Performance Analysis of Algebraic Soft-Decision Decoding of Reed–Solomon Codes

We investigate the decoding region for algebraic soft-decision decoding (ASD) of Reed–Solomon (RS) codes in a discrete, memoryless, additive-noise channel. An expression is derived for the error correction radius within which the soft-decision decoder produces a list that contains the transmitted codeword. The error radius for ASD is shown to be larger than that of Guruswami–Sudan (GS) hard-decision decoding for a subset of low and medium-rate codes. These results are also extended to multivariable interpolation in the sense of Parvaresh and Vardy.