Reliability in Source Coding with Side Information

TL;DR

This paper investigates error exponents in source coding with side information, providing bounds for lossless and lossy cases, and interprets the problem as a game between nature and the code designer, with detailed analysis for Gaussian and binary-erasure scenarios.

Contribution

It extends existing results on source-coding error exponents by deriving tight bounds and interpreting the problem as a strategic game, including analysis of test channel choices.

Findings

Derived tight bounds for error exponents in source coding with side information.

Interpreted the bounds as a game between nature and the code designer.

Analyzed Gaussian and binary-erasure cases in detail.

Abstract

We study error exponents for source coding with side information. Both achievable exponents and converse bounds are obtained for the following two cases: lossless source coding with coded information (SCCSI) and lossy source coding with full side information (Wyner-Ziv). These results recover and extend several existing results on source-coding error exponents and are tight in some circumstances. Our bounds have a natural interpretation as a two-player game between nature and the code designer, with nature seeking to minimize the exponent and the code designer seeking to maximize it. In the Wyner-Ziv problem our analysis exposes a tension in the choice of test channel with the optimal test channel balancing two competing error events. The Gaussian and binary-erasure cases are examined in detail.