On the Codebook-Level Duality Between Slepian-Woif Coding and Channel Coding

A codebook-level duality between Slepian-Wolf coding and channel coding is established. Specifically, it is shown that using linear codes over Z M (the ring of integers mod M), each Slepian-Wolf coding problem is equivalent to a channel coding problem for a semi-symmetric additive channel under optimal decoding, belief propagation decoding, and minimum entropy decoding. Various notions of symmetric channels are discussed and their connections with semi-symmetric additive channels are clarified.