Soft decision decoding of Reed-Solomon codes using the extended erasure magnitude matrix

Systems using nonbinary block codes, such as Reed-Solomon codes are usually implemented using hard-decision decoding algorithms that take advantage of the algebraic structure of the codes. This paper presents an efficient soft-decision decoding algorithm that uses the algebraic structure of the codes to provide better performance results than standard hard decision methods, but with less complexity than existing soft-decision algorithms. A set of candidate codewords are compared to the received word, and the codeword closest to the received word is chosen as the near maximum likelihood decoded word. The extended erasure magnitude matrix is developed and used to provide an efficient method of decoding the candidate codewords