A Chase-type Koetter-Vardy algorithm for soft-decision Reed-Solomon decoding

With polynomial complexity, algebraic soft-decision (ASD) decoding of Reed-Solomon (RS) codes can achieve significant coding gain over hard-decision decoding. Compared to other existing ASD algorithms, the low-complexity Chase (LCC) decoding that tests 2^η vectors has lower hardware complexity since the multiplicities of the involved interpolation points are all one. However, its complexity increases significantly with η. On the other hand, magnetic recording uses long RS codes, and hence larger η needs to be adopted to achieve good performance. This paper proposes a novel scheme to integrate the Kötter-Vardy (KV) scheme into the Chase decoding. To reduce the hardware complexity, the maximum multiplicity is limited to two. Nevertheless, the proposed KV-LCC scheme can achieve similar performance as the LCC algorithm by using a much smaller η. In addition, a simplified (S-) version of the KV-LCC scheme is developed without losing coding gain. To achieve similar performance as the LCC algorithm, the S-KV-LCC decoding requires 63% less multiplications for a (458, 410) RS code over GF(2¹⁰).