A hybrid decoding of Reed-Muller codes

Abstract

In this article, a hybrid decoding algorithm for Reed-Muller codes is presented. Unlike the conventional algorithm, the presented algorithm ends recursive decomposition when R(1, m) and R(m - 1, m) appeared. A simplified maximum-likelihood algorithm based on fast Hadamard transform is also exploited to decode the systematic code through its special structure. As a result, the presented hybrid decoding algorithm reduces the number of floating-point multiplications significantly as compared with the conventional algorithms. In addition, the new algorithm has better error performance than the conventional ones.