BZPEERPapers, people, evidence and research paths
Menu

Discover

SearchFind papers, people, topics, institutions and opportunities from one place.GraphSee how papers, authors, topics and evidence connect.

Research tools

HomeContinue from the papers, people and topics that matter now.CollectionsTurn saved papers into reading lists, evidence maps and shareable context.ResearchReconstruct the path that led you from search to paper to question.CollaborationMove from a paper, topic or expert request into a focused thread.PublishCreate full-text research articles with metadata, formulas and versions.

Network

ExpertsFind specialists whose work and reviews explain why they can help.CommunitiesJoin research groups organized around papers, topics and shared evidence.

Opportunities

ListingsBrowse roles, calls and collaborations connected to real research context.

Account

Log inReturn to your saved papers, graph views and active threads.Create accountStart saving papers, building a research trail and joining teams.
Log inCreate account

Source author record

Chao Tian

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

ResearcherUnclaimed source record
Information Theorymath.ITComputer VisionMachine LearningArtificial IntelligenceComputational GeometryData Structures and Algorithmseess.SPInformation Retrievalmath-phmath.COmath.MPmath.OC

Catalog footprint

What is connected

36works
13topics
4close collaborators

Actions

Connect this record

Log in to claim
Open graphBrowse works

Research graph

See the researcher in context

Open full explorer

Inspect adjacent papers, topics, institutions and collaborators without losing the researcher page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

Published work

36 published item(s)

preprint2026arXiv

Fusing in 3D: Free-Viewpoint Fusion Rendering with a 3D Infrared-Visible Scene Representation

Infrared-visible image fusion aims to integrate infrared and visible information into a single fused image. Existing 2D fusion methods focus on fusing images from fixed camera viewpoints, neglecting a comprehensive understanding of complex scenarios, which results in the loss of critical information about the scene. To address this limitation, we propose a novel Infrared-Visible Gaussian Fusion (IVGF) framework, which reconstructs scene geometry from multimodal 2D inputs and enables direct rendering of fused images. Specifically, we propose a cross-modal adjustment (CMA) module that modulates the opacity of Gaussians to solve the problem of cross-modal conflicts. Moreover, to preserve the distinctive features from both modalities, we introduce a fusion loss that guides the optimization of CMA, thus ensuring that the fused image retains the critical characteristics of each modality. Comprehensive qualitative and quantitative experiments demonstrate the effectiveness of the proposed method.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Modality-Decoupled RGB-Thermal Object Detector via Query Fusion

The advantage of RGB-Thermal (RGB-T) detection lies in its ability to perform modality fusion and integrate cross-modality complementary information, enabling robust detection under diverse illumination and weather conditions. However, under extreme conditions where one modality exhibits poor quality and disturbs detection, modality separation is necessary to mitigate the impact of noise. To address this problem, we propose a Modality-Decoupled RGB-T detection framework with Query Fusion (MDQF) to balance modality complementation and separation. In this framework, DETR-like detectors are employed as separate branches for the RGB and TIR images, with query fusion interspersed between the two branches in each refinement stage. Herein, query fusion is performed by feeding the high-quality queries from one branch to the other one after query selection and adaptation. This design effectively excludes the degraded modality and corrects the predictions using high-quality queries. Moreover, the decoupled framework allows us to optimize each individual branch with unpaired RGB or TIR images, eliminating the need for paired RGB-T data. Extensive experiments demonstrate that our approach delivers superior performance to existing RGB-T detectors and achieves better modality independence.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Report of the 5th PVUW Challenge: Towards More Diverse Modalities in Pixel-Level Understanding

This report summarizes the objectives, datasets, and top-performing methodologies of the 2026 Pixel-level Video Understanding in the Wild (PVUW) Challenge, hosted at CVPR 2026, which evaluates state-of-the-art models under highly unconstrained conditions. To provide a comprehensive assessment, the 2026 edition features three specialized tracks: the MOSE track for tracking objects within densely cluttered and severely occluded scenarios; the MeViS-Text track for localizing targets via motion-focused linguistic expressions; and the newly inaugurated MeViS-Audio track, which pioneers acoustic-driven object segmentation. By introducing previously unreleased challenging data and analyzing the cutting-edge, multimodal solutions submitted by participants, this report highlights the community's latest technical advancements and charts promising future directions for robust video scene comprehension.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Trust It or Not: Evidential Uncertainty for Feed-Forward 3D Reconstruction with Trust3R

