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

摘要

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 de- coding error probability. This condition is derived by general- izing the ideas of binary perfect and quasi-perfect codes, which are known to be optimum on the binary symmetric channel. An application of the ufficient condition shows that the code pre- sented by Hamada and Fujiware (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.