Factorization-free Low-complexity Chase soft-decision decoding of Reed-Solomon codes

Abstract

Algebraic soft-decision decoding (ASD) of Reed-Solomon (RS) codes can provide substantial coding gain with polynomial complexity. Among practical ASD algorithms, the Low-complexity Chase (LCC) algorithm can achieve similar or higher coding gain with lower complexity. The major steps of ASD algorithms are the interpolation and factorization. Applying the re-encoding and coordinate transformation, the complexity of these two steps can be greatly reduced at the cost of an extra hard-decision decoder. Backward interpolation has been proposed to enable the sharing of intermediate results among the multiple interpolations of the LCC decoding. However, not much work has been done on further optimizing the factorization step, which consumes a significant proportion of the area and can become a speed bottleneck of the overall decoder. In this paper, a novel scheme is proposed for the LCC decoding to eliminate the factorization step and the key equation solver in the extra hard-decision decoder. Compared to prior LCC decoders, the proposed factorization-free LCC decoder can achieve the same throughput with 19% less area for a (255, 239) RS code with η = 3.