Geometric foundation models hold promise for unconstrained dense geometry prediction from uncalibrated images. However, in current feed-forward designs, their predicted confidence scores are heuristic, lack probabilistic interpretation, and often fail to indicate where and how much the predicted geometry can be trusted. To address this gap, we present Trust3R, a lightweight evidential uncertainty framework for feed-forward 3D reconstruction. Trust3R combines gated residual mean refinement with a Normal-Inverse-Wishart evidential head, yielding a closed-form multivariate Student-t distribution for per-point geometric uncertainty. This design provides probabilistically grounded pointmap uncertainty estimates while adding moderate inference overhead. We evaluate on diverse indoor and outdoor benchmarks and compare against MASt3R's built-in confidence map as well as common uncertainty-aware baselines spanning single-pass heteroscedastic regression and sampling-based methods such as MC dropout and deep ensembles. Experimental results show that Trust3R consistently improves risk-coverage and sparsification, and generally improves geometric accuracy. These gains are reflected in stronger uncertainty ranking across benchmarks, with 25% lower AURC and 41% lower AUSE on ScanNet++, providing a practical reliability signal for uncertainty-aware weighting in downstream geometry pipelines. The project page and code are available at https://trust3r-z.github.io/.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

A Shannon-Theoretic Approach to the Storage-Retrieval Tradeoff in PIR Systems

We consider the storage-retrieval rate tradeoff in private information retrieval (PIR) systems using a Shannon-theoretic approach. Our focus is mostly on the canonical two-message two-database case, for which a coding scheme based on random codebook generation and the binning technique is proposed. This coding scheme reveals a hidden connection between PIR and the classic multiple description source coding problem. We first show that when the retrieval rate is kept optimal, the proposed non-linear scheme can achieve better performance over any linear scheme. Moreover, a non-trivial storage-retrieval rate tradeoff can be achieved beyond space-sharing between this extreme point and the other optimal extreme point, achieved by the retrieve-everything strategy. We further show that with a method akin to the expurgation technique, one can extract a zero-error PIR code from the random code. Outer bounds are also studied and compared to establish the superiority of the non-linear codes over linear codes.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A New Approach to Compute Information Theoretic Outer Bounds and Its Application to Regenerating Codes

The study of the fundamental limits of information systems is a central theme in information theory. Both the traditional analytical approach and the recently proposed computational approach have significant limitations, where the former is mainly due to its reliance on human ingenuity, and the latter due to its exponential memory and computational complexity. In this work, we propose a new computational approach to tackle the problem with much lower memory and computational requirements, which can naturally utilize certain intuitions, but also can maintain the strong computational advantage of the existing computational approach. A reformulation of the underlying optimization problem is first proposed, which converts the large linear program to a maximin problem. This leads to an iterative solving procedure, which uses the LP dual to carry over learned evidence between iterations. The key in the reformulated problem is the selection of good information inequalities, with which a relaxed LP can be formed. A particularly powerful intuition is a potentially optimal code construction, and we provide a method that directly utilizes it in the new algorithm. As an application, we derive a tighter outer bound for the storage-repair tradeoff for the $(6,5,5)$ regenerating code problem, which involves at least 30 random variables and is impossible to compute with the previously known computational approach.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Approximate Top-$m$ Arm Identification with Heterogeneous Reward Variances

We study the effect of reward variance heterogeneity in the approximate top-$m$ arm identification setting. In this setting, the reward for the $i$-th arm follows a $σ^2_i$-sub-Gaussian distribution, and the agent needs to incorporate this knowledge to minimize the expected number of arm pulls to identify $m$ arms with the largest means within error $ε$ out of the $n$ arms, with probability at least $1-δ$. We show that the worst-case sample complexity of this problem is $$Θ\left( \sum_{i =1}^n \frac{σ_i^2}{ε^2} \ln\frac{1}δ + \sum_{i \in G^{m}} \frac{σ_i^2}{ε^2} \ln(m) + \sum_{j \in G^{l}} \frac{σ_j^2}{ε^2} \text{Ent}(σ^2_{G^{r}}) \right),$$ where $G^{m}, G^{l}, G^{r}$ are certain specific subsets of the overall arm set $\{1, 2, \ldots, n\}$, and $\text{Ent}(\cdot)$ is an entropy-like function which measures the heterogeneity of the variance proxies. The upper bound of the complexity is obtained using a divide-and-conquer style algorithm, while the matching lower bound relies on the study of a dual formulation.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Improved Weakly Private Information Retrieval Codes

