  The performance of algebraic soft-decision decoding of Reed-Solomon codes
using bit-level soft information is investigated. Optimal multiplicity
assignment strategies of algebraic soft-decision decoding with infinite cost
are first studied over erasure channels and the binary symmetric channel. The
corresponding decoding radii are calculated in closed forms and tight bounds on
the error probability are derived. The multiplicity assignment strategy and the
corresponding performance analysis are then generalized to characterize the
decoding region of algebraic softdecision decoding over a mixed error and
bit-level erasure channel. The bit-level decoding region of the proposed
multiplicity assignment strategy is shown to be significantly larger than that
of conventional Berlekamp-Massey decoding. As an application, a bit-level
generalized minimum distance decoding algorithm is proposed. The proposed
decoding compares favorably with many other Reed-Solomon soft-decision decoding
algorithms over various channels. Moreover, owing to the simplicity of the
proposed bit-level generalized minimum distance decoding, its performance can
be tightly bounded using order statistics.
