One-shot source coding with coded side information available at the decoder

TL;DR

This paper introduces a one-shot achievable rate region for source coding with coded side information at the decoder, using smooth max Renyi entropy and divergence, and connects it to asymptotic limits.

Contribution

It proposes a novel one-shot rate region characterization for source coding with helper, based on smooth Renyi measures, bridging to asymptotic information theory.

Findings

Achievable rate region expressed via smooth max Renyi entropy and divergence.

Asymptotic limit matches known spectral-sup entropy and mutual information rates.

Framework unifies one-shot and asymptotic source coding with helper scenarios.

Abstract

One-shot achievable rate region for source coding when coded side information is available at the decoder (source coding with a helper) is proposed. The achievable region proposed is in terms of conditional smooth max Renyi entropy and smooth max Renyi divergence. Asymptotically (in the limit of large block lengths) this region is quantified in terms of spectral-sup conditional entropy rate and spectral- sup mutual information rate. In particular, it coincides with the rate region derived in the limit of unlimited independent and identically distributed copies of the sources.