Nonasymptotic noisy lossy source coding

This paper shows new general nonasymptotic achievability and converse bounds and performs their dispersion analysis for the lossy compression problem in which the compressor observes the source through a noisy channel. While this problem is asymptotically equivalent to a noiseless lossy source coding problem with a modified distortion function, nonasymptotically there is a noticeable gap in how fast their minimum achievable coding rates approach the common rate-distortion function, as evidenced both by the refined asymptotic analysis (dispersion) and the numerical results. The size of the gap between the dispersions of the noisy problem and the asymptotically equivalent noiseless problem depends on the stochastic variability of the channel through which the compressor observes the source.Comment: IEEE Transactions on Information Theory, 201

The Three-Terminal Interactive Lossy Source Coding Problem

The three-node multiterminal lossy source coding problem is investigated. We derive an inner bound to the general rate-distortion region of this problem which is a natural extension of the seminal work by Kaspi'85 on the interactive two-terminal source coding problem. It is shown that this (rather involved) inner bound contains several rate-distortion regions of some relevant source coding settings. In this way, besides the non-trivial extension of the interactive two terminal problem, our results can be seen as a generalization and hence unification of several previous works in the field. Specializing to particular cases we obtain novel rate-distortion regions for several lossy source coding problems. We finish by describing some of the open problems and challenges. However, the general three-node multiterminal lossy source coding problem seems to offer a formidable mathematical complexity.Comment: New version with changes suggested by reviewers.Revised and resubmitted to IEEE Transactions on Information Theory. 92 pages, 11 figures, 1 tabl

Critical Behavior in Lossy Source Coding

The following critical phenomenon was recently discovered. When a memoryless source is compressed using a variable-length fixed-distortion code, the fastest convergence rate of the (pointwise) compression ratio to the optimal $R(D)$ bits/symbol is either $O(\sqrt{n})$ or $O(\log n)$. We show it is always $O(\sqrt{n})$, except for discrete, uniformly distributed sources.Comment: 2 figure

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.Comment: 22 pages, added proofs, to be presented at ISIT 201

Lossy Source Coding via Spatially Coupled LDGM Ensembles

We study a new encoding scheme for lossy source compression based on spatially coupled low-density generator-matrix codes. We develop a belief-propagation guided-decimation algorithm, and show that this algorithm allows to approach the optimal distortion of spatially coupled ensembles. Moreover, using the survey propagation formalism, we also observe that the optimal distortions of the spatially coupled and individual code ensembles are the same. Since regular low-density generator-matrix codes are known to achieve the Shannon rate-distortion bound under optimal encoding as the degrees grow, our results suggest that spatial coupling can be used to reach the rate-distortion bound, under a {\it low complexity} belief-propagation guided-decimation algorithm. This problem is analogous to the MAX-XORSAT problem in computer science.Comment: Submitted to ISIT 201

Second-Order Coding Rates for Conditional Rate-Distortion

This paper characterizes the second-order coding rates for lossy source coding with side information available at both the encoder and the decoder. We first provide non-asymptotic bounds for this problem and then specialize the non-asymptotic bounds for three different scenarios: discrete memoryless sources, Gaussian sources, and Markov sources. We obtain the second-order coding rates for these settings. It is interesting to observe that the second-order coding rate for Gaussian source coding with Gaussian side information available at both the encoder and the decoder is the same as that for Gaussian source coding without side information. Furthermore, regardless of the variance of the side information, the dispersion is $1/2$ nats squared per source symbol.Comment: 20 pages, 2 figures, second-order coding rates, finite blocklength, network information theor