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Mikael Skoglund

Mikael Skoglund appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Information Theorymath.ITMachine Learningmath.OCSystems and Controleess.SPeess.SYComputational ComplexityCryptography and SecurityDistributed, Parallel, and Cluster ComputingDiscrete Mathematicseess.IVGenomicsInformation Retrievalmath.COmath.DSMultiagent SystemsNetworking and Internet ArchitecturePerformance

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Published work

90 published item(s)

preprint2026arXiv

A Hierarchical Sampling Framework for bounding the Generalization Error of Federated Learning

We study expected generalization bounds for the Hierarchical Federated Learning (HFL) setup using Wasserstein distance. We introduce a generalized framework in which data is sampled hierarchically, and we model it with a multi-layered tree structure that induces dependencies among the clients' datasets. We derive generalization bounds in terms of Wasserstein distance under the Lipschitz assumption on the loss function, by applying a supersample construction that allows us to measure the sensitivity of the algorithm to the change of a single node in the sampling tree. By leveraging the FL structure, we recover and strictly imply existing state-of-the-art conditional mutual information (CMI) bounds in the case of bounded losses. We also show that our bound can be applied together with Differential Privacy assumptions, to recover generalization bounds based on algorithmic privacy. To assess the tightness of our bounds, we study the Gaussian Location Model (GLM) and show that we recover the actual asymptotic rate of the generalization error.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Dobrushin Coefficients of Private Mechanisms Beyond Local Differential Privacy

We investigate Dobrushin coefficients of discrete Markov kernels that have bounded pointwise maximal leakage (PML) with respect to all distributions with a minimum probability mass bounded away from zero by a constant $c>0$. This definition recovers local differential privacy (LDP) for $c\to 0$. We derive achievable bounds on contraction in terms of a kernels PML guarantees, and provide mechanism constructions that achieve the presented bounds. Further, we extend the results to general $f$-divergences by an application of Binette's inequality. Our analysis yields tighter bounds for mechanisms satisfying LDP and extends beyond the LDP regime to any discrete kernel.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Generalizing the Fano inequality further

Interactive statistical decision making (ISDM) features algorithm-dependent data generated through interaction. Existing information-theoretic lower bounds in ISDM largely target expected risk, while tail-sensitive objectives are less developed. We generalize the interactive Fano framework of Chen et al. by replacing the hard success event with a randomized one-bit statistic representing an arbitrary bounded transform of the loss. This yields a Bernoulli f-divergence inequality, which we invert to obtain a two-sided interval for the transform, recovering the previous result as a special case. Instantiating the transform with a bounded hinge and using the Rockafellar-Uryasev representation, we derive lower bounds on the prior-predictive (Bayesian) CVaR of bounded losses. For KL divergence with the mixture reference distribution, the bound becomes explicit in terms of mutual information via Pinsker's inequality.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Land-then-transport: A Flow Matching-Based Generative Decoder for Wireless Image Transmission

Due to strict rate and reliability demands, wireless image transmission remains difficult for both classical layered designs and joint source-channel coding (JSCC), especially under low latency. Diffusion-based generative decoders can deliver strong perceptual quality by leveraging learned image priors, but iterative stochastic denoising leads to high decoding delay. To enable low-latency decoding, we propose a flow-matching (FM) generative decoder under a new land-then-transport (LTT) paradigm that tightly integrates the physical wireless channel into a continuous-time probability flow. For AWGN channels, we build a Gaussian smoothing path whose noise schedule indexes effective noise levels, and derive a closed-form teacher velocity field along this path. A neural-network student vector field is trained by conditional flow matching, yielding a deterministic, channel-aware ODE decoder with complexity linear in the number of ODE steps. At inference, it only needs an estimate of the effective noise variance to set the ODE starting time. We further show that Rayleigh fading and MIMO channels can be mapped, via linear MMSE equalization and singular-value-domain processing, to AWGN-equivalent channels with calibrated starting times. Therefore, the same probability path and trained velocity field can be reused for Rayleigh and MIMO without retraining. Experiments on MNIST, Fashion-MNIST, and DIV2K over AWGN, Rayleigh, and MIMO demonstrate consistent gains over JPEG2000+LDPC, DeepJSCC, and diffusion-based baselines, while achieving good perceptual quality with only a few ODE steps. Overall, LTT provides a deterministic, physically interpretable, and computation-efficient framework for generative wireless image decoding across diverse channels.

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preprint2026arXiv

On the Impact of Channel Aging and Doppler-Affected Clutter on OFDM ISAC Systems

The temporal evolution of the propagation environment plays a central role in integrated sensing and communication (ISAC) systems. A slow-time evolution manifests as channel aging in communication links, while a fast-time one is associated with structured clutter with non-zero Doppler. Nevertheless, the joint impact of these two phenomena on ISAC performance has been largely overlooked. This addresses this research gap in a network utilizing orthogonal frequency division multiplexing waveforms. Here, a base station simultaneously serves multiple user equipment (UE) devices and performs monostatic sensing. Channel aging is captured through an autoregressive model with exponential correlation decay. In contrast, clutter is modeled as a collection of uncorrelated, coherent patches with non-zero Doppler, resulting in a Kronecker-separable covariance structure. We propose an aging-aware channel estimator that uses prior pilot observations to estimate the time-varying UE channels, characterized by a non-isotropic multipath fading structure. The clutter's structure enables a novel low-complexity sensing pipeline: clutter statistics are estimated from raw data and subsequently used to suppress the clutter's action, after which target parameters are extracted through range-angle and range-velocity maps. We evaluate the influence of frame length and pilot history on channel estimation accuracy and demonstrate substantial performance gains over block fading in low-to-moderate mobility regimes. The sensing pipeline is implemented in a clutter-dominated environment, demonstrating that effective clutter suppression can be achieved under practical configurations. Furthermore, our results show that dedicated sensing streams are required, as communication beams provide insufficient range resolution.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Privacy-Utility Trade-offs Under Multi-Level Point-Wise Leakage Constraints

An information-theoretic privacy mechanism design is studied, where an agent observes useful data $Y$ which is correlated with the private data $X$. The agent wants to reveal the information to a user, hence, the agent utilizes a privacy mechanism to produce disclosed data $U$ that can be revealed. We assume that the agent has no direct access to $X$, i.e., the private data is hidden. We study privacy mechanism design that maximizes the disclosed information about $Y$, measured by the mutual information between $Y$ and $U$, while satisfying a point-wise constraint with different privacy leakage budgets. We introduce a new measure, called the \emph{multi-level point-wise leakage}, which allows us to impose different leakage levels for different realizations of $U$. In contrast to previous studies on point-wise measures, which use the same leakage level for each realization, we consider a more general scenario in which each data point can leak information up to a different threshold. As a result, this concept also covers cases in which some data points should not leak any information about the private data, i.e., they must satisfy perfect privacy. In other words, a combination of perfect privacy and non-zero leakage can be considered. When the leakage is sufficiently small, concepts from information geometry allow us to locally approximate the mutual information. We show that when the leakage matrix $P_{X|Y}$ is invertible, utilizing this approximation leads to a quadratic optimization problem that has closed-form solution under some constraints. In particular, we show that it is sufficient to consider only binary $U$ to attain the optimal utility. This leads to simple privacy designs with low complexity which are based on finding the maximum singular value and singular vector of a matrix.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Sparse Point-wise Privacy Leakage: Mechanism Design and Fundamental Limits

We study an information-theoretic privacy mechanism design problem, where an agent observes useful data $Y$ that is arbitrarily correlated with sensitive data $X$, and design disclosed data $U$ generated from $Y$ (the agent has no direct access to $X$). We introduce \emph{sparse point-wise privacy leakage}, a worst-case privacy criterion that enforces two simultaneous constraints for every disclosed symbol $u\in\mathcal{U}$: (i) $u$ may be correlated with at most $N$ realizations of $X$, and (ii) the total leakage toward those realizations is bounded. In the high-privacy regime, we use concepts from information geometry to obtain a local quadratic approximation of mutual information which measures utility between $U$ and $Y$. When the leakage matrix $P_{X|Y}$ is invertible, this approximation reduces the design problem to a sparse quadratic maximization, known as the Rayleigh-quotient problem, with an $\ell_0$ constraint. We further show that, for the approximated problem, one can without loss of optimality restrict attention to a binary released variable $U$ with a uniform distribution. For small alphabet sizes, the exact sparsity-constrained optimum can be computed via combinatorial support enumeration, which quickly becomes intractable as the dimension grows. For general dimensions, the resulting sparse Rayleigh-quotient maximization is NP-hard and closely related to sparse principal component analysis (PCA). We propose a convex semidefinite programming (SDP) relaxation that is solvable in polynomial time and provides a tractable surrogate for the NP-hard design, together with a simple rounding procedure to recover a feasible leakage direction. We also identify a sparsity threshold beyond which the sparse optimum saturates at the unconstrained spectral value and the SDP relaxation becomes tight.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Bounds for Privacy-Utility Trade-off with Non-zero Leakage

The design of privacy mechanisms for two scenarios is studied where the private data is hidden or observable. In the first scenario, an agent observes useful data $Y$, which is correlated with private data $X$, and wants to disclose the useful information to a user. A privacy mechanism is employed to generate data $U$ that maximizes the revealed information about $Y$ while satisfying a privacy criterion. In the second scenario, the agent has additionally access to the private data. To this end, the Functional Representation Lemma and Strong Functional Representation Lemma are extended relaxing the independence condition and thereby allowing a certain leakage. Lower bounds on privacy-utility trade-off are derived for the second scenario as well as upper bounds for both scenarios. In particular, for the case where no leakage is allowed, our upper and lower bounds improve previous bounds.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

An Information-Theoretic Analysis of Bayesian Reinforcement Learning

Building on the framework introduced by Xu and Raginksy [1] for supervised learning problems, we study the best achievable performance for model-based Bayesian reinforcement learning problems. With this purpose, we define minimum Bayesian regret (MBR) as the difference between the maximum expected cumulative reward obtainable either by learning from the collected data or by knowing the environment and its dynamics. We specialize this definition to reinforcement learning problems modeled as Markov decision processes (MDPs) whose kernel parameters are unknown to the agent and whose uncertainty is expressed by a prior distribution. One method for deriving upper bounds on the MBR is presented and specific bounds based on the relative entropy and the Wasserstein distance are given. We then focus on two particular cases of MDPs, the multi-armed bandit problem (MAB) and the online optimization with partial feedback problem. For the latter problem, we show that our bounds can recover from below the current information-theoretic bounds by Russo and Van Roy [2].

