A Practical and Optimal Symmetric Slepian-Wolf Compression Strategy Using Syndrome Formers and Inverse Syndrome Formers

This paper considers symmetric Slepian-Wolf coding of two binary memoryless sources. A constructive coding approach, termed the symmetric SF-ISF framework (SSIF), is proposed. The idea is to first recover the difference pattern between the sources using the syndrome former (SF) and the inverse syndrome former (ISF) of the linear channel code, and to subsequently recover individual source sequences through syndrome former partitioning. The proposed framework can be efficiently applied to a general linear channel code, incurs no rate loss when converting the channel code to the Slepian-Wolf code, and can achieve an arbitrary point in the Slepian-Wolf rate region. The feasibility and optimality of the framework is rigorously proven using properties of linear codes and cosets, and further demonstrated using low-density parity-check (LDPC) codes.