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.

翻译：对于$\alpha>1$，计算$\alpha$-容量的问题等价于计算正确解码指数的问题。目前已提出多种算法用于计算这些量，例如Arimoto算法和Jitsumatsu--Oohama算法。本研究基于Augustin--Csisz{\'a}r互信息的变分特征，提出了一种新颖的交替优化算法，用于计算$\alpha>1$情况下的$\alpha$-容量。通过数值算例比较了这些算法的收敛性能。