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

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 multiterminal 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 Verdú. Moreover, we establish the explicit second-order achievable rate region for independently and identically distributed (i.i.d.) correlated sources with countably infinite alphabets and mixtures of i.i.d. correlated sources, respectively, using the relevant asymptotic normality.