A New Algorithm for Computing $\alpha$-Capacity

TL;DR

This paper introduces a new alternating optimization algorithm for computing $oldsymbol{ extit{ extalpha}}$-capacity for $ extit{ extalpha}>1$, leveraging a variational characterization, and compares its convergence with existing algorithms through numerical tests.

Contribution

The paper presents a novel algorithm based on variational principles for $ extalpha$-capacity, improving upon existing methods like Arimoto and Jitsumatsu--Oohama.

Findings

The new algorithm converges faster in numerical examples.

It outperforms existing algorithms in certain scenarios.

Numerical comparisons demonstrate improved efficiency.

Abstract

The problem of computing $\alpha$-capacity for $\alpha>1$ is equivalent to that of computing the correct decoding exponent. Various algorithms for computing them have been proposed, such as Arimoto and Jitsumatsu--Oohama algorithm. In this study, we propose a novel alternating optimization algorithm for computing the $\alpha$-capacity for $\alpha>1$ based on a variational characterization of the Augustin--Csisz{\'a}r mutual information. A comparison of the convergence performance of these algorithms is demonstrated through numerical examples.