case is $C=\left(1+\frac{K}{N}+\frac{K^2}{N^2}+\cdots+\frac{K^{M-1}}{N^{M-1}}\right)^{-1}=(1+R_c+R_c^2+\cdots+R_c^{M-1})^{-1}=\frac{1-R_c}{1-R_c^M}$ , where $R_c$ is the rate of the $(N,K)$ code used. The capacity is a function of the code rate and the number of messages only regardless of the explicit structure of the storage code. The result implies a fundamental tradeoff between the optimal retrieval cost and the storage cost. The result generalizes the achievability and converse results for the classical PIR with replicating databases to the case of coded databases.

Energy Harvesting Transmitters that Heat Up: Throughput Maximization under Temperature Constraints

Motivated by damage due to heating in sensor operation, we consider the throughput optimal offline data scheduling problem in an energy harvesting transmitter such that the resulting temperature increase remains below a critical level. We model the temperature dynamics of the transmitter as a linear system and determine the optimal transmit power policy under such temperature constraints as well as energy harvesting constraints over an AWGN channel. We first derive the structural properties of the solution for the general case with multiple energy arrivals. We show that the optimal power policy is piecewise monotone decreasing with possible jumps at the energy harvesting instants. We derive analytical expressions for the optimal solution in the single energy arrival case. We show that, in the single energy arrival case, the optimal power is monotone decreasing, the resulting temperature is monotone increasing, and both remain constant after the temperature hits the critical level. We then generalize the solution for the multiple energy arrival case.

Energy Harvesting Wireless Communications: A Review of Recent Advances

This article summarizes recent contributions in the broad area of energy harvesting wireless communications. In particular, we provide the current state of the art for wireless networks composed of energy harvesting nodes, starting from the information-theoretic performance limits to transmission scheduling policies and resource allocation, medium access and networking issues. The emerging related area of energy transfer for self-sustaining energy harvesting wireless networks is considered in detail covering both energy cooperation aspects and simultaneous energy and information transfer. Various potential models with energy harvesting nodes at different network scales are reviewed as well as models for energy consumption at the nodes.

Optimal Energy and Data Routing in Networks with Energy Cooperation

We consider the delay minimization problem in an energy harvesting communication network with energy cooperation. In this network, nodes harvest energy from nature for use in data transmission, and may transfer a portion of their harvested energies to neighboring nodes through energy cooperation. For fixed data and energy routing topologies, we determine the optimum data rates, transmit powers and energy transfers, subject to flow and energy conservation constraints, in order to minimize the network delay. We start with a simplified problem with fixed data flows and optimize energy management at each node for the case of a single energy harvest per node. This is tantamount to distributing each node's available energy over its outgoing data links and energy transfers to neighboring nodes. For this case, with no energy cooperation, we show that each node should allocate more power to links with more noise and/or more data flow. In addition, when there is energy cooperation, our numerical results indicate that, energy is routed from nodes with lower data loads to nodes with higher data loads. We extend this setting to the case of multiple energy harvests per node over time. In this case, we optimize each node's energy management over its outgoing data links and its energy transfers to neighboring nodes, over multiple time slots. For this case, with no energy cooperation, we show that, for any given node, the sum of powers on the outgoing links is equal to the single-link optimal power over time. Finally, we consider the problem of joint flow control and energy management for the entire network. We determine the necessary conditions for joint optimality of a power control, energy transfer and routing policy. We provide an iterative algorithm that updates the data and energy flows, and power distribution over outgoing data links. We show convergence to a Pareto-optimal operating point.

Optimal Policies for Wireless Networks with Energy Harvesting Transmitters and Receivers: Effects of Decoding Costs

We consider the effects of decoding costs in energy harvesting communication systems. In our setting, receivers, in addition to transmitters, rely solely on energy harvested from nature, and need to spend some energy in order to decode their intended packets. We model the decoding energy as an increasing convex function of the rate of the incoming data. In this setting, in addition to the traditional energy causality constraints at the transmitters, we have the decoding causality constraints at the receivers, where energy spent by the receiver for decoding cannot exceed its harvested energy. We first consider the point-to-point single-user problem where the goal is to maximize the total throughput by a given deadline subject to both energy and decoding causality constraints. We show that decoding costs at the receiver can be represented as generalized data arrivals at the transmitter, and thereby moving all system constraints to the transmitter side. Then, we consider several multi-user settings. We start with a two-hop network where the relay and the destination have decoding costs, and show that separable policies, where the transmitter's throughput is maximized irrespective of the relay's transmission energy profile, are optimal. Next, we consider the multiple access channel (MAC) and the broadcast channel (BC) where the transmitters and the receivers harvest energy from nature, and characterize the maximum departure region. In all multi-user settings considered, we decompose our problems into inner and outer problems. We solve the inner problems by exploiting the structure of the particular model, and solve the outer problems by water-filling algorithms.

