Weak variable-length Slepian-Wolf coding with linked encoders for mixed sources

Coding problems for correlated information sources were first investigated by Slepian and Wolf. They considered the data compression system, called the SW system, where two sequences emitted from correlated sources are separately encoded to codewords, and sent to a single decoder which has to output the original sequence pairs with a small probability or error. In this paper, we investigate the coding problem of a modified SW system allowing two encoders to communicate with zero rate. First, we consider the fixed-length coding and clarify that the admissible rate region for general sources is equal to that of the original SW system. Next, we investigate the variable-length coding having the asymptotically vanishing probability of error. We clarify the admissible rate region for mixed sources characterized by two ergodic sources and show that this region is strictly wider than that for fixed-length codes. Further, we investigate the universal coding problem for memoryless sources in the system and show that the SW system with linked encoders has much more flexibility than the original SW system.