Chang's lemma via Pinsker's inequality

TL;DR

This paper presents a concise information-theoretic proof of Chang's lemma using Pinsker's inequality, offering a new perspective on the inequality's foundation.

Contribution

It introduces a novel proof technique for Chang's lemma based on information theory, differing from previous combinatorial or algebraic approaches.

Findings

Provides a simplified proof of Chang's lemma

Utilizes Pinsker's inequality in a new context

Enhances understanding of the lemma's informational basis

Abstract

Extending the idea in [Impagliazzo, R., Moore, C. and Russell, A., An entropic proof of Chang's inequality. SIAM Journal on Discrete Mathematics, 28(1), pp.173-176.] we give a short information theoretic proof for Chang's lemma that is based on Pinsker's inequality.