论文标题
在Arimoto-Blahut算法中二阶复发公式的收敛速度证明
On a Proof of the Convergence Speed of a Second-order Recurrence Formula in the Arimoto-Blahut Algorithm
论文作者
论文摘要
在[8]（Nakagawa等，IEEE Trans。，2021）中，我们研究了Arimoto-Blahut算法的收敛速度。在[8]中，通过重点关注二阶非线性复发公式，该公式由Arimoto-Blahut算法的定义功能的一阶和二阶术语组成，分析了$ O（1/N）$的收敛性。然而，在[8]中，假定无限数量的不平等现象为“猜想”，并根据猜想给出了证据。在本文中，我们报告了一类通道矩阵的订单$ o（1/n）$的收敛证明，而无需假设猜想。证明的正确性将通过几个数值示例确认。
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 $O(1/N)$ 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 $O(1/N)$ for a class of channel matrices without assuming the conjecture. The correctness of the proof will be confirmed by several numerical examples.
