Two algorithms for soft-decision decoding of Reed-Solomon codes, with application to multilevel coded modulations

In this paper two symbol-level soft-decision decoding algorithms for Reed-Solomon codes, derived form the Ordered Statistics (OS) and from the Generalized Minimum- Distance (GMD) decoding methods, are presented and analyzed. Both the OS and the GMD algorithms are based on the idea of producing a list of candidate code words, among which the one having the larger likelihood is selected as output. We propose variants of the mentioned algorithms that allow to finely tune the size of the list in order to obtain the desired decoding complexity. The method proposed by Agrawal and Vardy for computing the error probability of the GMD algorithm is extended to our decoding methods. Examples are presented where these algorithms are applied to singly-extended Reed-Solomon codes over GF(16) used as outer codes in a 128-dimensional coded modulation scheme that attains good performance, with manageable decoding complexity.