  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.