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Asynchronous Parallel Incremental Block-Coordinate Descent for Decentralized Machine Learning

Machine learning (ML) is a key technique for big-data-driven modelling and analysis of massive Internet of Things (IoT) based intelligent and ubiquitous computing. For fast-increasing applications and data amounts, distributed learning is a promising emerging paradigm since it is often impractical or inefficient to share/aggregate data to a centralized location from distinct ones. This paper studies the problem of training an ML model over decentralized systems, where data are distributed over many user devices and the learning algorithm run on-device, with the aim of relaxing the burden at a central entity/server. Although gossip-based approaches have been used for this purpose in different use cases, they suffer from high communication costs, especially when the number of devices is large. To mitigate this, incremental-based methods are proposed. We first introduce incremental block-coordinate descent (I-BCD) for the decentralized ML, which can reduce communication costs at the expense of running time. To accelerate the convergence speed, an asynchronous parallel incremental BCD (API-BCD) method is proposed, where multiple devices/agents are active in an asynchronous fashion. We derive convergence properties for the proposed methods. Simulation results also show that our API-BCD method outperforms state of the art in terms of running time and communication costs.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Bounds for Privacy-Utility Trade-off with Per-letter Privacy Constraints and Non-zero Leakage

An information theoretic privacy mechanism design problem for two scenarios is studied where the private data is either hidden or observable. In each scenario, privacy leakage constraints are considered using two different measures. In these scenarios the private data is hidden or observable. In the first scenario, an agent observes useful data $Y$ that is correlated with private data $X$, and wishes to disclose the useful information to a user. A privacy mechanism is designed to generate disclosed data $U$ which maximizes the revealed information about $Y$ while satisfying a per-letter privacy constraint. In the second scenario, the agent has additionally access to the private data. First, the Functional Representation Lemma and Strong Functional Representation Lemma are extended by relaxing the independence condition to find a lower bound considering the second scenario. Next, lower bounds as well as upper bounds on privacy-utility trade-off are derived for both scenarios. In particular, for the case where $X$ is deterministic function of $Y$, we show that our upper and lower bounds are asymptotically optimal considering the first scenario.

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preprint2022arXiv

Continuous-Time Channel Gain Control for Minimum-Information Kalman-Bucy Filtering

We consider the problem of estimating a continuous-time Gauss-Markov source process observed through a vector Gaussian channel with an adjustable channel gain matrix. For a given (generally time-varying) channel gain matrix, we provide formulas to compute (i) the mean-square estimation error attainable by the classical Kalman-Bucy filter, and (ii) the mutual information between the source process and its Kalman-Bucy estimate. We then formulate a novel "optimal channel gain control problem" where the objective is to control the channel gain matrix strategically to minimize the weighted sum of these two performance metrics. To develop insights into the optimal solution, we first consider the problem of controlling a time-varying channel gain over a finite time interval. A necessary optimality condition is derived based on Pontryagin's minimum principle. For a scalar system, we show that the optimal channel gain is a piece-wise constant signal with at most two switches. We also consider the problem of designing the optimal time-invariant gain to minimize the average cost over an infinite time horizon. A novel semidefinite programming (SDP) heuristic is proposed and the exactness of the solution is discussed.

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preprint2022arXiv

Goodput Maximization with Quantized Feedback in the Finite Blocklength Regime for Quasi-Static Channels

In this paper, we study a quantized feedback scheme to maximize the goodput of a finite blocklength communication scenario over a quasi-static fading channel. It is assumed that the receiver has perfect channel state information (CSI) and sends back the CSI to the transmitter over a resolution-limited error-free feedback channel. With this partial CSI, the transmitter is supposed to select the optimum transmission rate, such that it maximizes the overall goodput of the communication system. This problem has been studied for the asymptotic blocklength regime, however, no solution has so far been presented for finite blocklength. Here, we study this problem in two cases: with and without constraint on reliability. We first formulate the optimization problems and analytically solve them. Iterative algorithms that successfully exploit the system parameters for both cases are presented. It is shown that although the achievable maximum goodput decreases with shorter blocklengths and higher reliability requirements, significant improvement can be achieved even with coarsely quantized feedback schemes.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Privacy signaling games with binary alphabets

In this paper, we consider a privacy signaling game problem for binary alphabets and single-bit transmission where a transmitter has a pair of messages, one of which is a casual message that needs to be conveyed, whereas the other message contains sensitive data and needs to be protected. The receiver wishes to estimate both messages to acquire as much information as possible. For this setup, we study the interactions between the transmitter and the receiver with non-aligned information-theoretic objectives (modeled by mutual information and hamming distance) due to the privacy concerns of the transmitter. We derive conditions under which Nash and/or Stackelberg equilibria exist and identify the optimal responses of the encoder and decoders strategies for each type of game. One particularly surprising result is that when both types of equilibria exist, they admit the same encoding and decoding strategies. We corroborate our analysis with simulation studies.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Secure Source Coding with Side-information at Decoder and Shared Key at Encoder and Decoder

We study the problem of rate-distortion-equivocation with side-information only available at the decoder when an independent private random key is shared between the sender and the receiver. The sender compresses the sequence, and the receiver reconstructs it such that the average distortion between the source and the output is limited. The equivocation is measured at an eavesdropper that intercepts the source encoded message, utilizing side-information correlated with the source and the side-information at the decoder. We have derived the entire achievable rate-distortion-equivocation region for this problem.

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preprint2022arXiv

Tighter expected generalization error bounds via Wasserstein distance

This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample setting from Steinke and Zakynthinou [1]. Moreover, when the loss function is bounded and the geometry of the space is ignored by the choice of the metric in the Wasserstein distance, these bounds recover from below (and thus, are tighter than) current bounds based on the relative entropy. In particular, they generate new, non-vacuous bounds based on the relative entropy. Therefore, these results can be seen as a bridge between works that account for the geometry of the hypothesis space and those based on the relative entropy, which is agnostic to such geometry. Furthermore, it is shown how to produce various new bounds based on different information measures (e.g., the lautum information or several $f$-divergences) based on these bounds and how to derive similar bounds with respect to the backward channel using the presented proof techniques.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

A Learning-Based Approach to Address Complexity-Reliability Tradeoff in OS Decoders

In this paper, we study the tradeoffs between complexity and reliability for decoding large linear block codes. We show that using artificial neural networks to predict the required order of an ordered statistics based decoder helps in reducing the average complexity and hence the latency of the decoder. We numerically validate the approach through Monte Carlo simulations.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Latency and Reliability Trade-off with Computational Complexity Constraints: OS Decoders and Generalizations

In this paper, we study the problem of latency and reliability trade-off in ultra-reliable low-latency communication (URLLC) in the presence of decoding complexity constraints. We consider linear block encoded codewords transmitted over a binary-input AWGN channel and decoded with order-statistic (OS) decoder. We first investigate the performance of OS decoders as a function of decoding complexity and propose an empirical model that accurately quantifies the corresponding trade-off. Next, a consistent way to compute the aggregate latency for complexity constrained receivers is presented, where the latency due to decoding is also included. It is shown that, with strict latency requirements, decoding latency cannot be neglected in complexity constrained receivers. Next, based on the proposed model, several optimization problems, relevant to the design of URLLC systems, are introduced and solved. It is shown that the decoding time has a drastic effect on the design of URLLC systems when constraints on decoding complexity are considered. Finally, it is also illustrated that the proposed model can closely describe the performance versus complexity trade-off for other candidate coding solutions for URLLC such as tail-biting convolutional codes, polar codes, and low-density parity-check codes.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Quadratic Signaling Games with Channel Combining Ratio

In this study, Nash and Stackelberg equilibria of single-stage and multi-stage quadratic signaling games between an encoder and a decoder are investigated. In the considered setup, the objective functions of the encoder and the decoder are misaligned, there is a noisy channel between the encoder and the decoder, the encoder has a soft power constraint, and the decoder has also noisy observation of the source to be estimated. We show that there exist only linear encoding and decoding strategies at the Stackelberg equilibrium, and derive the equilibrium strategies and costs. Regarding the Nash equilibrium, we explicitly characterize affine equilibria for the single-stage setup and show that the optimal encoder (resp. decoder) is affine for an affine decoder (resp. encoder) for the multi-stage setup. For the decoder side, between the information coming from the encoder and noisy observation of the source, our results describe what should be the combining ratio of these two channels. Regarding the encoder, we derive the conditions under which it is meaningful to transmit a message.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

A Hybrid Model-based and Data-driven Approach to Spectrum Sharing in mmWave Cellular Networks

Inter-operator spectrum sharing in millimeter-wave bands has the potential of substantially increasing the spectrum utilization and providing a larger bandwidth to individual user equipment at the expense of increasing inter-operator interference. Unfortunately, traditional model-based spectrum sharing schemes make idealistic assumptions about inter-operator coordination mechanisms in terms of latency and protocol overhead, while being sensitive to missing channel state information. In this paper, we propose hybrid model-based and data-driven multi-operator spectrum sharing mechanisms, which incorporate model-based beamforming and user association complemented by data-driven model refinements. Our solution has the same computational complexity as a model-based approach but has the major advantage of having substantially less signaling overhead. We discuss how limited channel state information and quantized codebook-based beamforming affect the learning and the spectrum sharing performance. We show that the proposed hybrid sharing scheme significantly improves spectrum utilization under realistic assumptions on inter-operator coordination and channel state information acquisition.

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preprint2020arXiv

Asynchronous Decentralized Learning of a Neural Network

In this work, we exploit an asynchronous computing framework namely ARock to learn a deep neural network called self-size estimating feedforward neural network (SSFN) in a decentralized scenario. Using this algorithm namely asynchronous decentralized SSFN (dSSFN), we provide the centralized equivalent solution under certain technical assumptions. Asynchronous dSSFN relaxes the communication bottleneck by allowing one node activation and one side communication, which reduces the communication overhead significantly, consequently increasing the learning speed. We compare asynchronous dSSFN with traditional synchronous dSSFN in the experimental results, which shows the competitive performance of asynchronous dSSFN, especially when the communication network is sparse.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Conditional Mutual Information Neural Estimator

Several recent works in communication systems have proposed to leverage the power of neural networks in the design of encoders and decoders. In this approach, these blocks can be tailored to maximize the transmission rate based on aggregated samples from the channel. Motivated by the fact that, in many communication schemes, the achievable transmission rate is determined by a conditional mutual information term, this paper focuses on neural-based estimators for this information-theoretic quantity. Our results are based on variational bounds for the KL-divergence and, in contrast to some previous works, we provide a mathematically rigorous lower bound. However, additional challenges with respect to the unconditional mutual information emerge due to the presence of a conditional density function which we address here.

