A New Iterative Algorithm for Computing the Correct Decoding Probability Exponent of Discrete Memoryless Channels

• Published in: IEEE transactions on information theory 2020-03, Vol.66 (3), p.1585-1606
• Main Authors: Jitsumatsu, Yutaka, Oohama, Yasutada
• Format: Article
• Language: English
• Subjects: Algorithms; Arimoto-Blahut algorithms; channel coding under cost constraint; Channels; Codes; correct decoding probability exponent; Decoding; Encoding; Iterative algorithms; Iterative methods; Memoryless systems; Minimization; Monte Carlo methods; Optimization; Probability distribution; Queuing theory; strong converse
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2019.2950678

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.