Closed forms of the achievable rate region for Wyner´s source coding systems

Wyner´s source coding system is one of the most fundamental fixed-length source coding systems with side information available only at the decoder. In this coding system, Wyner showed the achievable rate region which is the set of rate pairs of encoders such that the probability of error can be made arbitrarily small for sufficiently large block length. However, the closed form of this region is not clarified because the region is expressed by the union of indefinitely many sets. This paper deals with two correlated sources whose conditional distribution is represented by binary input output symmetric channels, and clarifies closed forms of the achievable rate region for Wyner´s source coding system.