The performance of algebraic soft-decision decoding of Reed-Solomon codes using bit-level soft information is investigated. Optimal multiplicity assignment strategies for algebraic soft-decision decoding (SDD) 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 SDD 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 SDD 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.

A rateless Slepian-Wolf coding (SWC) scheme based on rate adaptive low-density-parity-check (LDPC) codes is presented. We first motivate the application of punctured LDPC codes in SWC. A general rate adaptive LDPC framework is then described. The main idea is to adjust the puncturing ratio in the specified variable nodes for rate adaptivity while keeping the bipartite graph structure intact. As a complement, a repetition scheme is proposed for high rate SWC. The asymptotic performance of the proposed scheme is analyzed by density evolution (DE) with universal coding bounds and finite code length performance is verified by computer simulations.

We consider coding schemes for channels with non-uniform inputs (NUI), where standard linear block codes can not be applied directly. We show that multilevel coding (MLC) with a set of linear codes and a deterministic mapper can achieve the information rate of the channel with NUI. The mapper, however, does not have to be one-to-one. As an application of the proposed MLC scheme, we present a rateless transmission scheme over the binary symmetric channel (BSC)

In this paper, we characterize the decoding region of algebraic soft decoding (ASD) [4] of Reed-Solomon (RS) codes over erasure channels and binary symmetric channel (BSC). Optimal multiplicity assignment strategies (MAS) are investigated and tight bounds are derived to show the ASD can significantly outperform conventional Berlekamp Massey (BM) decoding over these channels for a wide code rate range. The analysis technique can also be extended to other channel models, e.g., RS coded modulation over erasure channels

We present a soft decision decoding algorithm for Reed Solomon (RS) codes using their binary image representations. The novelty of the proposed decoding algorithm is in reducing the submatrix corresponding to the less reliable bits to a sparse nature prior to each decoding iteration and in adapting the parity check matrix from one iteration to another. Simulation results show that the new method provides significant gain over hard decision decoding (HDD) and compares favorably with other popular soft decision decoding methods [R. Koetter et al., 2003].