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The second-order achievable rate region in Slepian-Wolf source coding systemsis investigated. The concept of second-order achievable rates, which enables usto make a finer evaluation of achievable rates, has already been introduced andanalyzed for general sources in the single-user source coding problem.Analogously, in this paper, we first define the second-order achievable rateregion for the Slepian-Wolf coding system to establish the source codingtheorem in the second- order sense. The Slepian-Wolf coding problem forcorrelated sources is one of typical problems in the multi-terminal informationtheory. In particular, Miyake and Kanaya, and Han have established thefirst-order source coding theorems for general correlated sources. On the otherhand, in general, the second-order achievable rate problem for the Slepian-Wolfcoding system with general sources remains still open up to present. In thispaper we present the analysis concerning the second- order achievable rates forgeneral sources which are based on the information spectrum methods developedby Han and Verdu. Moreover, we establish the explicit second-order achievablerate region for i.i.d. correlated sources with countably infinite alphabets andmixed correlated sources, respectively, using the relevant asymptoticnormality.

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