Optimal list decoding from noisy entropy inequality

TL;DR

This paper applies a noisy entropy inequality to binary codes, demonstrating that capacity-achieving codes on the binary erasure channel have optimal list decoding sizes on certain binary symmetric channels, especially when the list size is exponentially large.

Contribution

It introduces a novel application of a noisy entropy inequality to analyze list decoding capabilities of capacity-achieving binary codes.

Findings

Capacity-achieving codes have optimal list sizes on some binary symmetric channels.

List decoding size can be exponentially large in certain regimes.

The approach links entropy inequalities to decoding performance.

Abstract

A noisy entropy inequality for boolean functions by Samorodnitsky is applied to binary codes. It is shown that a binary code that achieves capacity on the binary erasure channel admits optimal list size for list decoding on some binary symmetric channels (in a regime where this optimal list size is exponentially large).