High-speed re-encoder design for algebraic soft-decision Reed-Solomon decoding

Algebraic soft-decision decoding (ASD) of Reed-Solomon (RS) codes can provide substantial coding gain with polynomial complexity. The major steps of ASD algorithms are the interpolation and factorization. To greatly reduce the complexity of these steps, the re-encoding and coordinate transformation techniques need to be applied. The implementation of these techniques requires a re-encoder and an erasure decoder. In re-encoded and transformed ASD decoders, these two blocks take a significant proportion of the overall area requirement and may limit the maximum achievable speed. A novel re-encoder design is proposed in this paper. In the proposed design, the erasure locator and evaluator polynomials are computed directly through multiplications and other involved computations are reformulated to reduce latency and area requirement. Scalable architectures for the proposed re-encoder are developed. When these architectures are applied to a (255, 239) RS code, our re-encoder can achieve 82% higher throughput than the previous design with 11% less area. With minor modifications, the proposed design can also be used to implement an efficient erasure decoder.