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preprint2020arXiv

Decentralized Beamforming Design for Intelligent Reflecting Surface-enhanced Cell-free Networks

Cell-free networks are considered as a promising distributed network architecture to satisfy the increasing number of users and high rate expectations in beyond-5G systems. However, to further enhance network capacity, an increasing number of high-cost base stations (BSs) are required. To address this problem and inspired by the cost-effective intelligent reflecting surface (IRS) technique, we propose a fully decentralized design framework for cooperative beamforming in IRS-aided cell-free networks. We first transform the centralized weighted sum-rate maximization problem into a tractable consensus optimization problem, and then an incremental alternating direction method of multipliers (ADMM) algorithm is proposed to locally update the beamformer. The complexity and convergence of the proposed method are analyzed, and these results show that the performance of the new scheme can asymptotically approach that of the centralized one as the number of iterations increases. Results also show that IRSs can significantly increase the system sum-rate of cell-free networks and the proposed method outperforms existing decentralized methods.

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preprint2020arXiv

Detecting State Transitions of a Markov Source: Sampling Frequency and Age Trade-off

We consider a finite-state Discrete-Time Markov Chain (DTMC) source that can be sampled for detecting the events when the DTMC transits to a new state. Our goal is to study the trade-off between sampling frequency and staleness in detecting the events. We argue that, for the problem at hand, using Age of Information (AoI) for quantifying the staleness of a sample is conservative and therefore, introduce \textit{age penalty} for this purpose. We study two optimization problems: minimize average age penalty subject to an average sampling frequency constraint, and minimize average sampling frequency subject to an average age penalty constraint; both are Constrained Markov Decision Problems. We solve them using linear programming approach and compute Markov policies that are optimal among all causal policies. Our numerical results demonstrate that the computed Markov policies not only outperform optimal periodic sampling policies, but also achieve sampling frequencies close to or lower than that of an optimal clairvoyant (non-causal) sampling policy, if a small age penalty is allowed.

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preprint2020arXiv

Empirical Coordination with Multiple Descriptions

We extend the framework of empirical coordination to a distributed setup where for a given action by nature, multiple descriptions of the action of the decoder are available. We adopt the coding strategy applied by El Gamal and Cover in \cite{gamal:1982} to get a lower bound of the coordination region. Then, we improve this region by applying the coding scheme applied by Zhang and Berger in \cite{zhang:1987}.

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preprint2020arXiv

Remote Empirical Coordination

We apply the framework of imperfect empirical coordination to a two-node setup where the action $X$ of the first node is not observed directly but via $L$ agents who observe independently impaired measurements $\hat X$ of the action. These $L$ agents, using a rate-limited communication that is available to all of them, help the second node to generate the action $Y$ in order to establish the desired coordinated behaviour. When $L<\infty$, we prove that it suffices $R_i\geq I\left(\hat X;\hat{Y}\right)$ for at least one agent whereas for $L\longrightarrow\infty$, we show that it suffices $R_i\geq I\left(\hat X;\hat Y|X\right)$ for all agents where $\hat Y$ is a random variable such that $X-\hat X-\hat Y$ and $\|p_{X,\hat Y}\left(x,y\right)-p_{X,Y}\left(x,y\right)\|_{TV}\leq Δ$ ( $Δ$ is the pre-specified fidelity).

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preprint2020arXiv

Secure Strong Coordination

We consider a network of two nodes separated by a noisy channel, in which the source and its reconstruction have to be strongly coordinated, while simultaneously satisfying the strong secrecy condition with respect to an outside observer of the noisy channel. In the case of non-causal encoding and decoding, we propose a joint source-channel coding scheme for the secure strong coordination region. Furthermore, we provide a complete characterization of the secure strong coordination region when the decoder has to reliably reconstruct the source sequence and the legitimate channel is more capable than the channel of the eavesdropper.

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preprint2020arXiv

Sequential Source Coding for Stochastic Systems Subject to Finite Rate Constraints

In this paper, we revisit the sequential source coding framework to analyze fundamental performance limitations of discrete-time stochastic control systems subject to feedback data-rate constraints in finite-time horizon. The basis of our results is a new characterization of the lower bound on the minimum total-rate achieved by sequential codes subject to a total (across time) distortion constraint and a computational algorithm that allocates optimally the rate-distortion for any fixed finite-time horizon. This characterization facilitates the derivation of analytical, non-asymptotic, and finite-dimensional lower and upper bounds in two control-related scenarios. (a) A parallel time-varying Gauss-Markov process with identically distributed spatial components that is quantized and transmitted through a noiseless channel to a minimum mean-squared error (MMSE) decoder. (b) A time-varying quantized LQG closed-loop control system, with identically distributed spatial components and with a random data-rate allocation. Our non-asymptotic lower bound on the quantized LQG control problem, reveals the absolute minimum data-rates for (mean square) stability of our time-varying plant for any fixed finite time horizon. We supplement our framework with illustrative simulation experiments.

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preprint2020arXiv

SSFN -- Self Size-estimating Feed-forward Network with Low Complexity, Limited Need for Human Intervention, and Consistent Behaviour across Trials

We design a self size-estimating feed-forward network (SSFN) using a joint optimization approach for estimation of number of layers, number of nodes and learning of weight matrices. The learning algorithm has a low computational complexity, preferably within few minutes using a laptop. In addition the algorithm has a limited need for human intervention to tune parameters. SSFN grows from a small-size network to a large-size network, guaranteeing a monotonically non-increasing cost with addition of nodes and layers. The learning approach uses judicious a combination of `lossless flow property' of some activation functions, convex optimization and instance of random matrix. Consistent performance -- low variation across Monte-Carlo trials -- is found for inference performance (classification accuracy) and estimation of network size.

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preprint2020arXiv

The Convex Information Bottleneck Lagrangian

The information bottleneck (IB) problem tackles the issue of obtaining relevant compressed representations $T$ of some random variable $X$ for the task of predicting $Y$. It is defined as a constrained optimization problem which maximizes the information the representation has about the task, $I(T;Y)$, while ensuring that a certain level of compression $r$ is achieved (i.e., $ I(X;T) \leq r$). For practical reasons, the problem is usually solved by maximizing the IB Lagrangian (i.e., $\mathcal{L}_{\text{IB}}(T;β) = I(T;Y) - βI(X;T)$) for many values of $β\in [0,1]$. Then, the curve of maximal $I(T;Y)$ for a given $I(X;T)$ is drawn and a representation with the desired predictability and compression is selected. It is known when $Y$ is a deterministic function of $X$, the IB curve cannot be explored and another Lagrangian has been proposed to tackle this problem: the squared IB Lagrangian: $\mathcal{L}_{\text{sq-IB}}(T;β_{\text{sq}})=I(T;Y)-β_{\text{sq}}I(X;T)^2$. In this paper, we (i) present a general family of Lagrangians which allow for the exploration of the IB curve in all scenarios; (ii) provide the exact one-to-one mapping between the Lagrange multiplier and the desired compression rate $r$ for known IB curve shapes; and (iii) show we can approximately obtain a specific compression level with the convex IB Lagrangian for both known and unknown IB curve shapes. This eliminates the burden of solving the optimization problem for many values of the Lagrange multiplier. That is, we prove that we can solve the original constrained problem with a single optimization.

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preprint2020arXiv

Transfer-Entropy-Regularized Markov Decision Processes

We consider the framework of transfer-entropy-regularized Markov Decision Process (TERMDP) in which the weighted sum of the classical state-dependent cost and the transfer entropy from the state random process to the control random process is minimized. Although TERMDPs are generally formulated as nonconvex optimization problems, we derive an analytical necessary optimality condition expressed as a finite set of nonlinear equations, based on which an iterative forward-backward computational procedure similar to the Arimoto-Blahut algorithm is proposed. It is shown that every limit point of the sequence generated by the proposed algorithm is a stationary point of the TERMDP. Applications of TERMDPs are discussed in the context of networked control systems theory and non-equilibrium thermodynamics. The proposed algorithm is applied to an information-constrained maze navigation problem, whereby we study how the price of information qualitatively alters the optimal decision polices.

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preprint2016arXiv

Effective Capacity of Retransmission Schemes - A Recurrence Relation Approach

We consider the effective capacity performance measure of persistent- and truncated-retransmission schemes that can involve any combination of multiple transmissions per packet, multiple communication modes, or multiple packet communication. We present a structured unified analytical approach, based on a random walk model and recurrence relation formulation, and give exact effective capacity expressions for persistent hybrid automatic repeat request (HARQ) and for truncated-retransmission schemes. For the latter, effective capacity expressions are given for systems with finite (infinite) time horizon on an algebraic (spectral radius-based) form of a special block companion matrix. In contrast to prior HARQ models, assuming infinite time horizon, the proposed method does not involve a non-trivial per case modeling step. We give effective capacity expressions for several important cases that have not been addressed before, e.g. persistent-HARQ, truncated-HARQ, network-coded ARQ (NC-ARQ), two-mode-ARQ, and multilayer-ARQ. We propose an alternative QoS parameter (instead of the commonly used moment generating function parameter) that represents explicitly the target delay and the delay violation probability. This also enables closed-form expressions for many of the studied systems. Moreover, we use the recently proposed matrix-exponential distributed (MED) modeling of wireless fading channels to provide the basis for numerous new effective capacity results for HARQ.

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preprint2016arXiv

Efficient Coded Cooperative Networks with Energy Harvesting and Wireless Power Transfer

The optimum off-line energy management scheme for multi-user multi-relay networks employing energy harvesting and wireless energy transfer is studied. Specifically, the users are capable of harvesting and transferring energy to each other over consecutive transmissions, though they have no fixed energy supplies. Meanwhile, network coding for the users' messages is conducted at the relays to enable cooperative transmission with source nodes in independent but not necessarily identically distributed (i.n.i.d.) Nakagami-$m$ fading channels. Therefore, a simultaneous two level cooperation, i.e., information-level and energy-level cooperation is conducted. The problem of energy efficiency (EE) maximization under constraints of the energy causality and a predefined outage probability threshold is formulated and shown to be non-convex. By exploiting fractional and geometric programming, a convex form-based iterative algorithm is developed to solve the problem efficiently. Close-to-optimal power allocation and energy cooperation policies across consecutive transmissions are found. Moreover, the effects of relay locations and wireless energy transmission efficiency are investigated and the performance comparison with the current state of solutions demonstrates that the proposed policies can manage the harvested energy more efficiently.

