Achievable rate regions for asynchronous Slepian-Wolf coding systems

The Slepian-Wolf (SW) coding system is a source coding system with two encoders and a decoder, where these encoders independently encode input sequences emitted from two correlated sources into fixed-length codewords, and the decoder reconstructs all input sequences from the codewords. In this paper, we consider the situation in which the SW coding system is asynchronous, i.e., each encoder runs with each delay from the base time. We assume that these delays are unknown to encoders and a decoder, but the maximum of delays is known to encoders and the decoder. For this asynchronous SW coding system, we clarify the achievable rate region, where the achievable rate region is the set of rate pairs of encoders such that the decoding error probability vanishes as the block length tends to infinity. Furthermore, we show an exponential bound of the error probability for this coding system by using Gallager´s random coding techniques.