  In this paper, a new algebraic soft-decision decoding algorithm for
Reed-Solomon code is presented. It is based on rational interpolation and the
interpolation points are constructed by Berlekamp-Messay algorithm. Unlike the
traditional K{\"o}tter-Vardy algorithm, new algorithm needs interpolation for
two smaller multiplicity matrixes, due to the corresponding factorization
algorithm for re-constructing codewords.
