Minimax R\'enyi Redundancy

TL;DR

This paper characterizes the redundancy in universal lossless compression using minimax Re9nyi divergence, linking it to maximal b5-mutual information and analyzing its asymptotic behavior.

Contribution

It introduces a novel characterization of redundancy via minimax Re9nyi divergence and establishes a generalized redundancy-capacity theorem.

Findings

Redundancy equals maximal b5-mutual information.

Asymptotic analysis of minimax Re9nyi divergence is provided.

Results hold up to a vanishing term in blocklength.

Abstract

The redundancy for universal lossless compression of discrete memoryless sources in Campbell's setting is characterized as a minimax R\'enyi divergence, which is shown to be equal to the maximal $\alpha$-mutual information via a generalized redundancy-capacity theorem. Special attention is placed on the analysis of the asymptotics of minimax R\'enyi divergence, which is determined up to a term vanishing in blocklength.