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

TL;DR

This paper introduces a significantly improved finite blocklength converse for Slepian-Wolf coding by extending linear programming methods and synthesizing new bounds from point-to-point source coding problems.

Contribution

It develops a simplified LP-based approach to derive tighter finite blocklength converses for Slepian-Wolf coding, improving upon previous bounds.

Findings

New finite blocklength converse surpasses previous bounds

LP-based framework effectively synthesizes bounds from point-to-point problems

Analytical simplification enables easier derivation of Slepian-Wolf converses

Abstract

A new finite blocklength converse for the Slepian- Wolf coding problem is presented which significantly improves on the best known converse for this problem, due to Miyake and Kanaya [2]. To obtain this converse, an extension of the linear programming (LP) based framework for finite blocklength point- to-point coding problems from [3] 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 metaconverses 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.