arXiv subjects

Aaron B. Wagner

Publications and source records attributed to Aaron B. Wagner.

At least 55 records · Page 3Linked to original sources

arXiv2016

LP Bounds for Rate-Distortion with Variable Side Information

We consider a rate-distortion problem with side information at multiple decoders. Several upper and lower bounds have been proposed for this general problem or special cases of it. We provide an upper bound for general instances of this problem, which takes the form of a linear program, by utilizing random binning and simultaneous decoding techniques and compare it with the existing bounds. We also provide a lower bound for the general problem, which was inspired by a linear-programming lower bound for index coding, and show that it subsumes most of the lower bounds in literature. Using these upper and lower bounds, we explicitly characterize the rate-distortion function of a problem that can be seen as a Gaussian analogue of the "odd-cycle" index coding problem.

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arXiv2015

A Rate-Distortion Approach to Index Coding

We approach index coding as a special case of rate-distortion with multiple receivers, each with some side information about the source. Specifically, using techniques developed for the rate-distortion problem, we provide two upper bounds and one lower bound on the optimal index coding rate. The upper bounds involve specific choices of the auxiliary random variables in the best existing scheme for the rate-distortion problem. The lower bound is based on a new lower bound for the general rate-distortion problem. The bounds are shown to coincide for a number of (groupcast) index coding instances, including all instances for which the number of decoders does not exceed three.

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arXiv2013

Refinement of the random coding bound

An improved pre-factor for the random coding bound is proved. Specifically, for channels with critical rate not equal to capacity, if a regularity condition is satisfied (resp. not satisfied), then for any $ε>0$ a pre-factor of $O(N^{-\frac{1}{2}\left( 1 - ε+ \barρ^\ast_R \right)})$ (resp. $O(N^{-\frac{1}{2}})$) is achievable for rates above the critical rate, where $N$ and $R$ is the blocklength and rate, respectively. The extra term $\barρ^\ast_R$ is related to the slope of the random coding exponent. Further, the relation of these bounds with the authors' recent refinement of the sphere-packing bound, as well as the pre-factor for the random coding bound below the critical rate, is discussed.

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arXiv2013

The third-order term in the normal approximation for singular channels

For a singular and symmetric discrete memoryless channel with positive dispersion, the third-order term in the normal approximation is shown to be upper bounded by a constant. This finding completes the characterization of the third-order term for symmetric discrete memoryless channels. The proof method is extended to asymmetric and singular channels with constant composition codes, and its connection to existing results, as well as its limitation in the error exponents regime, are discussed.

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arXiv2013

Information embedding and the triple role of control

We consider the problem of information embedding where the encoder modifies a white Gaussian host signal in a power-constrained manner to encode a message, and the decoder recovers both the embedded message and the modified host signal. This partially extends the recent work of Sumszyk and Steinberg to the continuous-alphabet Gaussian setting. Through a control-theoretic lens, we observe that the problem is a minimalist example of what is called the "triple role" of control actions. We show that a dirty-paper-coding strategy achieves the optimal rate for perfect recovery of the modified host and the message for any message rate. For imperfect recovery of the modified host, by deriving bounds on the minimum mean-square error (MMSE) in recovering the modified host signal, we show that DPC-based strategies are guaranteed to attain within a uniform constant factor of 16 of the optimal weighted sum of power required in host signal modification and the MMSE in the modified host signal reconstruction for all weights and all message rates. When specialized to the zero-rate case, our results provide the tightest known lower bounds on the asymptotic costs for the vector version of a famous open problem in decentralized control: the Witsenhausen counterexample. Numerically, this tighter bound helps us characterize the asymptotically optimal costs for the vector Witsenhausen problem to within a factor of 1.3 for all problem parameters, improving on the earlier best known bound of 2.

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arXiv2012

Refinement of the Sphere-Packing Bound: Asymmetric Channels

We provide a refinement of the sphere-packing bound for constant composition codes over asymmetric discrete memoryless channels that improves the pre-factor in front of the exponential term. The order of our pre-factor is $Ω(N^{-1/2(1+ε+ ρ_{R}^{\ast})})$ for any $ε>0$, where $ρ_{R}^{\ast}$ is the maximum absolute-value subdifferential of the sphere-packing exponent at rate $R$ and $N$ is the blocklength.

