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

摘要

We investigate the decoding region for Algebraic Soft-Decision Decoding (ASD)of Reed-Solomon codes in a discrete, memoryless, additive-noise channel. Anexpression is derived for the error correction radius within which thesoft-decision decoder produces a list that contains the transmitted codeword.The error radius for ASD is shown to be larger than that of Guruswami-Sudanhard-decision decoding for a subset of low-rate codes. These results are alsoextended to multivariable interpolation in the sense of Parvaresh and Vardy. Anupper bound is then presented for ASD's probability of error, where an error isdefined as the event that the decoder selects an erroneous codeword from itslist. This new definition gives a more accurate bound on the probability oferror of ASD than the results available in the literature.