Analysis of the Convergence Speed of the Arimoto-Blahut Algorithm by the Second Order Recurrence Formula
Abstract
In this paper, we investigate the convergence speed of the Arimoto-Blahut algorithm. For many channel matrices the convergence is exponential, but for some channel matrices it is slower than exponential. By analyzing the Taylor expansion of the defining function of the Arimoto-Blahut algorithm, we will make the conditions clear for the exponential or slower convergence. The analysis of the slow convergence is new in this paper. Based on the analysis, we will compare the convergence speed of the Arimoto-Blahut algorithm numerically with the values obtained in our theorems for several channel matrices. The purpose of this paper is a complete understanding of the convergence speed of the Arimoto-Blahut algorithm.
Keywords
Cite
@article{arxiv.2009.08780,
title = {Analysis of the Convergence Speed of the Arimoto-Blahut Algorithm by the Second Order Recurrence Formula},
author = {Kenji Nakagawa and Yoshinori Takei and Shin-ichiro Hara and Kohei Watabe},
journal= {arXiv preprint arXiv:2009.08780},
year = {2020}
}
Comments
45 pages, 9 figures, submitted to IEEE Transactions on Information Theory. arXiv admin note: substantial text overlap with arXiv:1809.00752