A New Algorithm for Computing $\hat{I}\pm$-Capacity

Abstract

The problem of computing $\hat{I}\pm$-capacity for $\hat{I}\pm >1$ 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 $\hat{I}\pm$-capacity for $\hat{I}\pm >1$ based on a variational characterization of the Augustin--Csisz{á}r mutual information. A comparison of the convergence performance of these algorithms is demonstrated through numerical examples.