We study the problem of weakly private information retrieval (W-PIR), where a user wishes to retrieve a desired message from $N$ non-colluding servers in a way that the privacy leakage regarding the desired message's identity is less than or equal to a threshold. We propose a new code construction which significantly improves upon the best known result in the literature, based on the following critical observation. In previous constructions, for the extreme case of minimum download, the retrieval pattern is to download the message directly from $N-1$ servers; however this causes leakage to all these $N-1$ servers, and a better retrieval pattern for this extreme case is to download the message directly from a single server. The proposed code construction allows a natural transition to such a pattern, and for both the maximal leakage metric and the mutual information leakage metric, significant improvements can be obtained. We provide explicit solutions, in contrast to a previous work by Lin et al., where only numerical solutions were obtained.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

On Top-$k$ Selection from $m$-wise Partial Rankings via Borda Counting

We analyze the performance of the Borda counting algorithm in a non-parametric model. The algorithm needs to utilize probabilistic rankings of the items within $m$-sized subsets to accurately determine which items are the overall top-$k$ items in a total of $n$ items. The Borda counting algorithm simply counts the cumulative scores for each item from these partial ranking observations. This generalizes a previous work of a similar nature by Shah et al. using probabilistic pairwise comparison data. The performance of the Borda counting algorithm critically depends on the associated score separation $Δ_k$ between the $k$-th item and the $(k+1)$-th item. Specifically, we show that if $Δ_k$ is greater than certain value, then the top-$k$ items selected by the algorithm is asymptotically accurate almost surely; if $Δ_k$ is below certain value, then the result will be inaccurate with a constant probability. In the special case of $m=2$, i.e., pairwise comparison, the resultant bound is tighter than that given by Shah et al., leading to a reduced gap between the error probability upper and lower bounds. These results are further extended to the approximate top-$k$ selection setting. Numerical experiments demonstrate the effectiveness and accuracy of the Borda counting algorithm, compared with the spectral MLE-based algorithm, particularly when the data does not necessarily follow an assumed parametric model.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Policy Optimization for Constrained MDPs with Provable Fast Global Convergence

We address the problem of finding the optimal policy of a constrained Markov decision process (CMDP) using a gradient descent-based algorithm. Previous results have shown that a primal-dual approach can achieve an $\mathcal{O}(1/\sqrt{T})$ global convergence rate for both the optimality gap and the constraint violation. We propose a new algorithm called policy mirror descent-primal dual (PMD-PD) algorithm that can provably achieve a faster $\mathcal{O}(\log(T)/T)$ convergence rate for both the optimality gap and the constraint violation. For the primal (policy) update, the PMD-PD algorithm utilizes a modified value function and performs natural policy gradient steps, which is equivalent to a mirror descent step with appropriate regularization. For the dual update, the PMD-PD algorithm uses modified Lagrange multipliers to ensure a faster convergence rate. We also present two extensions of this approach to the settings with zero constraint violation and sample-based estimation. Experimental results demonstrate the faster convergence rate and the better performance of the PMD-PD algorithm compared with existing policy gradient-based algorithms.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Stochastic Chaining and Strengthened Information-Theoretic Generalization Bounds

We propose a new approach to apply the chaining technique in conjunction with information-theoretic measures to bound the generalization error of machine learning algorithms. Different from the deterministic chaining approach based on hierarchical partitions of a metric space, previously proposed by Asadi et al., we propose a stochastic chaining approach, which replaces the hierarchical partitions with an abstracted Markovian model borrowed from successive refinement source coding. This approach has three benefits over deterministic chaining: 1) the metric space is not necessarily bounded, 2) facilitation of subsequent analysis to yield more explicit bound, and 3) further opportunity to optimize the bound by removing the geometric rigidity of the partitions. The proposed approach includes the traditional chaining as a special case, and can therefore also utilize any deterministic chaining construction. We illustrate these benefits using the problem of estimating Gaussian mean and that of phase retrieval. For the former, we derive a bound that provides an order-wise improvement over previous results, and for the latter we provide a stochastic chain that allows optimization over the chaining parameter.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Capacity-Achieving Private Information Retrieval Codes from MDS-Coded Databases with Minimum Message Size

