A Tight Uniform Continuity Bound for Equivocation

TL;DR

This paper establishes a precise and tight bound on how much the conditional Shannon entropy can change when the underlying probability distributions are close, measured by total variation distance.

Contribution

It introduces a new tight uniform continuity bound for the conditional Shannon entropy based on total variation distance.

Findings

The bound is proven to be tight.

It applies to discrete finitely supported random variables.

The result improves understanding of entropy stability.

Abstract

We prove a tight uniform continuity bound for the conditional Shannon entropy of discrete finitely supported random variables in terms of total variation distance.