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arXiv2012

Moderate Deviations in Channel Coding

We consider block codes whose rate converges to the channel capacity with increasing block length at a certain speed and examine the best possible decay of the probability of error. We prove that a moderate deviation principle holds for all convergence rates between the large deviation and the central limit theorem regimes.

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arXiv2011

Rate Region of the Vector Gaussian One-Helper Source-Coding Problem

We determine the rate region of the vector Gaussian one-helper source-coding problem under a covariance matrix distortion constraint. The rate region is achieved by a simple scheme that separates the lossy vector quantization from the lossless spatial compression. The converse is established by extending and combining three analysis techniques that have been employed in the past to obtain partial results for the problem.

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arXiv2011

Reliability in Source Coding with Side Information

We study error exponents for source coding with side information. Both achievable exponents and converse bounds are obtained for the following two cases: lossless source coding with coded information (SCCSI) and lossy source coding with full side information (Wyner-Ziv). These results recover and extend several existing results on source-coding error exponents and are tight in some circumstances. Our bounds have a natural interpretation as a two-player game between nature and the code designer, with nature seeking to minimize the exponent and the code designer seeking to maximize it. In the Wyner-Ziv problem our analysis exposes a tension in the choice of test channel with the optimal test channel balancing two competing error events. The Gaussian and binary-erasure cases are examined in detail.

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arXiv2011

Optimality of Binning for Distributed Hypothesis Testing

We study a hypothesis testing problem in which data is compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and exponents of the type 2 error probability when the type 1 error probability is at most a fixed value. For related problems in distributed source coding, schemes based on random binning perform well and often optimal. For distributed hypothesis testing, however, the use of binning is hindered by the fact that the overall error probability may be dominated by errors in binning process. We show that despite this complication, binning is optimal for a class of problems in which the goal is to "test against conditional independence." We then use this optimality result to give an outer bound for a more general class of instances of the problem.

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arXiv2010

The Degraded Poisson Wiretap Channel

Providing security guarantees for wireless communication is critically important for today's applications. While previous work in this area has concentrated on radio frequency (RF) channels, providing security guarantees for RF channels is inherently difficult because they are prone to rapid variations due small scale fading. Wireless optical communication, on the other hand, is inherently more secure than RF communication due to the intrinsic aspects of the signal propagation in the optical and near-optical frequency range. In this paper, secure communication over wireless optical links is examined by studying the secrecy capacity of a direct detection system. For the degraded Poisson wiretap channel, a closed-form expression of the secrecy capacity is given. A complete characterization of the general rate-equivocation region is also presented. For achievability, an optimal code is explicitly constructed by using the structured code designed by Wyner for the Poisson channel. The converse is proved in two different ways: the first method relies only on simple properties of the conditional expectation and basic information theoretical inequalities, whereas the second method hinges on the recent link established between minimum mean square estimation and mutual information in Poisson channels.

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arXiv2010

Information embedding meets distributed control

We consider the problem of information embedding where the encoder modifies a white Gaussian host signal in a power-constrained manner to encode the message, and the decoder recovers both the embedded message and the modified host signal. This extends the recent work of Sumszyk and Steinberg to the continuous-alphabet Gaussian setting. We show that a dirty-paper-coding based strategy achieves the optimal rate for perfect recovery of the modified host and the message. We also provide bounds for the extension wherein the modified host signal is recovered only to within a specified distortion. When specialized to the zero-rate case, our results provide the tightest known lower bounds on the asymptotic costs for the vector version of a famous open problem in distributed control -- the Witsenhausen counterexample. Using this bound, we characterize the asymptotically optimal costs for the vector Witsenhausen problem numerically to within a factor of 1.3 for all problem parameters, improving on the earlier best known bound of 2.

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arXiv2010

Erasure Multiple Descriptions

We consider a binary erasure version of the n-channel multiple descriptions problem with symmetric descriptions, i.e., the rates of the n descriptions are the same and the distortion constraint depends only on the number of messages received. We consider the case where there is no excess rate for every k out of n descriptions. Our goal is to characterize the achievable distortions D_1, D_2,...,D_n. We measure the fidelity of reconstruction using two distortion criteria: an average-case distortion criterion, under which distortion is measured by taking the average of the per-letter distortion over all source sequences, and a worst-case distortion criterion, under which distortion is measured by taking the maximum of the per-letter distortion over all source sequences. We present achievability schemes, based on random binning for average-case distortion and systematic MDS (maximum distance separable) codes for worst-case distortion, and prove optimality results for the corresponding achievable distortion regions. We then use the binary erasure multiple descriptions setup to propose a layered coding framework for multiple descriptions, which we then apply to vector Gaussian multiple descriptions and prove its optimality for symmetric scalar Gaussian multiple descriptions with two levels of receivers and no excess rate for the central receiver. We also prove a new outer bound for the general multi-terminal source coding problem and use it to prove an optimality result for the robust binary erasure CEO problem. For the latter, we provide a tight lower bound on the distortion for \ell messages for any coding scheme that achieves the minimum achievable distortion for k messages where k is less than or equal to \ell.