We consider constructing capacity-achieving linear codes with minimum message size for private information retrieval (PIR) from $N$ non-colluding databases, where each message is coded using maximum distance separable (MDS) codes, such that it can be recovered from accessing the contents of any $T$ databases. It is shown that the minimum message size (sometimes also referred to as the sub-packetization factor) is significantly, in fact exponentially, lower than previously believed. More precisely, when $K>T/\textbf{gcd}(N,T)$ where $K$ is the total number of messages in the system and $\textbf{gcd}(\cdot,\cdot)$ means the greatest common divisor, we establish, by providing both novel code constructions and a matching converse, the minimum message size as $\textbf{lcm}(N-T,T)$, where $\textbf{lcm}(\cdot,\cdot)$ means the least common multiple. On the other hand, when $K$ is small, we show that it is in fact possible to design codes with a message size even smaller than $\textbf{lcm}(N-T,T)$.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Individually Conditional Individual Mutual Information Bound on Generalization Error

We propose a new information-theoretic bound on generalization error based on a combination of the error decomposition technique of Bu et al. and the conditional mutual information (CMI) construction of Steinke and Zakynthinou. In a previous work, Haghifam et al. proposed a different bound combining the two aforementioned techniques, which we refer to as the conditional individual mutual information (CIMI) bound. However, in a simple Gaussian setting, both the CMI and the CIMI bounds are order-wise worse than that by Bu et al.. This observation motivated us to propose the new bound, which overcomes this issue by reducing the conditioning terms in the conditional mutual information. In the process of establishing this bound, a conditional decoupling lemma is established, which also leads to a meaningful dichotomy and comparison among these information-theoretic bounds.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

New Results on the Storage-Retrieval Tradeoff in Private Information Retrieval Systems

In a private information retrieval (PIR) system, the user needs to retrieve one of the possible messages from a set of storage servers, but wishes to keep the identity of requested message private from any given server. Existing efforts in this area have made it clear that the efficiency of the retrieval will be impacted significantly by the amount of the storage space allowed at the servers. In this work, we consider the tradeoff between the storage cost and the retrieval cost. We first present three fundamental results: 1) a regime-wise 2-approximate characterization of the optimal tradeoff, 2) a cyclic permutation lemma that can produce more sophisticated codes from simpler ones, and 3) a relaxed entropic linear program (LP) lower bound that has a polynomial complexity. Equipped with the cyclic permutation lemma, we then propose two novel code constructions, and by applying the lemma, obtain new storage-retrieval points. Furthermore, we derive more explicit lower bounds by utilizing only a subset of the constraints in the relaxed entropic LP in a systematic manner. Though the new upper bound and lower bound do not lead to a more precise approximate characterization in general, they are significantly tighter than the existing art.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

On the Information Leakage in Private Information Retrieval Systems

We consider information leakage to the user in private information retrieval (PIR) systems. Information leakage can be measured in terms of individual message leakage or total leakage. Individual message leakage, or simply individual leakage, is defined as the amount of information that the user can obtain on any individual message that is not being requested, and the total leakage is defined as the amount of information that the user can obtain about all the other messages except the one being requested. In this work, we characterize the tradeoff between the minimum download cost and the individual leakage, and that for the total leakage, respectively. New codes are proposed to achieve these optimal tradeoffs, which are also shown to be optimal in terms of the message size. We further characterize the optimal tradeoff between the minimum amount of common randomness and the total leakage. Moreover, we show that under individual leakage, common randomness is in fact unnecessary when there are more than two messages.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Weakly Secure Symmetric Multilevel Diversity Coding

Multilevel diversity coding is a classical coding model where multiple mutually independent information messages are encoded, such that different reliability requirements can be afforded to different messages. It is well known that {\em superposition coding}, namely separately encoding the independent messages, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999). In the current paper, we consider weakly secure SMDC where security constraints are injected on each individual message, and provide a complete characterization of the conditions under which superposition coding is sum-rate optimal. Two joint coding strategies, which lead to rate savings compared to superposition coding, are proposed, where some coding components for one message can be used as the encryption key for another. By applying different variants of Han's inequality, we show that the lack of opportunity to apply these two coding strategies directly implies the optimality of superposition coding. It is further shown that under a set of particular security constraints, one of the proposed joint coding strategies can be used to construct a code that achieves the optimal rate region.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Caching and Delivery via Interference Elimination

