A general and optimal framework to achieve the entire rate region for Slepian–Wolf coding

This paper considers symmetric Slepian–Wolf (SW) coding of two memoryless binary symmetric sources. We propose a simple and general framework, termed the Symmetric SF–ISF Framework (SSIF), (i) which can be efficiently applied to any linear channel code, (ii) which incurs no rate loss when converting the channel code to the Slepian–Wolf code, and (iii) which can achieve an arbitrary point in the Slepian–Wolf rate region. The proposed SW encoder implements the binning approach through a syndrome former (SF). The proposed SW decoder performs optimal estimation by first recovering the difference pattern between the sources using a matching inverse syndrome former (ISF), and subsequently recovering individual source sequences through syndrome former partitioning. Through rigorous proof and discussion, we show that the proposed framework is capable of achieving any rate pair promised by the theory. Hamming codes, turbo product codes, turbo codes and LDPC codes are provided as examples to demonstrate the generality and efficiency of the framework.