Distributed code constructions for the entire Slepian-Wolf rate region for arbitrarily correlated sources

Slepian-Wolf coding tackles the problem of distributed encoding of correlated discrete-alphabet sources for decoding at a common receiver. In this work, we propose a distributed linear block code construction for attaining any point on the Slepian-Wolf achievable rate region for arbitrarily correlated sources using only a single code. Specifically, our prescription allows for any arbitrary memoryless joint probability distribution over any arbitrary number of distributed sources, and allows for any arbitrary rate combination that lies in the Slepian-Wolf achievable region. Special cases of our framework include the single source case (wherein our construction reduces to an entropy coder), source coding with side-information at the receiver (so-called corner points of the Slepian-Wolf region), and specific source correlation models (such as induced by a virtual Binary Symmetric Channel model). In this work, we describe how to use low density parity check (LDPC) codes in the proposed framework to solve the general Slepian-Wolf problem constructively.