We propose a new caching scheme where linear combinations of the file segments are cached at the users, for the cases where the number of files is no greater than the number of users. When a user requests a certain file in the delivery phase, the other file segments in the cached linear combinations can be viewed as interferences. The proposed scheme combines rank metric codes and maximum distance separable codes to facilitate the decoding and elimination of these interferences, and also to simultaneously deliver useful contents to the intended users. The performance of the proposed scheme can be explicitly evaluated, and we show that the tradeoff points achieved by this scheme can strictly improve known tradeoff inner bounds in the literature; for certain special cases, the new tradeoff points can be shown to be optimal.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Multilevel Diversity Coding with Regeneration

Digital contents in large scale distributed storage systems may have different reliability and access delay requirements, and for this reason, erasure codes with different strengths need to be utilized to achieve the best storage efficiency. At the same time, in such large scale distributed storage systems, nodes fail on a regular basis, and the contents stored on them need to be regenerated and stored on other healthy nodes, the efficiency of which is an important factor affecting the overall quality of service. In this work, we formulate the problem of multilevel diversity coding with regeneration to address these considerations, for which the storage vs. repair-bandwidth tradeoff is investigated. We show that the extreme point on this tradeoff corresponding to the minimum possible storage can be achieved by a simple coding scheme, where contents with different reliability requirements are encoded separately with individual regenerating codes without any mixing. On the other hand, we establish the complete storage-repair-bandwidth tradeoff for the case of four storage nodes, which reveals that codes mixing different contents can strictly improve this tradeoff over the separate coding solution.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Broadcasting Correlated Vector Gaussians

The problem of sending two correlated vector Gaussian sources over a bandwidth-matched two-user scalar Gaussian broadcast channel is studied in this work, where each receiver wishes to reconstruct its target source under a covariance distortion constraint. We derive a lower bound on the optimal tradeoff between the transmit power and the achievable reconstruction distortion pair. Our derivation is based on a new bounding technique which involves the introduction of appropriate remote sources. Furthermore, it is shown that this lower bound is achievable by a class of hybrid schemes for the special case where the weak receiver wishes to reconstruct a scalar source under the mean squared error distortion constraint.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Multilevel Diversity Coding with Regeneration: Separate Coding Achieves the MBR Point

The problem of multilevel diversity coding with regeneration is considered in this work. Two new outer bounds on the optimal tradeoffs between the normalized storage capacity and repair bandwidth are established, by which the optimality of separate coding at the minimum-bandwidth-regeneration (MBR) point follows immediately. This resolves a question left open in a previous work by Tian and Liu.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Characterizing the Rate Region of the (4,3,3) Exact-Repair Regenerating Codes

Exact-repair regenerating codes are considered for the case (n,k,d)=(4,3,3), for which a complete characterization of the rate region is provided. This characterization answers in the affirmative the open question whether there exists a non-vanishing gap between the optimal bandwidth-storage tradeoff of the functional-repair regenerating codes (i.e., the cut-set bound) and that of the exact-repair regenerating codes. To obtain an explicit information theoretic converse, a computer-aided proof (CAP) approach based on primal and dual relation is developed. This CAP approach extends Yeung's linear programming (LP) method, which was previously only used on information theoretic problems with a few random variables due to the exponential growth of the number of variables in the corresponding LP problem. The symmetry in the exact-repair regenerating code problem allows an effective reduction of the number of variables, and together with several other problem-specific reductions, the LP problem is reduced to a manageable scale. For the achievability, only one non-trivial corner point of the rate region needs to be addressed in this case, for which an explicit binary code construction is given.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Exact-Repair Regenerating Codes Via Layered Erasure Correction and Block Designs

A new class of exact-repair regenerating codes is constructed by combining two layers of erasure correction codes together with combinatorial block designs, e.g., Steiner systems, balanced incomplete block designs and t-designs. The proposed codes have the "uncoded repair" property where the nodes participating in the repair simply transfer part of the stored data directly, without performing any computation. The layered error correction structure makes the decoding process rather straightforward, and in general the complexity is low. We show that this construction is able to achieve performance better than time-sharing between the minimum storage regenerating codes and the minimum repair-bandwidth regenerating codes.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Gaussian State Amplification with Noisy State Observations

The problem of simultaneous message transmission and state amplification in a Gaussian channel with additive Gaussian state is studied when the sender has imperfect noncausal knowledge of the state sequence. Inner and outer bounds to the rate--state-distortion region are provided. The coding scheme underlying the inner bound combines analog signaling and Gelfand-Pinsker coding, where the latter deviates from the operating point of Costa's dirty paper coding.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Optimality and Approximate Optimality of Source-Channel Separation in Networks

