Distance Threshold Viterbi Decoding of Reed-Muller codes

In this paper we introduce a novel complexity reduction approach for the optimal decoding of Reed-Muller codes that uses Viterbi algorithm. We have adopted the guaranteed error correction capability of the Reed-Muller code, to be used as a simple rule for eliminating some states and branches from the trellis structure of the Reed-Muller block code. The proposed algorithm can be considered a quasi-optimum algorithm as the method of decoding involves a smaller number of summation and comparisons compared to the optimal Viterbi algorithm. The proposed algorithm can achieve a complexity reduction by an order of one-third over both AWGN and Rayleigh fading channels with negligible error performance loss.