A hybrid decoding of Reed–Muller codes

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.