We consider the source-channel separation architecture for lossy source coding in communication networks. It is shown that the separation approach is optimal in two general scenarios, and is approximately optimal in a third scenario. The two scenarios for which separation is optimal complement each other: the first is when the memoryless sources at source nodes are arbitrarily correlated, each of which is to be reconstructed at possibly multiple destinations within certain distortions, but the channels in this network are synchronized, orthogonal and memoryless point-to-point channels; the second is when the memoryless sources are mutually independent, each of which is to be reconstructed only at one destination within a certain distortion, but the channels are general, including multi-user channels such as multiple access, broadcast, interference and relay channels, possibly with feedback. The third scenario, for which we demonstrate approximate optimality of source-channel separation, generalizes the second scenario by allowing each source to be reconstructed at multiple destinations with different distortions. For this case, the loss from optimality by using the separation approach can be upper-bounded when a "difference" distortion measure is taken, and in the special case of quadratic distortion measure, this leads to universal constant bounds.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Rate Region of the (4,3,3) Exact-Repair Regenerating Codes

Exact-repair regenerating codes are considered for the case (n,k,d)=(4,3,3), for which a complete characterization of the rate region is provided. This characterization answers in the affirmative the open question whether there exists a non-vanishing gap between the optimal bandwidth-storage tradeoff of the functional-repair regenerating codes (i.e., the cut-set bound) and that of the exact-repair regenerating codes. The converse proof relies on the existence of symmetric optimal solutions. For the achievability, only one non-trivial corner point of the rate region needs to be addressed, for which an explicit binary code construction is given.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Vector cross product in n-dimensional vector space

The definition of vector cross product (VCP) introduced by Eckmann only exists in thethree- and the seven- dimensional vector space. In this paper, according to the orthogonal completeness, magnitude of basis vector cross product and all kinds of combinations of basis vector $\hat{e}_i$, the generalized definition of VCP in the odd n-dimensional vector space is given by introducing a cross term $X_{AB}$. In addition, the definition is validated by reducing the generalization definition to the fundamental three- and seven-dimensional vector space.

0 citations0 reviewsNo code linkedOpen access
preprint2013arXiv

Worst-Case Expected-Capacity Loss of Slow-Fading Channels

For delay-limited communication over block-fading channels, the difference between the ergodic capacity and the maximum achievable expected rate for coding over a finite number of coherent blocks represents a fundamental measure of the penalty incurred by the delay constraint. This paper introduces a notion of worst-case expected-capacity loss. Focusing on the slow-fading scenario (one-block delay), the worst-case additive and multiplicative expected-capacity losses are precisely characterized for the point-to-point fading channel. Extension to the problem of writing on fading paper is also considered, where both the ergodic capacity and the additive expected-capacity loss over one-block delay are characterized to within one bit per channel use.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Minimum Expected Distortion in Gaussian Source Coding with Fading Side Information

An encoder, subject to a rate constraint, wishes to describe a Gaussian source under squared error distortion. The decoder, besides receiving the encoder's description, also observes side information consisting of uncompressed source symbol subject to slow fading and noise. The decoder knows the fading realization but the encoder knows only its distribution. The rate-distortion function that simultaneously satisfies the distortion constraints for all fading states was derived by Heegard and Berger. A layered encoding strategy is considered in which each codeword layer targets a given fading state. When the side-information channel has two discrete fading states, the expected distortion is minimized by optimally allocating the encoding rate between the two codeword layers. For multiple fading states, the minimum expected distortion is formulated as the solution of a convex optimization problem with linearly many variables and constraints. Through a limiting process on the primal and dual solutions, it is shown that single-layer rate allocation is optimal when the fading probability density function is continuous and quasiconcave (e.g., Rayleigh, Rician, Nakagami, and log-normal). In particular, under Rayleigh fading, the optimal single codeword layer targets the least favorable state as if the side information was absent.

