Non-asymptotic fixed-rate Slepian-Wolf coding theorem

Traditionally, Slepian-Wolf (SW) coding theorem relies on source sequences with length tending to infinity. However, in practice, the source sequences are of finite length. Towards closing this gap, we obtain non-asymptotic achievability and non-asymptotic converse for the fixed-rate SW coding by applying the NEP theorem. Furthermore, combining those converse and achievability, we show that the best SW coding rate has a Taylor-type expansion with respect to δ_n(ϵ) which measures the relative magnitude of the error probability ϵ and block length n. In addition, based on the Taylor-type expansion, we develop some reliable approximations (dubbed SO and NEP) for R_n(ϵ). Numerical comparison with the converse and achievability further shows that while the normal approximation and redundancy approximation reported in the literature can be either below converse or above the achievability in some cases, the SO and NEP approximations are always reliable and can serve as the benchmark for practical SW code design.