Soft-decision decoding of Reed-Solomon codes on magnetic recording channels with erasures

A soft-decision Reed-Solomon decoding algorithm has been recently proposed by Koetter and Vardy, which provides significant coding gains by fully utilizing channel output reliability information. The algorithm converts this reliability information into a set of interpolation points and their multiplicities, and consists of three day steps: multiplicity matrix calculation, soft interpolation, and polynomial factorization. Large coding gains have been observed only for low-rate codes in additive white Gaussian noise channels, and with very high decoding complexity. Here we present a new suboptimal algorithm for computing the multiplicity matrix, discuss architectures for soft-decision decoders and evaluate the performance of the soft-decision algorithm on magnetic recording channels in the presence of erasures.