On the Duality Between Slepian–Wolf Coding and Channel Coding Under Mismatched Decoding

In this paper, Slepian–Wolf coding with a mismatched decoding metric is studied. Two different dualities between Slepian–Wolf coding and channel coding under mismatched decoding are established. These two dualities provide a systematic framework for comparing linear Slepian–Wolf codes, nonlinear Slepian–Wolf codes, and variable-rate Slepian–Wolf codes. In contrast with the fact that linear codes suffice to achieve the Slepian–Wolf limit under matched decoding, the minimum rate achievable with nonlinear Slepian–Wolf codes under mismatched decoding can be strictly lower than that achievable with linear Slepian–Wolf codes.