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 [Formula: see text] and [Formula: see text] 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.
Highlights
Error correcting codes (ECC) introduce controlled redundancy to correct errors that might have happened in the channel during signal transmission
A binary code C is linear if the sum of any two codewords in C is a legal codeword in C, that is, it is closed under modulo-2 addition in F2n
A linear code C is a linear subspace of F2n
Summary
Error correcting codes (ECC) introduce controlled redundancy to correct errors that might have happened in the channel during signal transmission. A hybrid decoding algorithm for RM codes is presented and analyzed. According to the stages of decomposition processes, the proposed hybrid algorithm exploits Green machine and Wagner decoding, as well as the traditional Plotkin recursive algorithm.
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