Secure Degrees of Freedom of Multi-user Networks: One-Time-Pads in the Air via Alignment

We revisit the recent secure degrees of freedom (s.d.o.f.) results for one-hop multi-user wireless networks by considering three fundamental wireless network structures: Gaussian wiretap channel with helpers, Gaussian multiple access wiretap channel, and Gaussian interference channel with secrecy constraints. We present main enabling tools and resulting communication schemes in an expository manner, along with key insights and design principles emerging from them. The main achievable schemes are based on real interference alignment, channel prefixing via cooperative jamming, and structured signalling. Real interference alignment enables aligning the cooperative jamming signals together with the message carrying signals at the eavesdroppers to protect them akin to one-time-pad protecting messages in wired systems. Real interference alignment also enables decodability at the legitimate receivers by rendering message carrying and cooperative jamming signals separable, and simultaneously aligning the cooperative jamming signals in the smallest possible sub-space. The main converse techniques are based on two key lemmas which quantify the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs; and the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. These two lemmas when applied according to the unique structure of individual networks provide tight converses. Finally, we present a blind cooperative jamming scheme for the helper network with no eavesdropper channel state information at the transmitters that achieves the same optimal s.d.o.f. as in the case of full eavesdropper channel state information.

Secure Degrees of Freedom of One-hop Wireless Networks with No Eavesdropper CSIT

We consider three channel models: the wiretap channel with $M$ helpers, the $K$ -user multiple access wiretap channel, and the $K$ -user interference channel with an external eavesdropper, when no eavesdropper's channel state information (CSI) is available at the transmitters. In each case, we establish the optimal sum secure degrees of freedom (s.d.o.f.) by providing achievable schemes and matching converses. We show that the unavailability of the eavesdropper's CSIT does not reduce the s.d.o.f. of the wiretap channel with helpers. However, there is loss in s.d.o.f. for both the multiple access wiretap channel and the interference channel with an external eavesdropper. In particular, we show that in the absence of eavesdropper's CSIT, the $K$ -user multiple access wiretap channel reduces to a wiretap channel with $(K-1)$ helpers from a sum s.d.o.f. perspective, and the optimal sum s.d.o.f. reduces from $\frac{K(K-1)}{K(K-1)+1}$ to $\frac{K-1}{K}$ . For the interference channel with an external eavesdropper, the optimal sum s.d.o.f. decreases from $\frac{K(K-1)}{2K-1}$ to $\frac{K-1}{2}$ in the absence of the eavesdropper's CSIT. Our results show that the lack of eavesdropper's CSIT does not have a significant impact on the optimal s.d.o.f. for any of the three channel models, especially when the number of users is large. This implies that physical layer security can be made robust to the unavailability of eavesdropper CSIT at high signal to noise ratio (SNR) regimes by careful modification of the achievable schemes as demonstrated in this paper.

Secure Degrees of Freedom Region of the Two-User MISO Broadcast Channel with Alternating CSIT

The two user multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM) is studied in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form $I_{i}$ , $i=1,2$ where $I_{1}, I_{2}\in \{\mathsf{P}, \mathsf{D}, \mathsf{N}\}$ , and the forms $\mathsf{P}$ , $\mathsf{D}$ and $\mathsf{N}$ correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate between $9$ possible states corresponding to all possible values of $I_{1}I_{2}$ , with each state occurring for $λ_{I_{1}I_{2}}$ fraction of the total duration. The main contribution of this paper is to establish the secure degrees of freedom (s.d.o.f.) region of the MISO BCCM with alternating CSIT with the symmetry assumption, where $λ_{I_{1} I_{2}}=λ_{I_{2}I_{1}}$ . The main technical contributions include developing a) novel achievable schemes for MISO BCCM with alternating CSIT with security constraints which also highlight the synergistic benefits of inter-state coding for secrecy, b) new converse proofs via local statistical equivalence and channel enhancement; and c) showing the interplay between various aspects of channel knowledge and their impact on s.d.o.f.

