Analysis of the Convergence Speed of the Arimoto-Blahut Algorithm by the Second-Order Recurrence Formula
Kenji Nakagawa, Yoshinori Takei, Shin-ichiro Hara, Kohei Watabe · IEEE Transactions on Information Theory · 2021
In this paper, we investigate the convergence speed of the Arimoto-Blahut algorithm. For many channel matrices, the convergence speed 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 in this paper is new. Based on this analysis, we will compare the convergence speeds of the Arimoto-Blahut algorithm numerically with the values obtained in our theorems for several channel matrices. The purpose of this paper is to obtain a complete understanding of the convergence speed of the Arimoto-Blahut algorithm.