Second-Order Source Coding Theorem for Slepian-Wolf Coding Problem

摘要

The second-order achievable rate region in Slepian-Wolf source coding problem is determined. The second-order achievable rate, which enables us a finer evaluation of the achievable rate, has been introduced and analyzed for general sources in the single source coding problem. Analogously, in this paper, we first define the second-order achievable rate region for the Slepian-Wolf coding problem and establish the source coding theorem in the second-order sense. The Slepian-Wolf coding problem for the correlated source is one of the typical problems in the multi-terminal information theory. Miyake and Kanaya, and Han have established the first-order source coding theorems for general correlated sources. On the other hand, there are few researches on the second-order achievable rates for the Slepian-Wolf coding problem. Our analysis concerning the second-order achievable rates for general sources is on the basis of the information-spectrum methods. Moreover, we compute the explicit second-order achievable rate region for i.i.d. correlated sources using the relevant asymptotic normality.%近年一対一の通信システムにおいて，その符号化レートの限界を詳細に評価する二次の符号化定理が注目を集めている．二対一の通信システムにおいては，補助情報を伴った情報源符号化において二次の符号化定理が導出されている．本研究ではSlepian-Wolf タイプの符号化システムにおいて，二次の達成可能符号化レート領域を導出する．得られた結果は相関を持つ一般情報源に対して有効であるが，さらに相関を持つ定常無記憶情報源に限定し，同領域を計算した．