Dueck and Körner’s reliability function for discrete memoryless channels for rates above the capacity coincides with Arimoto’s exponent of correct decoding probability. The two exponent functions are described by seemingly different optimization problems over the space of probability distributions. Arimoto gave an iterative algorithm for solving the optimization problem that appears in his exponent function. However, no algorithm to solve the optimization problem that appears in Dueck and Körner’s exponent has been proposed. This paper proposes a new iterative algorithm for solving the minimization problem in Dueck and Körner’s exponent. In the proposed algorithm, a double minimization form with respect to two joint distributions on input and output symbols is introduced. This double minimization is connected to another double minimization that appears in Arimoto’s algorithm. Such a connection leads to a quadruple minimization problem, by which the match of Arimoto and Dueck-Körner exponents is easily proved.

中文翻译：

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一种计算离散无记忆信道正确解码概率指数的新迭代算法

Dueck 和 Körner 的离散无记忆信道的可靠性函数与容量以上的速率与 Arimoto 的正确解码概率指数相吻合。这两个指数函数由概率分布空间上看似不同的优化问题描述。Arimoto 给出了一个迭代算法来解决出现在他的指数函数中的优化问题。但是，没有提出解决 Dueck 和 Körner 指数中出现的优化问题的算法。本文提出了一种新的迭代算法来解决 Dueck 和 Körner 指数中的最小化问题。在所提出的算法中，引入了关于输入和输出符号的两个联合分布的双重最小化形式。这种双重最小化与 Arimoto 算法中出现的另一个双重最小化有关。这种联系导致了四重极小化问题，很容易证明 Arimoto 和 Dueck-Körner 指数的匹配。