Abstract: An algorithmic soft-decision decoding method for Reed-Solomon codes proceeds as follows. Given the reliability matrix Π showing the probability that a code symbol of a particular value was transmitted at each position, computing a multiplicity matrix M which determines the interpolation points and their multiplicities. Given this multiplicity matrix M, soft interpolation is performed to find the non-trivial polynomial QM(X,Y) of the lowest (weighted) degree whose zeros and their multiplicities are as specified by the matrix M. Given this non-trivial polynomial QM(X,Y), all factors of QM(X,Y) of type Y−ƒ(X) are found, where ƒ(X) is a polynomial in X whose degree is less than the dimension k of the Reed-Solomon code. Given these polynomials ƒ(X), a codeword is reconstructed from each of them, and the most likely of these codewords selected as the output of the algorithm.