preprint2014arXiv

Polar Coding for the General Wiretap Channel

Information-theoretic work for wiretap channels is mostly based on random coding schemes. Designing practical coding schemes to achieve information-theoretic security is an important problem. By applying the two recently developed techniques for polar codes, we propose a polar coding scheme to achieve the secrecy capacity of the general wiretap channel.

preprint2014arXiv

Secure Degrees of Freedom Regions of Multiple Access and Interference Channels: The Polytope Structure

The sum secure degrees of freedom (s.d.o.f.) of two fundamental multi-user network structures, the K-user Gaussian multiple access (MAC) wiretap channel and the K-user interference channel (IC) with secrecy constraints, have been determined recently as K(K-1)/(K(K-1)+1) [1,2] and K(K-1)/(2K-1) [3,4], respectively. In this paper, we determine the entire s.d.o.f. regions of these two channel models. The converse for the MAC follows from a middle step in the converse of [1,2]. The converse for the IC includes constraints both due to secrecy as well as due to interference. Although the portion of the region close to the optimum sum s.d.o.f. point is governed by the upper bounds due to secrecy constraints, the other portions of the region are governed by the upper bounds due to interference constraints. Different from the existing literature, in order to fully understand the characterization of the s.d.o.f. region of the IC, one has to study the 4-user case, i.e., the 2 or 3-user cases do not illustrate the generality of the problem. In order to prove the achievability, we use the polytope structure of the converse region. In both MAC and IC cases, we develop explicit schemes that achieve the extreme points of the polytope region given by the converse. Specifically, the extreme points of the MAC region are achieved by an m-user MAC wiretap channel with (K-m) helpers, i.e., by setting (K-m) users' secure rates to zero and utilizing them as pure (structured) cooperative jammers. The extreme points of the IC region are achieved by a (K-m)-user IC with confidential messages, m helpers, and N external eavesdroppers, for m>=1 and a finite N. A byproduct of our results in this paper is that the sum s.d.o.f. is achieved only at one extreme point of the s.d.o.f. region, which is the symmetric-rate extreme point, for both MAC and IC channel models.

preprint2014arXiv

The Binary Energy Harvesting Channel with a Unit-Sized Battery

We consider a binary energy harvesting communication channel with a finite-sized battery at the transmitter. In this model, the channel input is constrained by the available energy at each channel use, which is driven by an external energy harvesting process, the size of the battery, and the previous channel inputs. We consider an abstraction where energy is harvested in binary units and stored in a battery with the capacity of a single unit, and the channel inputs are binary. Viewing the available energy in the battery as a state, this is a state-dependent channel with input-dependent states, memory in the states, and causal state information available at the transmitter only. We find an equivalent representation for this channel based on the timings of the symbols, and determine the capacity of the resulting equivalent timing channel via an auxiliary random variable. We give achievable rates based on certain selections of this auxiliary random variable which resemble lattice coding for the timing channel. We develop upper bounds for the capacity by using a genie-aided method, and also by quantifying the leakage of the state information to the receiver. We show that the proposed achievable rates are asymptotically capacity achieving for small energy harvesting rates. We extend the results to the case of ternary channel inputs. Our achievable rates give the capacity of the binary channel within 0.03 bits/channel use, the ternary channel within 0.05 bits/channel use, and outperform basic Shannon strategies that only consider instantaneous battery states, for all parameter values.

Binary Energy Harvesting Channel with Finite Energy Storage

We consider the capacity of an energy harvesting communication channel with a finite-sized battery. As an abstraction of this problem, we consider a system where energy arrives at the encoder in multiples of a fixed quantity, and the physical layer is modeled accordingly as a finite discrete alphabet channel based on this fixed quantity. Further, for tractability, we consider the case of binary energy arrivals into a unit-capacity battery over a noiseless binary channel. Viewing the available energy as state, this is a state-dependent channel with causal state information available only at the transmitter. Further, the state is correlated over time and the channel inputs modify the future states. We show that this channel is equivalent to an additive geometric-noise timing channel with causal information of the noise available at the transmitter.We provide a single-letter capacity expression involving an auxiliary random variable, and evaluate this expression with certain auxiliary random variable selection, which resembles noise concentration and lattice-type coding in the timing channel. We evaluate the achievable rates by the proposed auxiliary selection and extend our results to noiseless ternary channels.

