On Zero-Error Source Coding with Feedback

TL;DR

This paper investigates zero-error source coding with limited feedback and side information, deriving achievable rate regions and demonstrating conditions where feedback suffices to reach optimal rates.

Contribution

It provides a new characterization of the rate region for zero-error coding with feedback and identifies classes of sources where minimal feedback achieves Slepian-Wolf rates.

Findings

Achievable rate region for arbitrary joint distributions.

Feedback can asymptotically achieve Slepian-Wolf bounds for certain sources.

Illustrative examples demonstrating the theoretical results.

Abstract

We consider the problem of zero error source coding with limited feedback when side information is present at the receiver. First, we derive an achievable rate region for arbitrary joint distributions on the source and the side information. When all source pairs of source and side information symbols are observable with non-zero probability, we show that this characterization gives the entire rate region. Next, we demonstrate a class of sources for which asymptotically zero feedback suffices to achieve zero-error coding at the rate promised by the Slepian-Wolf bound for asymptotically lossless coding. Finally, we illustrate these results with the aid of three simple examples.