VLSI architectures for soft-decision decoding of Reed-Solomon codes

In this paper, we present architectures for bivariate polynomial interpolation and factorization; the two main steps in algebraic soft-decision decoding of Reed-Solomon codes. We present an efficient formulation of the interpolation algorithm in which dependencies among the discrepancy coefficient computations are utilized to reduce interpolation complexity. Interpolation and factorization complexity is also reduced by using an FFT-like formulation for univariate polynomial translation. The modifications required to incorporate recently proposed algorithm level modifications for efficient interpolation and factorization are also presented. We determine the latency and hardware requirements for soft-decoding a [255, 239] Reed-Solomon code using the proposed architectures.