Slepian-Wolf coding with a mismatched decoder

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 linear Slepian-Wolf codes under mismatched decoding can be strictly higher than that achievable with nonlinear Slepian-Wolf codes.