A Sufficient Condition for a Code to Achieve the Minimum Decoding Error Probability--Generalization of Perfect and Quasi-Perfect Codes

Mitsuru HAMADA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.10   pp.1870-1877
Publication Date: 2000/10/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
error-correcting code,  perfect code,  quasi-perfect code,  optimum code,  

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A sufficient condition for a code to be optimum on discrete channels with finite input and output alphabets is given, where being optimum means achieving the minimum decoding error probability. This condition is derived by generalizing the ideas of binary perfect and quasi-perfect codes, which are known to be optimum on the binary symmetric channel. An application of the sufficient condition shows that the code presented by Hamada and Fujiwara (1997) is optimum on the q-ary channel model proposed by Fuja and Heegard (1990), where q is a prime power with some restriction. The channel model is subject to two types of additive errors of (in general) different probabilities.