Improved Finite Blocklength Converses for Slepian–Wolf Coding via Linear Programming

A new finite blocklength converse for the Slepian–Wolf coding problem, which significantly improves on the best-known converse due to Miyake and Kanaya, is presented. To obtain this converse, an extension of the linear programming (LP)-based framework for finite blocklength point-to-point coding problems is employed. However, a direct application of this framework demands a complicated analysis for the Slepian–Wolf problem. An analytically simpler approach is presented, wherein LP-based finite blocklength converses for this problem are synthesized from point-to-point lossless source coding problems with perfect side-information at the decoder. New finite blocklength converses for these point-to-point problems are derived by employing the LP-based framework, and the new converse for Slepian–Wolf coding is obtained by an appropriate combination of these converses.