Geometry of Arimoto Algorithm

Abstract: In information theory, the channel capacity, which indicates how efficient a given channel is, plays an important role. The best-used algorithm for evaluating the channel capacity is Arimoto algorithm. This paper aims to reveal an information geometric structure of Arimoto algorithm. In the process of trying to reveal an information geometric structure of Arimoto algorithm, a new algorithm that monotonically increases the Kullback-Leibler divergence is proposed, which is called "the Backward em-algorithm." Since the Backward em-algorithm is available in many cases where we need to increase the Kullback-Leibler divergence, it has a lot of potential to be applied to many problems of statistics and information theory.