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

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 dist...

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Bibliographic Details
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
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Summary: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.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2019.2950678