# Geometry of Arimoto Algorithm

## TL;DR

This paper explores the geometric structure of the Arimoto algorithm in information theory and introduces a new algorithm, the Backward em-algorithm, that monotonically increases Kullback-Leibler divergence, with broad potential applications.

## Contribution

It reveals the information geometric structure of the Arimoto algorithm and proposes the Backward em-algorithm for increasing Kullback-Leibler divergence.

## Key findings

- Revealed geometric structure of Arimoto algorithm
- Proposed the Backward em-algorithm for divergence increase
- Potential applications in statistics and information theory

## 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.