On a Proof of the Convergence Speed of a Second-order Recurrence Formula in the Arimoto-Blahut Algorithm
Information Theory
2022-09-13 v1 Numerical Analysis
math.IT
Numerical Analysis
Abstract
In [8] (Nakagawa, et.al., IEEE Trans. IT, 2021), we investigated the convergence speed of the Arimoto-Blahut algorithm. In [8], the convergence of the order was analyzed by focusing on the second-order nonlinear recurrence formula consisting of the first- and second-order terms of the Taylor expansion of the defining function of the Arimoto-Blahut algorithm. However, in [8], an infinite number of inequalities were assumed as a "conjecture," and proofs were given based on the conjecture. In this paper, we report a proof of the convergence of the order for a class of channel matrices without assuming the conjecture. The correctness of the proof will be confirmed by several numerical examples.
Keywords
Cite
@article{arxiv.2209.04961,
title = {On a Proof of the Convergence Speed of a Second-order Recurrence Formula in the Arimoto-Blahut Algorithm},
author = {Kenji Nakagawa and Yoshinori Takei and Shin-ichiro Hara},
journal= {arXiv preprint arXiv:2209.04961},
year = {2022}
}
Comments
28 pages, 6 figures