Energy Cooperation in Energy Harvesting Communications

In energy harvesting communications, users transmit messages using energy harvested from nature during the course of communication. With an optimum transmit policy, the performance of the system depends only on the energy arrival profiles. In this paper, we introduce the concept of energy cooperation, where a user wirelessly transmits a portion of its energy to another energy harvesting user. This enables shaping and optimization of the energy arrivals at the energy-receiving node, and improves the overall system performance, despite the loss incurred in energy transfer. We consider several basic multi-user network structures with energy harvesting and wireless energy transfer capabilities: relay channel, two-way channel and multiple access channel. We determine energy management policies that maximize the system throughput within a given duration using a Lagrangian formulation and the resulting KKT optimality conditions. We develop a two-dimensional directional water-filling algorithm which optimally controls the flow of harvested energy in two dimensions: in time (from past to future) and among users (from energy-transferring to energy-receiving) and show that a generalized version of this algorithm achieves the boundary of the capacity region of the two-way channel.

Optimal Scheduling for Energy Harvesting Transmitters with Hybrid Energy Storage

We consider data transmission with an energy harvesting transmitter which has a hybrid energy storage unit composed of a perfectly efficient super-capacitor (SC) and an inefficient battery. The SC has finite space for energy storage while the battery has unlimited space. The transmitter can choose to store the harvested energy in the SC or in the battery. The energy is drained from the SC and the battery simultaneously. In this setting, we consider the offline throughput maximization problem by a deadline over a point-to-point channel. In contrast to previous works, the hybrid energy storage model with finite and unlimited storage capacities imposes a generalized set of constraints on the transmission policy. As such, we show that the solution generalizes that for a single battery and is obtained by applying directional water-filling algorithm multiple times.

Secure Degrees of Freedom of K-User Gaussian Interference Channels: A Unified View

We determine the exact sum secure degrees of freedom (d.o.f.) of the K-user Gaussian interference channel. We consider three different secrecy constraints: 1) K-user interference channel with one external eavesdropper (IC-EE), 2) K-user interference channel with confidential messages (IC-CM), and 3) K-user interference channel with confidential messages and one external eavesdropper (IC-CM-EE). We show that for all of these three cases, the exact sum secure d.o.f. is K(K-1)/(2K-1). We show converses for IC-EE and IC-CM, which imply a converse for IC-CM-EE. We show achievability for IC-CM-EE, which implies achievability for IC-EE and IC-CM. We develop the converses by relating the channel inputs of interfering users to the reliable rates of the interfered users, and by quantifying the secrecy penalty in terms of the eavesdroppers' observations. Our achievability uses structured signaling, structured cooperative jamming, channel prefixing, and asymptotic real interference alignment. While the traditional interference alignment provides some amount of secrecy by mixing unintended signals in a smaller sub-space at every receiver, in order to attain the optimum sum secure d.o.f., we incorporate structured cooperative jamming into the achievable scheme, and intricately design the structure of all of the transmitted signals jointly.

Secure Degrees of Freedom of the Gaussian Wiretap Channel with Helpers and No Eavesdropper CSI: Blind Cooperative Jamming

We consider the Gaussian wiretap channel with M helpers, where no eavesdropper channel state information (CSI) is available at the legitimate entities. The exact secure d.o.f. of the Gaussian wiretap channel with M helpers with perfect CSI at the transmitters was found in [1], [2] to be M/(M+1). One of the key ingredients of the optimal achievable scheme in [1], [2] is to align cooperative jamming signals with the information symbols at the eavesdropper to limit the information leakage rate. This required perfect eavesdropper CSI at the transmitters. Motivated by the recent result in [3], we propose a new achievable scheme in which cooperative jamming signals span the entire space of the eavesdropper, but are not exactly aligned with the information symbols. We show that this scheme achieves the same secure d.o.f. of M/(M+1) in [1], [2] but does not require any eavesdropper CSI; the transmitters blindly cooperative jam the eavesdropper.

