一种改进的Reed-Muller码递归构造方法

一般对Reed-Muller码的递归构造方法是对长码进行递归分解,直到不能再分解为止,即出现无冗余码和重复码时结束分解.提出了一种针对Reed-Muller码的递归构造改进方法,该改进方法比常规方法在递归分解的两端均提早一步结束对码字的分解,即出现双正交码和单奇偶校验码时结束分解,并对单奇偶校验码采用系统形式.对于双正交码,利用快速哈达玛变换实现快速的最大似然译码;对于单奇偶校验码,利用该码系统形式的特殊构造实现了简化的最大似然译码算法.对改进的译码算法的复杂度进行了详细的分析,并与其他已有的算法进行对比,结果表明,该算法具有更低的复杂度,尤其对于高码率的码型.此外,性能仿真结果表明,该译码算法具有更低的误码率.

Improved recursive constructing method of Reed-Muller codes

Reed-Muller code can be recursively decomposed and the decomposition is conventionally ended at repetition codes and non-redundancy codes, where repetition codes and non-redundancy codes cannot be decomposed further. In this paper, we propose a modified recursive structure of Reed-Muller code in which the recursive decompositions are ended one step earlier, i. e. decompositions are ended at dual-orthogonal codes or single parity check codes. Moreover, for single parity check code, the systematic form is used. In the decoding algorithm, we use fast Hadamard transform to simplify the maximum likelihood decoding of dual-orthogonal code. We also use simplified maximum likelihood decoder to decode the systematic single parity check code through its special structure. We analyze the decoding complexity of the proposed decoding algorithm and compare the complexity with two other existing algorithms. The analysis shows that the proposed algorithm has lower complexity, especially for the high-rate codes. In addition, the simulation results indicate that the proposed algorithm decreases the bit-error rate slightly.