Algebraic Soft-Decision Decoding of Reed-Solomon Codes Using Bit-level Soft Information

The performance of algebraic soft-decision decoding (ASD) of Reed-Solomon (RS) codes using bit-level soft information is investigated. Optimal multiplicity assignment strategies (MAS) of ASD with infinite cost are first studied over erasure channels and binary symmetric channels (BSC). The corresponding decoding radii are calculated in closed forms and tight bounds on the error probability are derived. The MAS and the corresponding performance analysis are then generalized to characterize the decoding region of ASD over a mixed error and bit-level erasure channel. The bit-level decoding region of the proposed MAS is shown to be significantly larger than that of conventional Berlekamp-Massey (BM) decoding. As an application, a bit-level generalized minimum distance (BGMD) decoding algorithm is proposed. The proposed BGMD compares favorably with many other RS soft-decision decoding (SDD) algorithms over various channels. Moreover, owing to the simplicity of BGMD, its performance can be tightly bounded using ordered statistics. Index Terms Algebraic Soft-decision Decoding, Bit-level Soft Information, Error and Erasure Decoding, Generalized Minimum Distance Decoding, Guruswami-Sudan Decoder, Koetter-Vardy Decoder, List Decoding, Multiplicity Assignment, Reed-Solomon codes.