Algebraic Soft-Decision Decoder Architectures for Long Reed–Solomon Codes

Algebraic soft-decision (ASD) decoders of Reed-Solomon (RS) codes can achieve significant coding gain with polynomial complexity. Most prior work on ASD decoder architecture design is for relatively short RS codes. However, one major application of RS codes, magnetic recording, usually requires a code length of 4Kbits or longer. For long RS codes, the low-complexity Chase (LCC) ASD decoding needs to interpolate over a large number of test vectors, which leads to long latency. This brief proposes a unified backward-forward interpolation scheme and a corresponding architecture for the LCC decoding. The proposed architecture can achieve almost twice the speed with only 40% area overhead. Another contribution of this brief is that the hardware complexity analysis for different ASD decoders is provided for the first time. For a (458, 410) RS code over GF(2
¹⁰
), the proposed LCC decoder can achieve much higher efficiency in terms of speed-over-area ratio than other ASD decoders with similar error-correcting performance.