New Algorithms for Computing Sibson Capacity and Arimoto Capacity

The Arimoto capacity and Sibson capacity, which are based on the Arimoto and Sibson 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 max characterizations of the Arimoto MI and Sibson MI. Moreover, we prove that all iterative algorithms for computing these capacities are equivalent under appropriate conditions imposed on their initial distributions