An Outer Bound for the Vector Gaussian CEO Problem

We study the vector Gaussian CEO problem, where there are an arbitrary number of agents each having a noisy observation of a vector Gaussian source. The goal of the agents is to describe the source to a central unit, which wants to reconstruct the source within a given distortion. The rate-distortion region of the vector Gaussian CEO problem is unknown in general. Here, we provide an outer bound for the rate-distortion region of the vector Gaussian CEO problem. We obtain our outer bound by evaluating an outer bound for the multi-terminal source coding problem by means of a technique relying on the de Bruijn identity and the properties of the Fisher information. Next, we show that our outer bound strictly improves upon the existing outer bounds for all system parameters. We show this strict improvement by providing a specific example, and showing that there exists a gap between our outer bound and the existing outer bounds. Although our outer bound improves upon the existing outer bounds, we show that our outer bound does not provide the exact rate-distortion region in general. To this end, we provide an example and show that the rate-distortion region is strictly contained in our outer bound for this example.

AWGN Channel under Time-Varying Amplitude Constraints with Causal Information at the Transmitter

We consider the classical AWGN channel where the channel input is constrained to an amplitude constraint that stochastically varies at each channel use, independent of the message. This is an abstraction of an energy harvesting transmitter where the code symbol energy at each channel use is determined by an exogenous energy arrival process and there is no battery for energy storage. At each channel use, an independent realization of the amplitude constraint process is observed by the transmitter causally. This scenario is a state-dependent channel with perfect causal state information at the transmitter. We derive the capacity of this channel using Shannon's coding scheme with causal state information. We prove that the code symbols must be selected from a finite set in the capacity achieving scheme, as in the case of Smith. We numerically study the binary on-off energy arrivals where the amplitude constraint is either zero or a non-zero constant.

Optimal Sum-Rate of the Vector Gaussian CEO Problem

This document is withdrawn due to an error in Lemma 4.

Secure Degrees of Freedom of One-hop Wireless Networks

We study the secure degrees of freedom (d.o.f.) of one-hop wireless networks by considering four fundamental Gaussian network structures: wiretap channel, broadcast channel with confidential messages, interference channel with confidential messages, and multiple access wiretap channel. The secure d.o.f. of the canonical Gaussian wiretap channel with no helpers is zero. It has been known that a strictly positive secure d.o.f. can be obtained in the Gaussian wiretap channel by using a helper which sends structured cooperative signals. We show that the exact secure d.o.f. of the Gaussian wiretap channel with a helper is 1/2. Our achievable scheme is based on real interference alignment and cooperative jamming, which renders the message signal and the cooperative jamming signal separable at the legitimate receiver, but aligns them perfectly at the eavesdropper preventing any reliable decoding of the message signal. Our converse is based on two key lemmas. The first lemma quantifies the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs. The second lemma quantifies the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. We extend this result to the case of M helpers, and show that the exact secure d.o.f. in this case is M/(M+1). We then generalize this approach to more general network structures with multiple messages. We show that the sum secure d.o.f. of the Gaussian broadcast channel with confidential messages and M helpers is 1, the sum secure d.o.f. of the two-user interference channel with confidential messages is 2/3, the sum secure d.o.f. of the two-user interference channel with confidential messages and M helpers is 1, and the sum secure d.o.f. of the K-user multiple access wiretap channel is K(K-1)/(K(K-1)+1).

Secure Source Coding with a Helper

We consider a secure source coding problem with a rate-limited helper. In particular, Alice observes an independent and identically distributed (i.i.d.) source X and wishes to transmit this source losslessly to Bob over a rate-limited link. A helper (Helen), observes an i.i.d. correlated source Y and can transmit information to Bob over a separate rate-limited link. A passive eavesdropper (Eve) can observe the coded output of Alice, i.e., the link from Alice to Bob is public. The uncertainty about the source X at Eve, is measured by the conditional entropy of the source given the coded output of Alice. We completely characterize the rate-equivocation region for this secure source coding model, where we show that Slepian-Wolf binning of X with respect to the coded side information received at Bob is optimal. We next consider a modification of this model in which Alice also has access to the coded output of Helen. For the two-sided helper model, we characterize the rate-equivocation region. While the availability of side information at Alice does not reduce the rate of transmission from Alice, it significantly enhances the resulting equivocation at Eve. In particular, the resulting equivocation for the two-sided helper case is shown to be min(H(X),R_y), i.e., one bit from the two-sided helper provides one bit of uncertainty at Eve. From this result, we infer that Slepian-Wolf binning of X is suboptimal and one can further decrease the information leakage to the eavesdropper by utilizing the side information at Alice. We finally generalize these results to the case in which there is additional un-coded side information W available at Bob and characterize the rate-equivocation regions under the assumption that Y-X-W forms a Markov chain.

