On the Codebook-Level Duality Between Slepian-Wolf 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 ${\BBZ}_{M}$ (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.