Second-Order Slepian-Wolf Coding Theorems for Non-Mixed and Mixed Sources

TL;DR

This paper extends second-order rate analysis to Slepian-Wolf source coding for correlated sources, providing explicit rate regions for i.i.d. and mixed sources using information spectrum methods and asymptotic normality.

Contribution

It defines the second-order achievable rate region for Slepian-Wolf coding and derives explicit regions for specific source types, advancing multi-terminal information theory.

Findings

Explicit second-order rate region for i.i.d. sources with countably infinite alphabets.

Explicit second-order rate region for mixed correlated sources.

Application of information spectrum methods and asymptotic normality.

Abstract

The second-order achievable rate region in Slepian-Wolf source coding systems is investigated. The concept of second-order achievable rates, which enables us to make a finer evaluation of achievable rates, has already been introduced and analyzed for general sources in the single-user source coding problem. Analogously, in this paper, we first define the second-order achievable rate region for the Slepian-Wolf coding system to establish the source coding theorem in the second- order sense. The Slepian-Wolf coding problem for correlated sources is one of typical problems in the multi-terminal information theory. In particular, Miyake and Kanaya, and Han have established the first-order source coding theorems for general correlated sources. On the other hand, in general, the second-order achievable rate problem for the Slepian-Wolf coding system with general sources remains still open up to present. In this paper we present the analysis concerning the second- order achievable rates for general sources which are based on the information spectrum methods developed by Han and Verdu. Moreover, we establish the explicit second-order achievable rate region for i.i.d. correlated sources with countably infinite alphabets and mixed correlated sources, respectively, using the relevant asymptotic normality.