Degrees of Freedom Region of the Gaussian MIMO Broadcast Channel with Common and Private Messages

We consider the Gaussian multiple-input multiple-output (MIMO) broadcast channel with common and private messages. We obtain the degrees of freedom (DoF) region of this channel. We first show that a parallel Gaussian broadcast channel with unmatched sub-channels can be constructed from any given Gaussian MIMO broadcast channel by using the generalized singular value decomposition (GSVD) and a relaxation on the power constraint for the channel input, in a way that the capacity region of the constructed parallel channel provides an outer bound for the capacity region of the original channel. The capacity region of the parallel Gaussian broadcast channel with unmatched sub-channels is known, using which we obtain an explicit outer bound for the DoF region of the Gaussian MIMO broadcast channel. We finally show that this outer bound for the DoF region can be attained both by the achievable scheme that uses a classical Gaussian coding for the common message and dirty-paper coding (DPC) for the private messages, as well as by a variation of the zero-forcing (ZF) scheme.

Multi-receiver Wiretap Channel with Public and Confidential Messages

We study the multi-receiver wiretap channel with public and confidential messages. In this channel, there is a transmitter that wishes to communicate with two legitimate users in the presence of an external eavesdropper. The transmitter sends a pair of public and confidential messages to each legitimate user. While there are no secrecy constraints on the public messages, confidential messages need to be transmitted in perfect secrecy. We study the discrete memoryless multi-receiver wiretap channel as well as its Gaussian multi-input multi-output (MIMO) instance. First, we consider the degraded discrete memoryless channel, and obtain an inner bound for the capacity region by using an achievable scheme that uses superposition coding and binning. Next, we obtain an outer bound, and show that this outer bound partially matches the inner bound, providing a partial characterization for the capacity region of the degraded channel model. Second, we obtain an inner bound for the general, not necessarily degraded, discrete memoryless channel by using Marton's inner bound, superposition coding, rate-splitting and binning. Third, we consider the degraded Gaussian MIMO channel, and show that, to evaluate both the inner and outer bounds, considering only jointly Gaussian auxiliary random variables and channel input is sufficient. Since the inner and outer bounds partially match, these sufficiency results provide a partial characterization of the capacity region of the degraded Gaussian MIMO channel. Finally, we provide an inner bound for the capacity region of the general, not necessarily degraded, Gaussian MIMO multi-receiver wiretap channel.

Secure Lossy Transmission of Vector Gaussian Sources

We study the secure lossy transmission of a vector Gaussian source to a legitimate user in the presence of an eavesdropper, where both the legitimate user and the eavesdropper have vector Gaussian side information. The aim of the transmitter is to describe the source to the legitimate user in a way that the legitimate user can reconstruct the source within a certain distortion level while the eavesdropper is kept ignorant of the source as much as possible as measured by the equivocation. We obtain an outer bound for the rate, equivocation and distortion region of this secure lossy transmission problem. This outer bound is tight when the transmission rate constraint is removed. In other words, we obtain the maximum equivocation at the eavesdropper when the legitimate user needs to reconstruct the source within a fixed distortion level while there is no constraint on the transmission rate. This characterization of the maximum equivocation involves two auxiliary random variables. We show that a non-trivial selection for both random variables may be necessary in general. The necessity of two auxiliary random variables also implies that, in general, Wyner-Ziv coding is suboptimal in the presence of an eavesdropper. In addition, we show that, even when there is no rate constraint on the legitimate link, uncoded transmission (deterministic or stochastic) is suboptimal; the presence of an eavesdropper necessitates the use of a coded scheme to attain the maximum equivocation.

