An algebraic construction of codes for Slepian-Wolf source networks

This article proposes an explicit construction of fixed-length codes for Slepian-Wolf (1973) source networks. The proposed code is linear, and has two-step encoding and decoding procedures similar to the concatenated code used for channel coding. Encoding and decoding of the code can be done in a polynomial order of the block length. The proposed code can achieve arbitrary small probability of error for ergodic sources with finite alphabets, if the pair of encoding rates is in the achievable region. Further, if the sources are memoryless, the proposed code can be modified to become universal and the probability of error vanishes exponentially as the block length tends to infinity