A New Algorithm for Computing $\alpha$-Capacity

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{á}r mutual information. A comparison of the convergence performance of these algorithms is demonstrated through numerical examples.