Dueck and Korner's reliability function for discrete memoryless channels for rates above the capacity coincides with Arimoto's exponent of correctdecodingprobability. The two exponent functions are described...
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Dueck and Korner's reliability function for discrete memoryless channels for rates above the capacity coincides with Arimoto's exponent of correctdecodingprobability. 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 Korner's exponent has been proposed. This paper proposes a new iterative algorithm for solving the minimization problem in Dueck and Korner'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-Korner exponents is easily proved.
For a discrete memoryless channel, a lower bound for the correct decoding probability exponent was derived by Arimoto. He also gave an iterative algorithm for computing the exponent. Subsequently, Dueck and Korner det...
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ISBN:
(纸本)9781467377041
For a discrete memoryless channel, a lower bound for the correct decoding probability exponent was derived by Arimoto. He also gave an iterative algorithm for computing the exponent. Subsequently, Dueck and Korner determined the optimal exponent function of the correctdecodingprobability. In this paper, a new iterative algorithm that computes Dueck and Korner's exponent is presented.
The form of Dueck and Korner's exponent function for correctdecodingprobability for discrete memoryless channels at rates above the capacity is similar to the form of Csiszar and Korner's exponent function f...
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ISBN:
(纸本)9781509018062
The form of Dueck and Korner's exponent function for correctdecodingprobability for discrete memoryless channels at rates above the capacity is similar to the form of Csiszar and Korner's exponent function for correctdecodingprobability in lossy source coding for discrete memoryless sources at rates below the rate distortion function. We recently gave a new algorithm for computing Dueck and Korner's exponent. In this paper, we give an algorithm for computing Csiszar and Korner's exponent. The proposed algorithm can also be used to compute cutoff rate and the rate distortion function.
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