Iterative Algebraic Soft Decision Decoding of Reed-Solomon Codes

In this paper, we propose an iterative soft decision decoding scheme for Reed Solomon codes with near maximum likelihood performance. The advantage of this decoding algorithm over previously proposed algorithms is its fast convergence in terms of the number of iterations required. This is achieved by combining two powerful soft decision decoding techniques which were previously regarded in the literature as competitive ones, namely, algebraic soft decision decoding and belief propagation based on adaptive parity check matrices. This algorithm could also be viewed as a multiplicity assignment scheme for the Guruswami-Sudan list decoding algorithm.