Transmission with Energy Harvesting Nodes in Fading Wireless Channels: Optimal Policies

Wireless systems comprised of rechargeable nodes have a significantly prolonged lifetime and are sustainable. A distinct characteristic of these systems is the fact that the nodes can harvest energy throughout the duration in which communication takes place. As such, transmission policies of the nodes need to adapt to these harvested energy arrivals. In this paper, we consider optimization of point-to-point data transmission with an energy harvesting transmitter which has a limited battery capacity, communicating in a wireless fading channel. We consider two objectives: maximizing the throughput by a deadline, and minimizing the transmission completion time of the communication session. We optimize these objectives by controlling the time sequence of transmit powers subject to energy storage capacity and causality constraints. We, first, study optimal offline policies. We introduce a directional water-filling algorithm which provides a simple and concise interpretation of the necessary optimality conditions. We show the optimality of an adaptive directional water-filling algorithm for the throughput maximization problem. We solve the transmission completion time minimization problem by utilizing its equivalence to its throughput maximization counterpart. Next, we consider online policies. We use stochastic dynamic programming to solve for the optimal online policy that maximizes the average number of bits delivered by a deadline under stochastic fading and energy arrival processes with causal channel state feedback. We also propose near-optimal policies with reduced complexity, and numerically study their performances along with the performances of the offline and online optimal policies under various different configurations.

Wiretap Channels: Implications of the More Capable Condition and Cyclic Shift Symmetry

Characterization of the rate-equivocation region of a general wiretap channel involves two auxiliary random variables: U, for rate splitting and V, for channel prefixing. Evaluation of regions involving auxiliary random variables is generally difficult. In this paper, we explore specific classes of wiretap channels for which the expression and evaluation of the rate-equivocation region are simpler. In particular, we show that when the main channel is more capable than the eavesdropping channel, V=X is optimal and the boundary of the rate-equivocation region can be achieved by varying U alone. Conversely, we show under a mild condition that if the main receiver is not more capable, then V=X is strictly suboptimal. Next, we focus on the class of cyclic shift symmetric wiretap channels. We explicitly determine the optimal selections of rate splitting U and channel prefixing V that achieve the boundary of the rate-equivocation region. We show that optimal U and V are determined via cyclic shifts of the solution of an auxiliary optimization problem that involves only one auxiliary random variable. In addition, we provide a sufficient condition for cyclic shift symmetric wiretap channels to have U=ϕas an optimal selection. Finally, we apply our results to the binary-input cyclic shift symmetric wiretap channels. We solve the corresponding constrained optimization problem by inspecting each point of the I(X;Y)-I(X;Z) function. We thoroughly characterize the rate-equivocation regions of the BSC-BEC and BEC-BSC wiretap channels. In particular, we find that U=ϕis optimal and the boundary of the rate-equivocation region is achieved by varying V alone for the BSC-BEC wiretap channel.

An Alternative Proof for the Capacity Region of the Degraded Gaussian MIMO Broadcast Channel

We provide an alternative proof for the capacity region of the degraded Gaussian multiple-input multiple-output (MIMO) broadcast channel. Our proof does not use the channel enhancement technique as opposed to the original proof of Weingertan {\it et. al.} and the alternative proof of Liu {\it et. al}. Our proof starts with the single-letter description of the capacity region of the degraded broadcast channel, and directly evaluates it for the degraded Gaussian MIMO broadcast channel by using two main technical tools. The first one is the generalized de Bruijn identity due to Palomar \emph{et. al.} which provides a connection between the differential entropy and the Fisher information matrix. The second tool we use is an inequality due to Dembo which lower bounds the differential entropy in terms of the Fisher information matrix.

Broadcasting with an Energy Harvesting Rechargeable Transmitter

In this paper, we investigate the transmission completion time minimization problem in a two-user additive white Gaussian noise (AWGN) broadcast channel, where the transmitter is able to harvest energy from the nature, using a rechargeable battery. The harvested energy is modeled to arrive at the transmitter randomly during the course of transmissions. The transmitter has a fixed number of packets to be delivered to each receiver. Our goal is to minimize the time by which all of the packets for both users are delivered to their respective destinations. To this end, we optimize the transmit powers and transmission rates intended for both users. We first analyze the structural properties of the optimal transmission policy. We prove that the optimal total transmit power has the same structure as the optimal single-user transmit power. We also prove that there exists a cut-off power level for the stronger user. If the optimal total transmit power is lower than this cut-off level, all transmit power is allocated to the stronger user, and when the optimal total transmit power is larger than this cut-off level, all transmit power above this level is allocated to the weaker user. Based on these structural properties of the optimal policy, we propose an algorithm that yields the globally optimal off-line scheduling policy. Our algorithm is based on the idea of reducing the two-user broadcast channel problem into a single-user problem as much as possible.