0 citations0 reviewsNo code linkedOpen access
preprint2011arXiv

Latent Capacity Region: A Case Study on Symmetric Broadcast With Common Messages

We consider the problem of broadcast with common messages, and focus on the case that the common message rate $R_{\mathcal{A}}$, i.e., the rate of the message intended for all the receivers in the set $\mathcal{A}$, is the same for all the set $\mathcal{A}$ of the same cardinality. Instead of attempting to characterize the capacity region of general broadcast channels, we only consider the structure of the capacity region that any broadcast channel should bear. The concept of latent capacity region is useful in capturing these underlying constraints, and we provide a complete characterization of the latent capacity region for the symmetric broadcast problem. The converse proof of this tight characterization relies on a deterministic broadcast channel model. The achievability proof generalizes the familiar rate transfer argument to include more involved erasure correction coding among messages, thus revealing an inherent connection between broadcast with common message and erasure correction codes.

0 citations0 reviewsNo code linkedOpen access
preprint2010arXiv

Approximate Characterizations for the Gaussian Source Broadcast Distortion Region

We consider the joint source-channel coding problem of sending a Gaussian source on a K-user Gaussian broadcast channel with bandwidth mismatch. A new outer bound to the achievable distortion region is derived using the technique of introducing more than one additional auxiliary random variable, which was previously used to derive sum-rate lower bound for the symmetric Gaussian multiple description problem. By combining this outer bound with the achievability result based on source-channel separation, we provide approximate characterizations of the achievable distortion region within constant multiplicative factors. Furthermore, we show that the results can be extended to general broadcast channels, and the performance of the source-channel separation based approach is also within the same constant multiplicative factors of the optimum.

0 citations0 reviewsNo code linkedOpen access
preprint2008arXiv

Approximating the Gaussian Multiple Description Rate Region Under Symmetric Distortion Constraints

We consider multiple description coding for the Gaussian source with K descriptions under the symmetric mean squared error distortion constraints, and provide an approximate characterization of the rate region. We show that the rate region can be sandwiched between two polytopes, between which the gap can be upper bounded by constants dependent on the number of descriptions, but independent of the exact distortion constraints. Underlying this result is an exact characterization of the lossless multi-level diversity source coding problem: a lossless counterpart of the MD problem. This connection provides a polytopic template for the inner and outer bounds to the rate region. In order to establish the outer bound, we generalize Ozarow's technique to introduce a strategic expansion of the original probability space by more than one random variables. For the symmetric rate case with any number of descriptions, we show that the gap between the upper bound and the lower bound for the individual description rate is no larger than 0.92 bit. The results developed in this work also suggest the "separation" approach of combining successive refinement quantization and lossless multi-level diversity coding is a competitive one, since it is only a constant away from the optimum. The results are further extended to general sources under the mean squared error distortion measure, where a similar but looser bound on the gap holds.

0 citations0 reviewsNo code linkedOpen access
preprint2007arXiv

Constant Weight Codes: A Geometric Approach Based on Dissections

We present a novel technique for encoding and decoding constant weight binary codes that uses a geometric interpretation of the codebook. Our technique is based on embedding the codebook in a Euclidean space of dimension equal to the weight of the code. The encoder and decoder mappings are then interpreted as a bijection between a certain hyper-rectangle and a polytope in this Euclidean space. An inductive dissection algorithm is developed for constructing such a bijection. We prove that the algorithm is correct and then analyze its complexity. The complexity depends on the weight of the code, rather than on the block length as in other algorithms. This approach is advantageous when the weight is smaller than the square root of the block length.

0 citations0 reviewsNo code linkedOpen access
preprint2005arXiv

Multiple Description Quantization via Gram-Schmidt Orthogonalization

The multiple description (MD) problem has received considerable attention as a model of information transmission over unreliable channels. A general framework for designing efficient multiple description quantization schemes is proposed in this paper. We provide a systematic treatment of the El Gamal-Cover (EGC) achievable MD rate-distortion region, and show that any point in the EGC region can be achieved via a successive quantization scheme along with quantization splitting. For the quadratic Gaussian case, the proposed scheme has an intrinsic connection with the Gram-Schmidt orthogonalization, which implies that the whole Gaussian MD rate-distortion region is achievable with a sequential dithered lattice-based quantization scheme as the dimension of the (optimal) lattice quantizers becomes large. Moreover, this scheme is shown to be universal for all i.i.d. smooth sources with performance no worse than that for an i.i.d. Gaussian source with the same variance and asymptotically optimal at high resolution. A class of low-complexity MD scalar quantizers in the proposed general framework also is constructed and is illustrated geometrically; the performance is analyzed in the high resolution regime, which exhibits a noticeable improvement over the existing MD scalar quantization schemes.

0 citations0 reviewsNo code linkedOpen access