Performance analysis of the adaptive parity check matrix based soft-decision decoding algorithm

A gradient descent, iterative soft-decision algorithm for decoding Reed-Solomon codes using adaptive parity check matrices has been proposed recently. This algorithm outperforms all known Reed-Solomon soft-decoding algorithms at moderate SNR. However, many applications operate at a high SNR with frame error rate requirements in the range of 10^-10 ∼ 10^-20. At these frame error rates, simulation based performance validation is prohibitive. In this paper, we present a model to analytically compute the soft-decoding algorithm performance. Using the insight obtained from this model, we propose a low complexity, non-iterative algorithm using adaptive parity check matrices, with a similar decoding performance as the original iterative algorithm. We also propose an extension to the non-iterative algorithm , which improves on the decoding performance of the iterative algorithm.