Abstract:

Bounded distance decoders are used to improve the throughout rate in hybrid automatic repeat request systems, which are able to correct t errors or less than t and detect more than t errors. Only error correcting decoders and only error detecting decoders are the two particular examples of the bounded distance decoders. Thus it is important to analyze the performance of the bounded distance decoders. In this paper, several properties on the Krautchouk polynomials are first introduced, and then two simple formulas for the probability of error decoding are derived from the weight distributions of linear block codes and their dual codes, respectively. Due to the applications of generator functions, we successfully obtain the analytic formulas of the probability of error decoding for the repeated codes, the Hamming codes and their dual codes. The computation method of probability of error decoding for the Golay code and some primitive BCH codes is discussed at last.

Key words: digital communication, information theory, error correcting code, bounded distance decoder, probability of error decoding