Iterating the Arimoto-Blahut algorithm for faster convergence

Abstract

The Arimoto-Blahut algorithm determines the capacity of a discrete memoryless channel through an iterative process in which the input probability distribution is adapted at each iteration. While it converges towards the capacity-achieving distribution for any discrete memoryless channel, the convergence can be slow when the channel has a large input alphabet. This is unfortunate when only a small number of the input letters are assigned non-zero probabilities in the capacity-achieving distribution. If we knew which input letters will end up with a probability of zero, we could eliminate these letters and operate the algorithm on a subset of the input alphabet. The algorithm would converge towards the same solution faster. We present an algorithm which makes use of this fact to speed up the convergence of the Arimoto-Blahut algorithm in such situations.