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preprint2016arXiv

Energy Efficient Cooperative Network Coding with Joint Relay Scheduling and Power Allocation

The energy efficiency (EE) of a multi-user multi-relay system with the maximum diversity network coding (MDNC) is studied. We explicitly find the connection among the outage probability, energy consumption and EE and formulate the maximizing EE problem under the outage probability constraints. Relay scheduling (RS) and power allocation (PA) are applied to schedule the relay states (transmitting, sleeping, \emph{etc}) and optimize the transmitting power under the practical channel and power consumption models. Since the optimization problem is NP-hard, to reduce computational complexity, the outage probability is first tightly approximated to a log-convex form. Further, the EE is converted into a subtractive form based on the fractional programming. Then a convex mixed-integer nonlinear problem (MINLP) is eventually obtained. With a generalized outer approximation (GOA) algorithm, RS and PA are solved in an iterative manner. The Pareto-optimal curves between the EE and the target outage probability show the EE gains from PA and RS. Moreover, by comparing with the no network coding (NoNC) scenario, we conclude that with the same number of relays, MDNC can lead to EE gains. However, if RS is implemented, NoNC can outperform MDNC in terms of the EE when more relays are needed in the MDNC scheme.

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preprint2016arXiv

Massive MIMO Pilot Retransmission Strategies for Robustification against Jamming

This letter proposes anti-jamming strategies based on pilot retransmission for a single user uplink massive MIMO under jamming attack. A jammer is assumed to attack the system both in the training and data transmission phases. We first derive an achievable rate which enables us to analyze the effect of jamming attacks on the system performance. Counter-attack strategies are then proposed to mitigate this effect under two different scenarios: random and deterministic jamming attacks. Numerical results illustrate our analysis and benefit of the proposed schemes.

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preprint2016arXiv

Multi-Phase Smart Relaying and Cooperative Jamming in Secure Cognitive Radio Networks

In this paper we investigate cooperative secure communications in a four-node cognitive radio network where the secondary receiver is treated as a potential eavesdropper with respect to the primary transmission. The secondary user is allowed to transmit his own signals under the condition that the primary user's secrecy rate and transmission scheme are intact. Under this setting we derive the secondary user's achievable rates and the related constraints to guarantee the primary user's weak secrecy rate, when Gelfand-Pinsker coding is used at the secondary transmitter. In addition, we propose a multi-phase transmission scheme to include 1) the phases of the clean relaying with cooperative jamming and 2) the latency to successfully decode the primary message at the secondary transmitter. A capacity upper bound for the secondary user is also derived. Numerical results show that: 1) the proposed scheme can outperform the traditional ones by properly selecting the secondary user's parameters of different transmission schemes according to the relative positions of the nodes; 2) the derived capacity upper bound is close to the secondary user's achievable rate within 0.3 bits/channel use, especially when the secondary transmitter/receiver is far/close enough to the primary receiver/transmitter, respectively. Thereby, a smart secondary transmitter is able to adapt its relaying and cooperative jamming to guarantee primary secrecy rates and to transmit its own data at the same time from relevant geometric positions.

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preprint2016arXiv

Rate of Prefix-free Codes in LQG Control Systems

In this paper, we consider a discrete time linear quadratic Gaussian (LQG) control problem in which state information of the plant is encoded in a variable-length binary codeword at every time step, and a control input is determined based on the codewords generated in the past. We derive a lower bound of the rate achievable by the class of prefix-free codes attaining the required LQG control performance. This lower bound coincides with the infimum of a certain directed information expression, and is computable by semidefinite programming (SDP). Based on a technique by Silva et al., we also provide an upper bound of the best achievable rate by constructing a controller equipped with a uniform quantizer with subtractive dither and Shannon-Fano coding. The gap between the obtained lower and upper bounds is less than $0.754r+1$ bits per time step regardless of the required LQG control performance, where $r$ is the rank of a signal-to-noise ratio matrix obtained by SDP, which is no greater than the dimension of the state.

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preprint2016arXiv

Strong Secrecy in Pairwise Key Agreement over a Generalized Multiple Access Channel

This paper considers the problem of pairwise key agreement without public communication between three users connected through a generalized multiple access channel (MAC). While two users control the channel inputs, all three users observe noisy outputs from the channel and each pair of users wishes to agree on a secret key hidden from the remaining user. We first develop a "pre-generated" key-agreement scheme based on secrecy codes for the generalized MAC, in which the channel is only used to distribute pre-generated secret keys. We then extend this scheme to include an additional layer of rate-limited secret-key generation by treating the observed channel outputs as induced sources. We characterize inner and outer bounds on the strong secret-key capacity region for both schemes. For a special case of the "pre-generated" scheme, we obtain an exact characterization. We also illustrate with some binary examples that exploiting the generalized nature of the generalized MAC may lead to significantly larger key-agreement rates.

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preprint2016arXiv

Subspace Estimation and Decomposition for Hybrid Analog-Digital Millimetre-Wave MIMO systems

In this work, we address the problem of channel estimation and precoding / combining for the so-called hybrid millimeter wave (mmWave) MIMO architecture. Our proposed channel estimation scheme exploits channel reciprocity in TDD MIMO systems, by using echoing, thereby allowing us to implement Krylov subspace methods in a fully distributed way. The latter results in estimating the right (resp. left) singular subspace of the channel at the transmitter (resp. receiver). Moreover, we also tackle the problem of subspace decomposition whereby the estimated right (resp. left) singular subspaces are approximated by a cascade of analog and digital precoder (resp. combiner), using an iterative method. Finally we compare our scheme with an equivalent fully digital case and conclude that a relatively similar performance can be achieved, however, with a drastically reduced number of RF chains - 4 ~ 8 times less (i.e., massive savings in cost and power consumption).

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preprint2016arXiv

Subspace Estimation and Decomposition for Large Millimeter-Wave MIMO systems

Channel estimation and precoding in hybrid analog-digital millimeter-wave (mmWave) MIMO systems is a fundamental problem that has yet to be addressed, before any of the promised gains can be harnessed. For that matter, we propose a method (based on the well-known Arnoldi iteration) exploiting channel reciprocity in TDD systems and the sparsity of the channel's eigenmodes, to estimate the right (resp. left) singular subspaces of the channel, at the BS (resp. MS). We first describe the algorithm in the context of conventional MIMO systems, and derive bounds on the estimation error in the presence of distortions at both BS and MS. We later identify obstacles that hinder the application of such an algorithm to the hybrid analog-digital architecture, and address them individually. In view of fulfilling the constraints imposed by the hybrid analog-digital architecture, we further propose an iterative algorithm for subspace decomposition, whereby the above estimated subspaces, are approximated by a cascade of analog and digital precoder / combiner. Finally, we evaluate the performance of our scheme against the perfect CSI, fully digital case (i.e., an equivalent conventional MIMO system), and conclude that similar performance can be achieved, especially at medium-to-high SNR (where the performance gap is less than 5%), however, with a drastically lower number of RF chains (4 to 8 times less).

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preprint2016arXiv

Symmetric Private Information Retrieval For MDS Coded Distributed Storage

A user wants to retrieve a file from a database without revealing the identity of the file retrieved at the database, which is known as the problem of private information retrieval (PIR). If it is further required that the user obtains no information about the database other than the desired file, the concept of symmetric private information retrieval (SPIR) is introduced to guarantee privacy for both parties. In this paper, the problem of SPIR is studied for a database stored among $N$ nodes in a distributed way, by using an $(N,M)$-MDS storage code. The information-theoretic capacity of SPIR, defined as the maximum number of symbols of the desired file retrieved per downloaded symbol, for the coded database is derived. It is shown that the SPIR capacity for coded database is $1-\frac{M}{N}$, when the amount of the shared common randomness of distributed nodes (unavailable at the user) is at least $\frac{M}{N-M}$ times the file size. Otherwise, the SPIR capacity for the coded database equals zero.

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preprint2016arXiv

The Matrix Exponential Distribution - A Tool for Wireless System Performance Analysis

In [1], we introduced a new, matrix algebraic, performance analysis framework for wireless systems with fading channels based on the matrix exponential distribution. The main idea was to use the compact, powerful, and easy-to-use, matrix exponential (ME)-distribution for i) modeling the unprocessed channel signal to noise ratio (SNR), ii) exploiting the closure property of the ME-distribution for SNR processing operations to give the effective channel random variable (r.v.) on ME-distribution form, and then to iii) express the performance measure in a closed-form based on ME-distribution matrix/vector parameters only. In this work, we aim to more clearly present, formalize, refine and develop this unified bottom-up analysis framework, show its versatility to handle important communication cases, performance evaluation levels, and performance metrics. The bivariate ME-distribution is introduced here as yet another useful ME-tool, e.g. to account for dependency among two r.v.s. We propose that the ME-distribution may, in addition to fading, also characterize the pdf of discrete-time signal r.v.s, thus extending the ME-distribution matrix form to new generalized 1D/2D-Gaussian-, and Rayleigh-, distribution-like matrix forms. Our findings here, strengthen the observation from [1], [2], and indicates that the ME-distribution can be a promising tool for wireless system modeling and performance analysis.

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preprint2016arXiv

Uncertain Wiretap Channels and Secure Estimation

Uncertain wiretap channels are introduced. Their zero-error secrecy capacity is defined. If the sensor-estimator channel is perfect, it is also calculated. Further properties are discussed. The problem of estimating a dynamical system with nonstochastic disturbances is studied where the sensor is connected to the estimator and an eavesdropper via an uncertain wiretap channel. The estimator should obtain a uniformly bounded estimation error whereas the eavesdropper's error should tend to infinity. It is proved that the system can be estimated securely if the zero-error capacity of the sensor-estimator channel is strictly larger than the logarithm of the system's unstable pole and the zero-error secrecy capacity of the uncertain wiretap channel is positive.

