TY - JOUR

T1 - A New iterative algorithm for computing the correct decoding probability exponent of discrete memoryless channels

AU - Jitsumatsu, Yutaka

AU - Oohama, Yasutada

N1 - Funding Information:
Manuscript received May 17, 2018; revised July 26, 2019; accepted September 29, 2019. Date of publication October 31, 2019; date of current version February 14, 2020. This work was supported in part by Japan Society for the Promotion of Science (JSPS) Grants-in-Aid for Scientific Research (KAKENHI) under Grant JP 23360172, Grant JP 25820162, Grant JP 16K000333, Grant JP 18H01438, and Grant JP 19K12156. This article was presented in part at ISIT2015.

PY - 2020/3

Y1 - 2020/3

N2 - 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.

AB - 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.

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U2 - 10.1109/TIT.2019.2950678

DO - 10.1109/TIT.2019.2950678

M3 - Article

AN - SCOPUS:85081064725

VL - 66

SP - 1585

EP - 1606

JO - IRE Professional Group on Information Theory

JF - IRE Professional Group on Information Theory

SN - 0018-9448

IS - 3

M1 - 8889422

ER -