Revisiting the Slepian-Wolf coding problem for general sources: A direct approach

This paper clarifies the ε-achievable rate region of the Slepian-Wolf (SW) coding problem for general sources. We propose new upper and lower bounds on the error probability of the SW coding system for finite block lengths. The proposed bounds are mathematically simple and characterized by an optimization problem on the subset of pairs of output sequences which is closely related to the smooth max-entropy, and are tighter than those obtained by Han. By using these bounds, we clarify the ε-achievable rate region. Further, we also show outer and inner bounds on the ε-achievable rate region in terms of the smooth max-entropy. These two bounds coincide when the error probability vanishes.