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preprint2015arXiv

Authentication With a Guessing Adversary

In this paper, we consider the authentication problem where a candidate measurement presented by an unidentified user is compared to a previously stored measurement of the legitimate user, the enrollment, with respect to a certain distortion criteria for authentication. An adversary wishes to impersonate the legitimate user by guessing the enrollment until the system authenticates him. For this setting, we study the minimum number of required guesses (on average) by the adversary for a successful impersonation attack and find the complete characterization of the asymptotic exponent of this metric, referred to as the deception exponent. Our result is a direct application of the results of the Guessing problem by Arikan and Merhav [19]. Paralleling the work in [19] we also extend this result to the case where the adversary may have access to additional side information correlated to the enrollment data. The paper is a revised version of a submission to IEEE WIFS 2015, with the referencing to the paper [19] clarified compared with the conference version.

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preprint2015arXiv

Design and Analysis of a Greedy Pursuit for Distributed Compressed Sensing

We consider a distributed compressed sensing scenario where many sensors measure correlated sparse signals and the sensors are connected through a network. Correlation between sparse signals is modeled by a partial common support-set. For such a scenario, the main objective of this paper is to develop a greedy pursuit algorithm. We develop a distributed parallel pursuit (DIPP) algorithm based on exchange of information about estimated support-sets at sensors. The exchange of information helps to improve estimation of the partial common support-set, that in turn helps to gradually improve estimation of support-sets in all sensors, leading to a better quality reconstruction performance. We provide restricted isometry property (RIP) based theoretical analysis on the algorithm's convergence and reconstruction performance. Under certain theoretical requirements on the quality of information exchange over network and RIP parameters of sensor nodes, we show that the DIPP algorithm converges to a performance level that depends on a scaled additive measurement noise power (convergence in theory) where the scaling coefficient is a function of RIP parameters and information processing quality parameters. Using simulations, we show practical reconstruction performance of DIPP vis-a-vis amount of undersampling, signal-to-measurement-noise ratios and network-connectivity conditions.

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preprint2015arXiv

Distributed Quantization for Measurement of Correlated Sparse Sources over Noisy Channels

In this paper, we design and analyze distributed vector quantization (VQ) for compressed measurements of correlated sparse sources over noisy channels. Inspired by the framework of compressed sensing (CS) for acquiring compressed measurements of the sparse sources, we develop optimized quantization schemes that enable distributed encoding and transmission of CS measurements over noisy channels followed by joint decoding at a decoder. The optimality is addressed with respect to minimizing the sum of mean-square error (MSE) distortions between the sparse sources and their reconstruction vectors at the decoder. We propose a VQ encoder-decoder design via an iterative algorithm, and derive a lower-bound on the end-to-end MSE of the studied distributed system. Through several simulation studies, we evaluate the performance of the proposed distributed scheme.

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preprint2015arXiv

Iterative Concave Rank Approximation for Recovering Low-Rank Matrices

In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values, and then minimize the resulting approximation subject to the linear constraints. The accuracy of the approximation is controlled via a scaling parameter $δ$, where a smaller $δ$ corresponds to a more accurate fitting. The consequent optimization problem for any finite $δ$ is nonconvex. Therefore, in order to decrease the risk of ending up in local minima, a series of optimizations is performed, starting with optimizing a rough approximation (a large $δ$) and followed by successively optimizing finer approximations of the rank with smaller $δ$'s. To solve the optimization problem for any $δ> 0$, it is converted to a new program in which the cost is a function of two auxiliary positive semidefinete variables. The paper shows that this new program is concave and applies a majorize-minimize technique to solve it which, in turn, leads to a few convex optimization iterations. This optimization scheme is also equivalent to a reweighted Nuclear Norm Minimization (NNM), where weighting update depends on the used approximating function. For any $δ> 0$, we derive a necessary and sufficient condition for the exact recovery which are weaker than those corresponding to NNM. On the numerical side, the proposed algorithm is compared to NNM and a reweighted NNM in solving affine rank minimization and matrix completion problems showing its considerable and consistent superiority in terms of success rate, especially, when the number of measurements decreases toward the lower-bound for the unique representation.

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preprint2015arXiv

Key Agreement over an Interference Channel with Noiseless Feedback: Achievable Region & Distributed Allocation

Secret key establishment leveraging the physical layer as a source of common randomness has been investigated in a range of settings. We investigate the problem of establishing, in an information-theoretic sense, a secret key between a user and a base-station (BS) (more generally, part of a wireless infrastructure), but for two such user-BS pairs attempting the key establishment simultaneously. The challenge in this novel setting lies in that a user can eavesdrop another BS-user communications. It is thus paramount to ensure the two keys are established with no leakage to the other user, in spite the interference across neighboring cells. We model the system with BS-user communication through an interference channel and user-BS communication through a public channel. We find the region including achievable secret key rates for the general case that the interference channel (IC) is discrete and memoryless. Our results are examined for a Gaussian IC. In this setup, we investigate the performance of different transmission schemes for power allocation. The chosen transmission scheme by each BS essentially affects the secret key rate of the other BS-user. Assuming base stations are trustworthy but that they seek to maximize the corresponding secret key rate, a game-theoretic setting arises to analyze the interaction between the base stations.We model our key agreement scenario in normal form for different power allocation schemes to understand performance without cooperation. Numerical simulations illustrate the inefficiency of the Nash equilibrium outcome and motivate further research on cooperative or coordinated schemes.

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preprint2015arXiv

Scalable Capacity Bounding Models for Wireless Networks

The framework of network equivalence theory developed by Koetter et al. introduces a notion of channel emulation to construct noiseless networks as upper (resp. lower) bounding models, which can be used to calculate the outer (resp. inner) bounds for the capacity region of the original noisy network. Based on the network equivalence framework, this paper presents scalable upper and lower bounding models for wireless networks with potentially many nodes. A channel decoupling method is proposed to decompose wireless networks into decoupled multiple-access channels (MACs) and broadcast channels (BCs). The upper bounding model, consisting of only point-to-point bit pipes, is constructed by firstly extending the "one-shot" upper bounding models developed by Calmon et al. and then integrating them with network equivalence tools. The lower bounding model, consisting of both point-to-point and point-to-points bit pipes, is constructed based on a two-step update of the lower bounding models to incorporate the broadcast nature of wireless transmission. The main advantages of the proposed methods are their simplicity and the fact that they can be extended easily to large networks with a complexity that grows linearly with the number of nodes. It is demonstrated that the resulting upper and lower bounds can approach the capacity in some setups.

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preprint2015arXiv

Secure Degrees of Freedom of Wireless X Networks Using Artificial Noise Alignment

The problem of transmitting confidential messages in $M \times K$ wireless X networks is considered, in which each transmitter intends to send one confidential message to every receiver. In particular, the secure degrees of freedom (SDOF) of the considered network are studied based on an artificial noise alignment (ANA) approach, which integrates interference alignment and artificial noise transmission. At first, an SDOF upper bound is derived for the $M \times K$ X network with confidential messages (XNCM) to be $\frac{K(M-1)}{K+M-2}$. By proposing an ANA approach, it is shown that the SDOF upper bound is tight when $K=2$ for the considered XNCM with time/frequency varying channels. For $K \geq 3$, it is shown that SDOF of $\frac{K(M-1)}{K+M-1}$ can be achieved, even when an external eavesdropper is present. The key idea of the proposed scheme is to inject artificial noise into the network, which can be aligned in the interference space at receivers for confidentiality. Moreover, for the network with no channel state information at transmitters, a blind ANA scheme is proposed to achieve SDOF of $\frac{K(M-1)}{K+M-1}$ for $K,M \geq 2$, with reconfigurable antennas at receivers. The proposed method provides a linear approach to secrecy coding and interference alignment.

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preprint2015arXiv

Secure Partial Repair in Wireless Caching Networks with Broadcast Channels

We study security in partial repair in wireless caching networks where parts of the stored packets in the caching nodes are susceptible to be erased. Let us denote a caching node that has lost parts of its stored packets as a sick caching node and a caching node that has not lost any packet as a healthy caching node. In partial repair, a set of caching nodes (among sick and healthy caching nodes) broadcast information to other sick caching nodes to recover the erased packets. The broadcast information from a caching node is assumed to be received without any error by all other caching nodes. All the sick caching nodes then are able to recover their erased packets, while using the broadcast information and the nonerased packets in their storage as side information. In this setting, if an eavesdropper overhears the broadcast channels, it might obtain some information about the stored file. We thus study secure partial repair in the senses of information-theoretically strong and weak security. In both senses, we investigate the secrecy caching capacity, namely, the maximum amount of information which can be stored in the caching network such that there is no leakage of information during a partial repair process. We then deduce the strong and weak secrecy caching capacities, and also derive the sufficient finite field sizes for achieving the capacities. Finally, we propose optimal secure codes for exact partial repair, in which the recovered packets are exactly the same as erased packets.

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preprint2014arXiv

Analysis of Democratic Voting Principles used in Distributed Greedy Algorithms

A key aspect for any greedy pursuit algorithm used in compressed sensing is a good support-set detection method. For distributed compressed sensing, we consider a setup where many sensors measure sparse signals that are correlated via the existence of a signals' intersection support-set. This intersection support-set is called the joint support-set. Estimation of the joint support-set has a high impact on the performance of a distributed greedy pursuit algorithm. This estimation can be achieved by exchanging local support-set estimates followed by a (consensus) voting method. In this paper we endeavor for a probabilistic analysis of two democratic voting principle that we call majority and consensus voting. In our analysis, we first model the input/output relation of a greedy algorithm (executed locally in a sensor) by a single parameter known as probability of miss. Based on this model, we analyze the voting principles and prove that the democratic voting principle has a merit to detect the joint support-set.

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preprint2014arXiv

Analysis-by-Synthesis Quantization for Compressed Sensing Measurements

We consider a resource-limited scenario where a sensor that uses compressed sensing (CS) collects a low number of measurements in order to observe a sparse signal, and the measurements are subsequently quantized at a low bit-rate followed by transmission or storage. For such a scenario, we design new algorithms for source coding with the objective of achieving good reconstruction performance of the sparse signal. Our approach is based on an analysis-by-synthesis principle at the encoder, consisting of two main steps: (1) the synthesis step uses a sparse signal reconstruction technique for measuring the direct effect of quantization of CS measurements on the final sparse signal reconstruction quality, and (2) the analysis step decides appropriate quantized values to maximize the final sparse signal reconstruction quality. Through simulations, we compare the performance of the proposed quantization algorithms vis-a-vis existing quantization schemes.

