Factorization Architecture by Direct Root Computation for Algebraic Soft-Decision Decoding of Reed-Solomon Codes

Abstract

Algebraic soft-decision decoding is a recent break-through in decoding of Reed-Solomon codes and significant decoding gain can be achieved over conventional hard-decision decoding. Bivariate polynomial factorization is an important step of the new decoding algorithm and contributes to a significant portion of the overall decoding latency. In this paper, a novel architecture based on direct root computation is proposed to greatly reduce the factorization latency. Direct root computation is feasible because in most practical applications of algebraic soft-decision decoding of RS codes, sufficient decoding gain can be achieved with a relatively low interpolation cost, which results in bivariate polynomial of small Y-degree. Compared with existing works, not only does our new architecture have a significantly smaller worst-case decoding latency, but it is also more area efficient.