Analysis of the Convergence Speed of the Arimoto-Blahut Algorithm by the Second Order Recurrence Formula

2020/09/17 by Kenji Nakagawa, Yoshinori Takei, Nakagawa, Kenji +5 · 1 citation
Computer Science · Engineering · #Advanced Wireless Communication Technologies #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques

paper · pdf · doi:10.48550/arxiv.2009.08780

openalex publication_date 2020/09/17 · openalex created_date 2020/09/25 · openalex updated_date 2026/07/28

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.

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