线性分组码限距离译码器的性能分析

PERFORMANCE ANALYSIS OF BOUNDED DISTANCE DECODERS FOR LINEAR LINEAR BLOCK CODES

为了提高自动重传请求(ARQ)系统的通过率,在混合ARQ系统中,使用限距离译码器改善系统的性能。在限距离译码时,线性分组码纠正重量≤Lt的错误图样,同时检测重量>t的错误图样。纯纠错译码器和纯检错译码器都是限距离译码器的特例。本文首先介绍了Krautchouk多项式的几个重要性质,然后,用线性分组码及其对偶码的重量分布,分别导出了两种形式的错误译码概率的简化计算公式。由于生成函数方法的使用,成功地得到了重复码、汉明码和扩展汉明码的错误译码概率的解析公式,最后,讨论了Golay码和某些本原BCH码错误译码概率的计算方法。

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.