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preprint2014arXiv

Analysis-by-Synthesis-based Quantization of Compressed Sensing Measurements

We consider a resource-constrained scenario where a compressed sensing- (CS) based sensor has a low number of measurements which are quantized at a low rate followed by transmission or storage. Applying this scenario, we develop a new quantizer design which aims to attain a high-quality reconstruction performance of a sparse source signal based on analysis-by-synthesis framework. Through simulations, we compare the performance of the proposed quantization algorithm vis-a-vis existing quantization methods.

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preprint2014arXiv

Channel-Optimized Vector Quantizer Design for Compressed Sensing Measurements

We consider vector-quantized (VQ) transmission of compressed sensing (CS) measurements over noisy channels. Adopting mean-square error (MSE) criterion to measure the distortion between a sparse vector and its reconstruction, we derive channel-optimized quantization principles for encoding CS measurement vector and reconstructing sparse source vector. The resulting necessary optimal conditions are used to develop an algorithm for training channel-optimized vector quantization (COVQ) of CS measurements by taking the end-to-end distortion measure into account.

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preprint2014arXiv

Communication and Interference Coordination

We study the problem of controlling the interference created to an external observer by a communication processes. We model the interference in terms of its type (empirical distribution), and we analyze the consequences of placing constraints on the admissible type. Considering a single interfering link, we characterize the communication-interference capacity region. Then, we look at a scenario where the interference is jointly created by two users allowed to coordinate their actions prior to transmission. In this case, the trade-off involves communication and interference as well as coordination. We establish an achievable communication-interference region and show that efficiency is significantly improved by coordination.

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preprint2014arXiv

Distributed Quantization for Compressed Sensing

We study distributed coding of compressed sensing (CS) measurements using vector quantizer (VQ). We develop a distributed framework for realizing optimized quantizer that enables encoding CS measurements of correlated sparse sources followed by joint decoding at a fusion center. The optimality of VQ encoder-decoder pairs is addressed by minimizing the sum of mean-square errors between the sparse sources and their reconstruction vectors at the fusion center. We derive a lower-bound on the end-to-end performance of the studied distributed system, and propose a practical encoder-decoder design through an iterative algorithm.

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preprint2014arXiv

Interference Alignment: Practical Challenges and Test-bed Implementation

Data traffic over wireless communication networks has experienced a tremendous growth in the last decade, and it is predicted to exponentially increase in the next decades. Enabling future wireless networks to fulfill this expectation is a challenging task both due to the scarcity of radio resources (e.g. spectrum and energy), and also the inherent characteristics of the wireless transmission medium. Wireless transmission is in general subject to two phenomena: fading and interference. The elegant interference alignment concept reveals that with proper transmission signalling design, different interference signals can in fact be aligned together, such that more radio resources can be assigned to the desired transmission. Although interference alignment can achieve a larger data rate compared to orthogonal transmission strategies, several challenges should be addressed to enable the deployment of this technique in future wireless networks For instance, to perform interference alignment, normally, global channel state information (CSI) is required to be perfectly known at all terminals. Clearly, acquiring such channel knowledge is a challenging problem in practice and proper channel training and channel state feedback techniques need to be deployed. In addition, since the channels are time-varying proper adaptive transmission is needed. This chapter review recent advances in practical aspects of interference alignment. It also presents recent test-bed implementations of signal processing algorithms for the realization of interference alignment.

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preprint2014arXiv

Joint Source-Channel Vector Quantization for Compressed Sensing

We study joint source-channel coding (JSCC) of compressed sensing (CS) measurements using vector quantizer (VQ). We develop a framework for realizing optimum JSCC schemes that enable encoding and transmitting CS measurements of a sparse source over discrete memoryless channels, and decoding the sparse source signal. For this purpose, the optimal design of encoder-decoder pair of a VQ is considered, where the optimality is addressed by minimizing end-to-end mean square error (MSE). We derive a theoretical lower-bound on the MSE performance, and propose a practical encoder-decoder design through an iterative algorithm. The resulting coding scheme is referred to as channel- optimized VQ for CS, coined COVQ-CS. In order to address the encoding complexity issue of the COVQ-CS, we propose to use a structured quantizer, namely low complexity multi-stage VQ (MSVQ). We derive new encoding and decoding conditions for the MSVQ, and then propose a practical encoder-decoder design algorithm referred to as channel-optimized MSVQ for CS, coined COMSVQ-CS. Through simulation studies, we compare the proposed schemes vis-a-vis relevant quantizers.

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preprint2014arXiv

Lossy Source Coding with Reconstruction Privacy

We consider the problem of lossy source coding with side information under a privacy constraint that the reconstruction sequence at a decoder should be kept secret to a certain extent from another terminal such as an eavesdropper, a sender, or a helper. We are interested in how the reconstruction privacy constraint at a particular terminal affects the rate-distortion tradeoff. In this work, we allow the decoder to use a random mapping, and give inner and outer bounds to the rate-distortion-equivocation region for different cases where the side information is available non-causally and causally at the decoder. In the special case where each reconstruction symbol depends only on the source description and current side information symbol, the complete rate-distortion-equivocation region is provided. A binary example illustrating a new tradeoff due to the new privacy constraint, and a gain from the use of a stochastic decoder is given.

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preprint2014arXiv

Multi layer Gelfand Pinsker Strategies for the Generalized Multiple Access Channel

We study a two-user state-dependent generalized multiple-access channel (GMAC) with correlated states. It is assumed that each encoder has \emph{noncausal} access to channel state information (CSI). We develop an achievable rate region by employing rate-splitting, block Markov encoding, Gelfand--Pinsker multicoding, superposition coding and joint typicality decoding. In the proposed scheme, the encoders use a partial decoding strategy to collaborate in the next block, and the receiver uses a backward decoding strategy with joint unique decoding at each stage. Our achievable rate region includes several previously known regions proposed in the literature for different scenarios of multiple-access and relay channels. Then, we consider two Gaussian GMACs with additive interference. In the first model, we assume that the interference is known noncausally at both of the encoders and construct a multi-layer Costa precoding scheme that removes \emph{completely} the effect of the interference. In the second model, we consider a doubly dirty Gaussian GMAC in which each of interferences is known noncausally only at one encoder. We derive an inner bound and analyze the achievable rate region for the latter model and interestingly prove that if one of the encoders knows the full CSI, there exists an achievable rate region which is \emph{independent} of the power of interference.

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preprint2014arXiv

On the Transmit Beamforming for MIMO Wiretap Channels: Large-System Analysis

With the growth of wireless networks, security has become a fundamental issue in wireless communications due to the broadcast nature of these networks. In this work, we consider MIMO wiretap channels in a fast fading environment, for which the overall performance is characterized by the ergodic MIMO secrecy rate. Unfortunately, the direct solution to finding ergodic secrecy rates is prohibitive due to the expectations in the rates expressions in this setting. To overcome this difficulty, we invoke the large-system assumption, which allows a deterministic approximation to the ergodic mutual information. Leveraging results from random matrix theory, we are able to characterize the achievable ergodic secrecy rates. Based on this characterization, we address the problem of covariance optimization at the transmitter. Our numerical results demonstrate a good match between the large-system approximation and the actual simulated secrecy rates, as well as some interesting features of the precoder optimization.

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preprint2014arXiv

Performance Bounds for Vector Quantized Compressive Sensing

In this paper, we endeavor for predicting the performance of quantized compressive sensing under the use of sparse reconstruction estimators. We assume that a high rate vector quantizer is used to encode the noisy compressive sensing measurement vector. Exploiting a block sparse source model, we use Gaussian mixture density for modeling the distribution of the source. This allows us to formulate an optimal rate allocation problem for the vector quantizer. Considering noisy CS quantized measurements, we analyze upper- and lower-bounds on reconstruction error performance guarantee of two estimators - convex relaxation based basis pursuit de-noising estimator and an oracle-assisted least-squares estimator.

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preprint2014arXiv

Performance Guarantees for Schatten-$p$ Quasi-Norm Minimization in Recovery of Low-Rank Matrices

We address some theoretical guarantees for Schatten-$p$ quasi-norm minimization ($p \in (0,1]$) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measurement operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition guarantees unique recovery of matrices of ranks equal or larger than what is guaranteed by nuclear norm minimization. Secondly, this sufficient condition leads to a theorem proving that all restricted isometry property (RIP) based sufficient conditions for $\ell_p$ quasi-norm minimization generalize to Schatten-$p$ quasi-norm minimization. Based on this theorem, we provide a few RIP-based recovery conditions.

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preprint2014arXiv

SEK: Sparsity exploiting $k$-mer-based estimation of bacterial community composition

Motivation: Estimation of bacterial community composition from a high-throughput sequenced sample is an important task in metagenomics applications. Since the sample sequence data typically harbors reads of variable lengths and different levels of biological and technical noise, accurate statistical analysis of such data is challenging. Currently popular estimation methods are typically very time consuming in a desktop computing environment. Results: Using sparsity enforcing methods from the general sparse signal processing field (such as compressed sensing), we derive a solution to the community composition estimation problem by a simultaneous assignment of all sample reads to a pre-processed reference database. A general statistical model based on kernel density estimation techniques is introduced for the assignment task and the model solution is obtained using convex optimization tools. Further, we design a greedy algorithm solution for a fast solution. Our approach offers a reasonably fast community composition estimation method which is shown to be more robust to input data variation than a recently introduced related method. Availability: A platform-independent Matlab implementation of the method is freely available at http://www.ee.kth.se/ctsoftware; source code that does not require access to Matlab is currently being tested and will be made available later through the above website.

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preprint2014arXiv

Zero-Delay Joint Source-Channel Coding for a Multivariate Gaussian on a Gaussian MAC

In this paper, communication of a Multivariate Gaussian over a Gaussian Multiple Access Channel is studied. Distributed zero-delay joint source-channel coding (JSCC) solutions to the problem are given. Both nonlinear and linear approaches are discussed. The performance upper bound (signal-to-distortion ratio) for arbitrary code length is also derived and Zero-delay cooperative JSCC is briefly addressed in order to provide an approximate bound on the performance of zero-delay schemes. The main contribution is a nonlinear hybrid discrete-analog JSSC scheme based on distributed quantization and a linear continuous mapping named Distributed Quantizer Linear Coder (DQLC). The DQLC has promising performance which improves with increasing correlation, and is robust against variations in noise level. The DQLC exhibits a constant gap to the performance upper bound as the signal-to-noise ratio (SNR) becomes large for any number of sources and values of correlation. Therefore it outperforms a linear solution (uncoded transmission) in any case when the SNR gets sufficiently large.