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arXiv2010

Rate Region of the Gaussian Scalar-Help-Vector Source-Coding Problem

We determine the rate region of the Gaussian scalar-help-vector source-coding problem under a covariance matrix distortion constraint. The rate region is achieved by a Gaussian achievable scheme. We introduce a novel outer bounding technique to establish the converse of the main result. Our approach is based on lower bounding the problem with a potentially reduced dimensional problem by projecting the main source and imposing the distortion constraint in certain directions determined by the optimal Gaussian scheme. We also prove several properties that the optimal solution to the point-to-point rate-distortion problem for a vector Gaussian source under a covariance matrix distortion constraint satisfies. These properties play an important role in our converse proof. We further establish an outer bound to the rate region of the more general problem in which there are distortion constraints on both the sources. The outer bound is partially tight in general. We also study its tightness in some nontrivial cases.

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arXiv2010

Improved Source Coding Exponents via Witsenhausen's Rate

We provide a novel upper-bound on Witsenhausen's rate, the rate required in the zero-error analogue of the Slepian-Wolf problem; our bound is given in terms of a new information-theoretic functional defined on a certain graph. We then use the functional to give a single letter lower-bound on the error exponent for the Slepian-Wolf problem under the vanishing error probability criterion, where the decoder has full (i.e. unencoded) side information. Our exponent stems from our new encoding scheme which makes use of source distribution only through the positions of the zeros in the `channel' matrix connecting the source with the side information, and in this sense is `semi-universal'. We demonstrate that our error exponent can beat the `expurgated' source-coding exponent of Csiszár and Körner, achievability of which requires the use of a non-universal maximum-likelihood decoder. An extension of our scheme to the lossy case (i.e. Wyner-Ziv) is given. For the case when the side information is a deterministic function of the source, the exponent of our improved scheme agrees with the sphere-packing bound exactly (thus determining the reliability function). An application of our functional to zero-error channel capacity is also given.

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arXiv2010

On the Vacationing CEO Problem: Achievable Rates and Outer Bounds

This paper studies a class of source coding problems that combines elements of the CEO problem with the multiple description problem. In this setting, noisy versions of one remote source are observed by two nodes with encoders (which is similar to the CEO problem). However, it differs from the CEO problem in that each node must generate multiple descriptions of the source. This problem is of interest in multiple scenarios in efficient communication over networks. In this paper, an achievable region and an outer bound are presented for this problem, which is shown to be sum rate optimal for a class of distortion constraints.

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arXiv2009

Source and Channel Simulation Using Arbitrary Randomness

Necessary and sufficient conditions for approximation of a general channel by a general source are proved. For the special case in which the channel input is deterministic, which corresponds to source simulation, we prove a stronger necessary condition. As the approximation criteria, vanishing variational distance between the original and the approximated quantity is used for both of the problems. Both necessary and sufficient conditions for the two problems are based on some individual properties of the sources and the channel and are relatively easy to evaluate. In particular, unlike prior results for this problem, our results do not require solving an optimization problem to test simulatability. The results are illustrated with several non-ergodic examples.

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arXiv2008

The Gaussian Many-Help-One Distributed Source Coding Problem

Jointly Gaussian memoryless sources are observed at N distinct terminals. The goal is to efficiently encode the observations in a distributed fashion so as to enable reconstruction of any one of the observations, say the first one, at the decoder subject to a quadratic fidelity criterion. Our main result is a precise characterization of the rate-distortion region when the covariance matrix of the sources satisfies a "tree-structure" condition. In this situation, a natural analog-digital separation scheme optimally trades off the distributed quantization rate tuples and the distortion in the reconstruction: each encoder consists of a point-to-point Gaussian vector quantizer followed by a Slepian-Wolf binning encoder. We also provide a partial converse that suggests that the tree structure condition is fundamental.

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