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 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{\alpha}阶Sibson互信息和Arimoto互信息（MI）的Sibson容量和Arimoto容量，分别是信道容量C的著名推广。本研究通过给出Sibson和Arimoto MI的新的变分刻画，推导出计算这些容量的新型交替优化算法。此外，我们证明，在对其初始分布施加适当条件的情况下，计算这些容量的所有迭代算法都是等价的。