Soft-Decision Decoding of Reed-Muller Codes as Generalized Multiple Concatenated Codes

In this paper, we present a new soft-decision decoding algorithm for Reed-Muller codes. It is based on the GMC decoding algorithm proposed by Schnabl and Bossert [1] which interprets Reed-Muller codes as generalized multiple concatenated codes. We extend the GMC algorithm to list-decoding (L-GMC). As a result, a SDML decoding algorithm for the first order Reed-Muller codes is obtained. Moreover, the performance achieved with L-GMC for Reed-Muller codes of higher order is considerably better compared to GMC. In particular, for the Reed-Muller codes of length ¢¡¤ £ , quasi SDML decoding performance is obtained at a computational complexity that is by far less than optimum decoding using the syndrome trellis [2]. Simulations will also show that for Reed-Muller codes up to a length 1024, the performance of L-GMC decoding is more than 1dB superior to conventional GMC decoding.