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preprint2013arXiv

A Two-Phase Maximum-Likelihood Sequence Estimation for Receivers with Partial CSI

The optimality of the conventional maximum likelihood sequence estimation (MLSE), also known as the Viterbi Algorithm (VA), relies on the assumption that the receiver has perfect knowledge of the channel coefficients or channel state information (CSI). However, in practical situations that fail the assumption, the MLSE method becomes suboptimal and then exhaustive checking is the only way to obtain the ML sequence. At this background, considering directly the ML criterion for partial CSI, we propose a two-phase low-complexity MLSE algorithm, in which the first phase performs the conventional MLSE algorithm in order to retain necessary information for the backward VA performed in the second phase. Simulations show that when the training sequence is moderately long in comparison with the entire data block such as 1/3 of the block, the proposed two-phase MLSE can approach the performance of the optimal exhaustive checking. In a normal case, where the training sequence consumes only 0.14 of the bandwidth, our proposed method still outperforms evidently the conventional MLSE.

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preprint2013arXiv

Coding for Computing Irreducible Markovian Functions of Sources with Memory

One open problem in source coding is to characterize the limits of representing losslessly a non-identity discrete function of the data encoded independently by the encoders of several correlated sources with memory. This paper investigates this problem under Markovian conditions, namely either the sources or the functions considered are Markovian. We propose using linear mappings over finite rings as encoders. If the function considered admits certain polynomial structure, the linear encoders can make use of this structure to establish "implicit collaboration" and boost the performance. In fact, this approach universally applies to any scenario (arbitrary function) because any discrete function admits a polynomial presentation of required format. There are several useful discoveries in the paper. The first says that linear encoder over non-field ring can be equally optimal for compressing data generated by an irreducible Markov source. Secondly, regarding the previous function-encoding problem, there are infinitely many circumstances where linear encoder over non-field ring strictly outperforms its field counterpart. To be more precise, it is seen that the set of coding rates achieved by linear encoder over certain non-field rings is strictly larger than the one achieved by the field version, regardless which finite field is considered. Therefore, in this sense, linear coding over finite field is not optimal. In addition, for certain scenarios where the sources do not possess the ergodic property, our ring approach is still able to offer a solution.

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preprint2013arXiv

Decentralized Minimum-Cost Repair for Distributed Storage Systems

There have been emerging lots of applications for distributed storage systems e.g., those in wireless sensor networks or cloud storage. Since storage nodes in wireless sensor networks have limited battery, it is valuable to find a repair scheme with optimal transmission costs (e.g., energy). The optimal-cost repair has been recently investigated in a centralized way. However a centralized control mechanism may not be available or is very expensive. For the scenarios, it is interesting to study optimal-cost repair in a decentralized setup. We formulate the optimal-cost repair as convex optimization problems for the network with convex transmission costs. Then we use primal and dual decomposition approaches to decouple the problem into subproblems to be solved locally. Thus, each surviving node, collaborating with other nodes, can minimize its transmission cost such that the global cost is minimized. We further study the optimality and convergence of the algorithms. Finally, we discuss the code construction and determine the field size for finding feasible network codes in our approaches.

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preprint2013arXiv

Distributed Greedy Pursuit Algorithms

For compressed sensing over arbitrarily connected networks, we consider the problem of estimating underlying sparse signals in a distributed manner. We introduce a new signal model that helps to describe inter-signal correlation among connected nodes. Based on this signal model along with a brief survey of existing greedy algorithms, we develop distributed greedy algorithms with low communication overhead. Incorporating appropriate modifications, we design two new distributed algorithms where the local algorithms are based on appropriately modified existing orthogonal matching pursuit and subspace pursuit. Further, by combining advantages of these two local algorithms, we design a new greedy algorithm that is well suited for a distributed scenario. By extensive simulations we demonstrate that the new algorithms in a sparsely connected network provide good performance, close to the performance of a centralized greedy solution.

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preprint2013arXiv

On the Design of Channel Estimators for given Signal Estimators and Detectors

The fundamental task of a digital receiver is to decide the transmitted symbols in the best possible way, i.e., with respect to an appropriately defined performance metric. Examples of usual performance metrics are the probability of error and the Mean Square Error (MSE) of a symbol estimator. In a coherent receiver, the symbol decisions are made based on the use of a channel estimate. This paper focuses on examining the optimality of usual estimators such as the minimum variance unbiased (MVU) and the minimum mean square error (MMSE) estimators for these metrics and on proposing better estimators whenever it is necessary. For illustration purposes, this study is performed on a toy channel model, namely a single input single output (SISO) flat fading channel with additive white Gaussian noise (AWGN). In this way, this paper highlights the design dependencies of channel estimators on target performance metrics.

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preprint2013arXiv

Optimized-Cost Repair in Multi-hop Distributed Storage Systems with Network Coding

In distributed storage systems reliability is achieved through redundancy stored at different nodes in the network. Then a data collector can reconstruct source information even though some nodes fail. To maintain reliability, an autonomous and efficient protocol should be used to repair the failed node. The repair process causes traffic and consequently transmission cost in the network. Recent results found the optimal trafficstorage tradeoff, and proposed regenerating codes to achieve the optimality. We aim at minimizing the transmission cost in the repair process. We consider the network topology in the repair, and accordingly modify information flow graphs. Then we analyze the cut requirement and based on the results, we formulate the minimum-cost as a linear programming problem for linear costs. We show that the solution of the linear problem establishes a fundamental lower bound of the repair-cost. We also show that this bound is achievable for minimum storage regenerating, which uses the optimal-cost minimum-storage regenerating (OCMSR) code. We propose surviving node cooperation which can efficiently reduce the repair cost. Further, the field size for the construction of OCMSR codes is discussed. We show the gain of optimal-cost repair in tandem, star, grid and fully connected networks.

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preprint2013arXiv

Secure Source Coding with a Public Helper

We consider secure multi-terminal source coding problems in the presence of a public helper. Two main scenarios are studied: 1) source coding with a helper where the coded side information from the helper is eavesdropped by an external eavesdropper; 2) triangular source coding with a helper where the helper is considered as a public terminal. We are interested in how the helper can support the source transmission subject to a constraint on the amount of information leaked due to its public nature. We characterize the tradeoff between transmission rate, incurred distortion, and information leakage rate at the helper/eavesdropper in the form of a rate-distortion-leakage region for various classes of problems.

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preprint2013arXiv

Stabilization of Linear Systems Over Gaussian Networks

The problem of remotely stabilizing a noisy linear time invariant plant over a Gaussian relay network is addressed. The network is comprised of a sensor node, a group of relay nodes and a remote controller. The sensor and the relay nodes operate subject to an average transmit power constraint and they can cooperate to communicate the observations of the plant's state to the remote controller. The communication links between all nodes are modeled as Gaussian channels. Necessary as well as sufficient conditions for mean-square stabilization over various network topologies are derived. The sufficient conditions are in general obtained using delay-free linear policies and the necessary conditions are obtained using information theoretic tools. Different settings where linear policies are optimal, asymptotically optimal (in certain parameters of the system) and suboptimal have been identified. For the case with noisy multi-dimensional sources controlled over scalar channels, it is shown that linear time varying policies lead to minimum capacity requirements, meeting the fundamental lower bound. For the case with noiseless sources and parallel channels, non-linear policies which meet the lower bound have been identified.

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preprint2013arXiv

Successive Secret Key Agreement over Generalized Multiple Access and Broadcast Channels

A secret key agreement framework between three users is considered in which each of the users 1 and 2 intends to share a secret key with user 3 and users 1 and 2 are eavesdroppers with respect to each other. There is a generalized discrete memoryless multiple access channel (GDMMAC) from users 1 and 2 to user 3 where the three users receive outputs from the channel. Furthermore, there is a broadcast channel (BC) from user 3 to users 1 and 2. Secret key sharing is intended where GDMMAC and BC can be successively used. In this framework, an inner bound of the secret key capacity region is derived. Moreover, for a special case where the channel inputs and outputs of the GDMAC and the BC form Markov chains in some order, the secret key capacity region is derived. Also the results are discussed through a binary example.

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preprint2012arXiv

Analysis of MMSE Estimation for Compressive Sensing of Block Sparse Signals

Minimum mean square error (MMSE) estimation of block sparse signals from noisy linear measurements is considered. Unlike in the standard compressive sensing setup where the non-zero entries of the signal are independently and uniformly distributed across the vector of interest, the information bearing components appear here in large mutually dependent clusters. Using the replica method from statistical physics, we derive a simple closed-form solution for the MMSE obtained by the optimum estimator. We show that the MMSE is a version of the Tse-Hanly formula with system load and MSE scaled by parameters that depend on the sparsity pattern of the source. It turns out that this is equal to the MSE obtained by a genie-aided MMSE estimator which is informed in advance about the exact locations of the non-zero blocks. The asymptotic results obtained by the non-rigorous replica method are found to have an excellent agreement with finite sized numerical simulations.

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preprint2012arXiv

Analysis of Sparse Representations Using Bi-Orthogonal Dictionaries

The sparse representation problem of recovering an N dimensional sparse vector x from M < N linear observations y = Dx given dictionary D is considered. The standard approach is to let the elements of the dictionary be independent and identically distributed (IID) zero-mean Gaussian and minimize the l1-norm of x under the constraint y = Dx. In this paper, the performance of l1-reconstruction is analyzed, when the dictionary is bi-orthogonal D = [O1 O2], where O1,O2 are independent and drawn uniformly according to the Haar measure on the group of orthogonal M x M matrices. By an application of the replica method, we obtain the critical conditions under which perfect l1-recovery is possible with bi-orthogonal dictionaries.