Capacity Region of Gaussian MIMO Broadcast Channels with Common and Confidential Messages

We study the two-user Gaussian multiple-input multiple-output (MIMO) broadcast channel with common and confidential messages. In this channel, the transmitter sends a common message to both users, and a confidential message to each user which needs to be kept perfectly secret from the other user. We obtain the entire capacity region of this channel. We also explore the connections between the capacity region we obtain for the Gaussian MIMO broadcast channel with common and confidential messages and the capacity region of its non-confidential counterpart, i.e., the Gaussian MIMO broadcast channel with common and private messages, which is not known completely.

Capacity-Equivocation Region of the Gaussian MIMO Wiretap Channel

We study the Gaussian multiple-input multiple-output (MIMO) wiretap channel, which consists of a transmitter, a legitimate user, and an eavesdropper. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to this common message, the legitimate user receives a private message, which is desired to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region of the Gaussian MIMO wiretap channel. This region contains all achievable common message, private message, and private message's equivocation (secrecy) rates. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar-Korner.

Ergodic Secret Alignment

In this paper, we introduce two new achievable schemes for the fading multiple access wiretap channel (MAC-WT). In the model that we consider, we assume that perfect knowledge of the state of all channels is available at all the nodes in a causal fashion. Our schemes use this knowledge together with the time varying nature of the channel model to align the interference from different users at the eavesdropper perfectly in a one-dimensional space while creating a higher dimensionality space for the interfering signals at the legitimate receiver hence allowing for better chance of recovery. While we achieve this alignment through signal scaling at the transmitters in our first scheme (scaling based alignment (SBA)), we let nature provide this alignment through the ergodicity of the channel coefficients in the second scheme (ergodic secret alignment (ESA)). For each scheme, we obtain the resulting achievable secrecy rate region. We show that the secrecy rates achieved by both schemes scale with SNR as 1/2log(SNR). Hence, we show the sub-optimality of the i.i.d. Gaussian signaling based schemes with and without cooperative jamming by showing that the secrecy rates achieved using i.i.d. Gaussian signaling with cooperative jamming do not scale with SNR. In addition, we introduce an improved version of our ESA scheme where we incorporate cooperative jamming to achieve higher secrecy rates. Moreover, we derive the necessary optimality conditions for the power control policy that maximizes the secrecy sum rate achievable by our ESA scheme when used solely and with cooperative jamming.

Gaussian MIMO Broadcast Channels with Common and Confidential Messages

We study the two-user Gaussian multiple-input multiple-output (MIMO) broadcast channel with common and confidential messages. In this channel, the transmitter sends a common message to both users, and a confidential message to each user which is kept perfectly secret from the other user. We obtain the entire capacity region of this channel. We also explore the connections between the capacity region we obtained for the Gaussian MIMO broadcast channel with common and confidential messages and the capacity region of its non-confidential counterpart, i.e., the Gaussian MIMO broadcast channel with common and private messages, which is not known completely.

Information-Theoretic Analysis of an Energy Harvesting Communication System

In energy harvesting communication systems, an exogenous recharge process supplies energy for the data transmission and arriving energy can be buffered in a battery before consumption. Transmission is interrupted if there is not sufficient energy. We address communication with such random energy arrivals in an information-theoretic setting. Based on the classical additive white Gaussian noise (AWGN) channel model, we study the coding problem with random energy arrivals at the transmitter. We show that the capacity of the AWGN channel with stochastic energy arrivals is equal to the capacity with an average power constraint equal to the average recharge rate. We provide two different capacity achieving schemes: {\it save-and-transmit} and {\it best-effort-transmit}. Next, we consider the case where energy arrivals have time-varying average in a larger time scale. We derive the optimal offline power allocation for maximum average throughput and provide an algorithm that finds the optimal power allocation.