Dual Domain Expurgated Error Exponents for Source Coding with Side Information

TL;DR

This paper presents a dual-domain expurgation method for source coding with side information, simplifying the derivation of error exponents and allowing for more general settings, with results matching known optimal exponents.

Contribution

It introduces a novel dual-domain expurgation technique for source coding with side information, enabling direct derivation of error exponents for more general scenarios.

Findings

Derived two new expurgated error exponents for different coding ensembles.

Showed the better exponent matches the Csiszár-Körner exponent.

Numerical examples illustrate differences and special cases of the exponents.

Abstract

We introduce an expurgation method for source coding with side information that enables direct dual-domain derivations of expurgated error exponents. Dual-domain methods yield optimization problems over few parameters, with any sub-optimal choice resulting in an achievable exponent, as opposed to primal-domain optimization over distributions. In addition, dual-domain methods naturally allow for general alphabets and/or memory. We derive two such expurgated error exponents for different random-coding ensembles in the case where the decoder is possibly mismatched with respect to the source and side information joint distribution. We show the better of the exponents coincides with the Csisz\'ar-K\"orner exponent obtained via a graph decomposition lemma. We show some numerical examples that illustrate the differences between the two exponents and show that in the case of source coding without side information, the expurgated exponent coincides with the error exponent of the source optimal code.