Application of Soft-Decision Decoders to Non Narrow-Sense Reed-Solomon Codes

Reed-Solomon (RS) codes are defined in several different ways which are not exactly equivalent. Distinct algorithms for encoding and decoding of RS codes have been developed based on the different definitions. This paper clarifies the relationships among the several definitions of RS codes, especially focusing on the connection between non-binary BCH codes, which are not necessarily narrow-sense, and Generalized Reed- Solomon (GRS) codes. With the relationships, we introduce code space conversion which converts objects of a GRS code into corresponding objects of another GRS code with the same dimension. This transformation can be used for the flexible application of the decoder designed for a specific RS code. We show that the interpolation-based soft-decision RS decoders can be applied to non narrow-sense RS codes using code space conversion.