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preprint2012arXiv

Coding With Action-dependent Side Information and Additional Reconstruction Requirements

Constrained lossy source coding and channel coding with side information problems which extend the classic Wyner-Ziv and Gel'fand-Pinsker problems are considered. Inspired by applications in sensor networking and control, we first consider lossy source coding with two-sided partial side information where the quality/availability of the side information can be influenced by a cost-constrained action sequence. A decoder reconstructs a source sequence subject to the distortion constraint, and at the same time, an encoder is additionally required to be able to estimate the decoder's reconstruction. Next, we consider the channel coding "dual" where the channel state is assumed to depend on the action sequence, and the decoder is required to decode both the transmitted message and channel input reliably. Implications on the fundamental limits of communication in discrete memoryless systems due to the additional reconstruction constraints are investigated. Single-letter expressions for the rate-distortion-cost function and channel capacity for the respective source and channel coding problems are derived. The dual relation between the two problems is discussed. Additionally, based on the two-stage coding structure and the additional reconstruction constraint of the channel coding problem, we discuss and give an interpretation of the two-stage coding condition which appears in the channel capacity expression. Besides the rate constraint on the message, this condition is a necessary and sufficient condition for reliable transmission of the channel input sequence over the channel in our "two-stage" communication problem. It is also shown in one example that there exists a case where the two-stage coding condition can be active in computing the capacity, and it thus can actively restrict the set of capacity achieving input distributions.

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preprint2012arXiv

Degrees of Freedom of Multi-hop MIMO Broadcast Networks with Delayed CSIT

We study the sum degrees of freedom (DoF) of a class of multi-layer relay-aided MIMO broadcast networks with delayed channel state information at transmitters (CSIT). In the assumed network a K-antenna source intends to communicate to K single-antenna destinations, with the help of N-2 layers of K full-duplex single-antenna relays. We consider two practical delayed CSIT feedback scenarios. If the source can obtain the CSI feedback signals from all layers, we prove the optimal sum DoF of the network to be K/(1+1/2+...+1/K). If the CSI feedback is only within each hop, we show that when K=2 the optimal sum DoF is 4/3, and when K >= 3 the sum DoF 3/2 is achievable. Our results reveal that the sum DoF performance in the considered class of N-layer MIMO broadcast networks with delayed CSIT may depend not on N, the number of layers in the network, but only on K, the number of antennas/terminals in each layer.

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preprint2012arXiv

Iterative Source-Channel Coding Approach to Witsenhausen's Counterexample

In 1968, Witsenhausen introduced his famous counterexample where he showed that even in the simple linear quadratic static team decision problem, complex nonlinear decisions could outperform any given linear decision. This problem has served as a benchmark problem for decades where researchers try to achieve the optimal solution. This paper introduces a systematic iterative source--channel coding approach to solve problems of the Witsenhausen Counterexample-character. The advantage of the presented approach is its simplicity. Also, no assumptions are made about the shape of the space of policies. The minimal cost obtained using the introduced method is 0.16692462, which is the lowest known to date.

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preprint2012arXiv

Secret Key Agreement Using Correlated Sources over the Generalized Multiple Access Channel

A secret key agreement setup between three users is considered in which each of the users 1 and 2 intends to share a secret key with user 3 and users 1 and 2 are eavesdroppers with respect to each other. The three users observe i.i.d. outputs of correlated sources and there is a generalized discrete memoryless multiple access channel (GDMMAC) from users 1 and 2 to user 3 for communication between the users. The secret key agreement is established using the correlated sources and the GDMMAC. In this setup, inner and outer bounds of the secret key capacity region are investigated. Moreover, for a special case where the channel inputs and outputs and the sources form Markov chains in some order, the secret key capacity region is derived. Also a Gaussian case is considered in this setup.

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preprint2012arXiv

Zero-Delay Joint Source-Channel Coding for a Bivariate Gaussian on a Gaussian MAC

In this paper, delay-free, low complexity, joint source-channel coding (JSCC) for transmission of two correlated Gaussian memoryless sources over a Gaussian Multiple Access Channel (GMAC) is considered. The main contributions of the paper are two distributed JSCC schemes: one discrete scheme based on nested scalar quantization, and one hybrid discrete-analog scheme based on a scalar quantizer and a linear continuous mapping. The proposed schemes show promising performance which improve with increasing correlation and are robust against variations in noise level. Both schemes exhibit a constant gap to the performance upper bound when the channel signal-to-noise ratio gets large.

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preprint2011arXiv

Bilayer LDPC Convolutional Codes for Half-Duplex Relay Channels

In this paper we present regular bilayer LDPC convolutional codes for half-duplex relay channels. For the binary erasure relay channel, we prove that the proposed code construction achieves the capacities for the source-relay link and the source-destination link provided that the channel conditions are known when designing the code. Meanwhile, this code enables the highest transmission rate with decode-and-forward relaying. In addition, its regular degree distributions can easily be computed from the channel parameters, which significantly simplifies the code optimization. Numerical results are provided for both binary erasure channels (BEC) and AWGN channels. In BECs, we can observe that the gaps between the decoding thresholds and the Shannon limits are impressively small. In AWGN channels, the bilayer LDPC convolutional code clearly outperforms its block code counterpart in terms of bit error rate.

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preprint2011arXiv

Performance Analysis and Design of Two Edge Type LDPC Codes for the BEC Wiretap Channel

We consider transmission over a wiretap channel where both the main channel and the wiretapper's channel are Binary Erasure Channels (BEC). We propose a code construction method using two edge type LDPC codes based on the coset encoding scheme. Using a standard LDPC ensemble with a given threshold over the BEC, we give a construction for a two edge type LDPC ensemble with the same threshold. If the given standard LDPC ensemble has degree two variable nodes, our construction gives rise to degree one variable nodes in the code used over the main channel. This results in zero threshold over the main channel. In order to circumvent this problem, we numerically optimize the degree distribution of the two edge type LDPC ensemble. We find that the resulting ensembles are able to perform close to the boundary of the rate-equivocation region of the wiretap channel. There are two performance criteria for a coding scheme used over a wiretap channel: reliability and secrecy. The reliability measure corresponds to the probability of decoding error for the intended receiver. This can be easily measured using density evolution recursion. However, it is more challenging to characterize secrecy, corresponding to the equivocation of the message for the wiretapper. Méasson, Montanari, and Urbanke have shown how the equivocation can be measured for a broad range of standard LDPC ensembles for transmission over the BEC under the point-to-point setup. By generalizing the method of Méasson, Montanari, and Urbanke to two edge type LDPC ensembles, we show how the equivocation for the wiretapper can be computed. We find that relatively simple constructions give very good secrecy performance and are close to the secrecy capacity. However finding explicit sequences of two edge type LDPC ensembles which achieve secrecy capacity is a more difficult problem. We pose it as an interesting open problem.

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preprint2011arXiv

Projection-Based and Look Ahead Strategies for Atom Selection

In this paper, we improve iterative greedy search algorithms in which atoms are selected serially over iterations, i.e., one-by-one over iterations. For serial atom selection, we devise two new schemes to select an atom from a set of potential atoms in each iteration. The two new schemes lead to two new algorithms. For both the algorithms, in each iteration, the set of potential atoms is found using a standard matched filter. In case of the first scheme, we propose an orthogonal projection strategy that selects an atom from the set of potential atoms. Then, for the second scheme, we propose a look ahead strategy such that the selection of an atom in the current iteration has an effect on the future iterations. The use of look ahead strategy requires a higher computational resource. To achieve a trade-off between performance and complexity, we use the two new schemes in cascade and develop a third new algorithm. Through experimental evaluations, we compare the proposed algorithms with existing greedy search and convex relaxation algorithms.

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preprint2011arXiv

Rate-Equivocation Optimal Spatially Coupled LDPC Codes for the BEC Wiretap Channel

We consider transmission over a wiretap channel where both the main channel and the wiretapper's channel are Binary Erasure Channels (BEC). We use convolutional LDPC ensembles based on the coset encoding scheme. More precisely, we consider regular two edge type convolutional LDPC ensembles. We show that such a construction achieves the whole rate-equivocation region of the BEC wiretap channel. Convolutional LDPC ensemble were introduced by Felström and Zigangirov and are known to have excellent thresholds. Recently, Kudekar, Richardson, and Urbanke proved that the phenomenon of "Spatial Coupling" converts MAP threshold into BP threshold for transmission over the BEC. The phenomenon of spatial coupling has been observed to hold for general binary memoryless symmetric channels. Hence, we conjecture that our construction is a universal rate-equivocation achieving construction when the main channel and wiretapper's channel are binary memoryless symmetric channels, and the wiretapper's channel is degraded with respect to the main channel.

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preprint2010arXiv

Bounds on Threshold of Regular Random $k$-SAT

We consider the regular model of formula generation in conjunctive normal form (CNF) introduced by Boufkhad et. al. We derive an upper bound on the satisfiability threshold and NAE-satisfiability threshold for regular random $k$-SAT for any $k \geq 3$. We show that these bounds matches with the corresponding bound for the uniform model of formula generation. We derive lower bound on the threshold by applying the second moment method to the number of satisfying assignments. For large $k$, we note that the obtained lower bounds on the threshold of a regular random formula converges to the lower bound obtained for the uniform model. Thus, we answer the question posed in \cite{AcM06} regarding the performance of the second moment method for regular random formulas.

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preprint2010arXiv

Bounds on Thresholds Related to Maximum Satisfiability of Regular Random Formulas

We consider the regular balanced model of formula generation in conjunctive normal form (CNF) introduced by Boufkhad, Dubois, Interian, and Selman. We say that a formula is $p$-satisfying if there is a truth assignment satisfying $1-2^{-k}+p 2^{-k}$ fraction of clauses. Using the first moment method we determine upper bound on the threshold clause density such that there are no $p$-satisfying assignments with high probability above this upper bound. There are two aspects in deriving the lower bound using the second moment method. The first aspect is, given any $p \in (0,1)$ and $k$, evaluate the lower bound on the threshold. This evaluation is numerical in nature. The second aspect is to derive the lower bound as a function of $p$ for large enough $k$. We address the first aspect and evaluate the lower bound on the $p$-satisfying threshold using the second moment method. We observe that as $k$ increases the lower bound seems to converge to the asymptotically derived lower bound for uniform model of formula generation by Achlioptas, Naor, and Peres.

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preprint2010arXiv

Nested Polar Codes for Wiretap and Relay Channels

We show that polar codes asymptotically achieve the whole capacity-equivocation region for the wiretap channel when the wiretapper's channel is degraded with respect to the main channel, and the weak secrecy notion is used. Our coding scheme also achieves the capacity of the physically degraded receiver-orthogonal relay channel. We show simulation results for moderate block length for the binary erasure wiretap channel, comparing polar codes and two edge type LDPC codes.

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