The Sibson and Arimoto capacity, which are based on the Sibson and Arimoto mutual information (MI) of order {\alpha}, respectively, are well-known generalizations of the channel capacity C. In this study, we derive novel alternating optimization algorithms for computing these capacities by providing new variational characterizations of the Sibson MI and Arimoto MI. Moreover, we prove that all iterative algorithms for computing these capacities are equivalent under appropriate conditions imposed on their initial distributions.

翻译：基于α阶Sibson互信息和Arimoto互信息的Sibson容量与Arimoto容量，是信道容量C的著名推广形式。本研究通过提供Sibson互信息与Arimoto互信息的新变分表征，推导了计算这两种容量的新型交替优化算法。此外，我们证明在初始分布满足适当条件的情况下，所有计算这些容量的迭代算法均具有等价性。