In this letter, we propose (1) a new sub-optimum minimum distance search (sub-MDS), whose search complexity is reduced considerably compared with optimum MDSs and (2) a termination criterion, called near optimality condition, to reduce the average number of decoding iterations with little degradation of error performance for the proposed decoding using sub-MDS iteratively. Consequently, the decoding algorithm can be applied to longer codes with feasible complexity. Simulation results for several Reed-Muller (RM) codes of lengths 256 and 512 are given.

In this paper, we present a new soft-decision iterative decoding algorithm using an efficient minimum distance search (MDS) algorithm. The proposed MDS algorithm is a top-down and recursive MDS algorithm, which finds a most likely codeword among the codewords at the minimum distance of the code from a given codeword. A search is made in each divided section by a "call by need" from the upper section. As a consequence, the search space and computational complexity are reduced significantly. The simulation results show that the proposed decoding algorithm achieves near error performance to the maximum likelihood decoding for any RM code of length 128 and suboptimal for the (256, 37), (256, 93) and (256, 163) RM codes.