Shigeaki Kuzuoka

Non-asymptotic and second-order achievability bounds for source coding with side-information

We present a novel achievability bound for the Wyner-Ahlswede-Körner (WAK) problem of lossless source coding with rate-limited side-information. This bound is proved using ideas from channel simulation and channel resolvability. The bound improves on all previous non-asymptotic bounds on the error probability of the WAK problem. We also present achievable second-order coding rates by applying the multidimensional Berry-Essèen theorem to our new non-asymptotic bound.

A simple technique for bounding the redundancy of source coding with side information

A simple technique for bounding the redundancy of Slepian-Wolf coding is given. We demonstrate that our simple technique gives the tight bound established by He et al. Our proof is so simple that it can be easily extended to the case where the source (Xⁿ, Y ⁿ) has an n-fold product distribution (i.e., (X₁, Y₁), ..., (X_n, Y_n) are independent but not necessarily identically distributed). It can be also applied to Wyner-Ahlswede-Körner coding and gives novel bounds of the redundancies of the coding rates of the encoder and the helper.

Universal Source Coding Over Generalized Complementary Delivery Networks

This paper deals with a universal coding problem for a certain kind of multiterminal source coding network called a generalized complementary delivery network. In this network, messages from multiple correlated sources are jointly encoded, and each decoder has access to some of the messages to enable it to reproduce the other messages. Both fixed-to-fixed length and fixed-to-variable length lossless coding schemes are considered. Explicit constructions of universal codes and the bounds of the error probabilities are clarified by using methods of types and graph-theoretical analysis.

Conditional Lempel-Ziv complexity and its application to source coding theorem with side information

This paper proposes the conditional LZ complexity and analyzes its property. Especially, we show an inequality corresponding to Zivs inequality concerning a distinct parsing of a pair of sequences. Further, as a byproduct of the result, we show a simple proof of the asymptotical optimality of Zivs universal source coding algorithm with side information.

Universal coding for correlated sources with complementary delivery

This report deals with a universal coding problem for a certain kind of multiterminal source coding system that we call the complementary delivery coding system. Both fixed-to- fixed length and fixed-to-variable length lossless coding schemes are considered. Explicit constructions of universal codes and the bounds of the error probabilities are clarified via type-theoretical and graph-theoretical analyses.

An Information-Spectrum Approach to Weak Variable-Length Source Coding With Side-Information

This paper studies variable-length (VL) source coding of general sources with side-information. Novel one-shot coding bounds for Slepian-Wolf (SW) coding, which give nonasymptotic tradeoff between the error probability and the codeword length of VL-SW coding, are established. One-shot results are applied to asymptotic analysis, and a general formula for the optimal coding rate achievable by weakly lossless VL-SW coding (i.e., VL-SW coding with vanishing error probability) is derived. Our general formula reveals how the encoder side-information and/or VL coding improve the optimal coding rate in the general setting. In addition, it is shown that if the encoder side-information is useless in weakly lossless VL coding then it is also useless even in the case where the error probability may be positive asymptotically.

Universal source coding for multiple decoders with side information

A multiterminal lossy source coding problem, which includes various problems such as the Wyner-Ziv problem and the complementary delivery problem as special cases, is considered. It is shown that any point in the achievable rate-distortion region can be attained even if the source statistics are not known.

A Dichotomy of Functions in Distributed Coding: An Information Spectral Approach

The problem of distributed data compression for function computation is considered, where: 1) the function to be computed is not necessarily symbolwise function and 2) the information source has memory and may not be stationary nor ergodic. We introduce the class of smooth sources and give a sufficient condition on functions so that the achievable rate region for computing coincides with the Slepian-Wolf region (i.e., the rate region for reproducing the entire source) for any smooth sources. Moreover, for symbolwise functions, the necessary and sufficient condition for the coincidence is established. Our result for the full side-information case is a generalization of the result by Ahlswede and Csiszár to sources with memory; our dichotomy theorem is different from Han and Kobayashis dichotomy theorem, which reveals an effect of memory in distributed function computation. All results are given not only for fixed-length coding but also for variable-length coding in a unified manner. Furthermore, for the full side-information case, the error probability in the moderate deviation regime is also investigated.

Universal Wyner–Ziv Coding for Distortion Constrained General Side Information

We investigate the Wyner-Ziv coding in which the statistics of the principal source is known but the statistics of the channel generating the side-information is unknown except that it is in a certain class. The class consists of channels such that the distortion between the principal source and the side-information is smaller than a threshold, but channels may be neither stationary nor ergodic. In this situation, we define a new rate-distortion function as the minimum rate such that there exists a Wyner-Ziv code that is universal for every channel in the class. Then, we show an upper bound and a lower bound on the rate-distortion function, and derive a matching condition such that the upper and lower bounds coincide.

An application of linear codes to Slepian-Wolf coding of individual sequences

This paper clarifies the adequacy of the linear channel coding approach for the Slepian-Wolf coding of individual sequences. Our result reveals that LDPC code ensembles give optimal code for the Slepian-Wolf coding of individual sequences.