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

摘要

The performance of algebraic soft-decision decoding of Reed-Solomon codesusing bit-level soft information is investigated. Optimal multiplicityassignment strategies of algebraic soft-decision decoding with infinite costare first studied over erasure channels and the binary symmetric channel. Thecorresponding decoding radii are calculated in closed forms and tight bounds onthe error probability are derived. The multiplicity assignment strategy and thecorresponding performance analysis are then generalized to characterize thedecoding region of algebraic softdecision decoding over a mixed error andbit-level erasure channel. The bit-level decoding region of the proposedmultiplicity assignment strategy is shown to be significantly larger than thatof conventional Berlekamp-Massey decoding. As an application, a bit-levelgeneralized minimum distance decoding algorithm is proposed. The proposeddecoding compares favorably with many other Reed-Solomon soft-decision decodingalgorithms over various channels. Moreover, owing to the simplicity of theproposed bit-level generalized minimum distance decoding, its performance canbe tightly bounded using order statistics.