Reformulated Euclidean Algorithm and Optimized (OREA) Architecture for Reed-Solomon Decoding

In this paper, we present a Reformulated Euclidean Algorithm (REA) and its optimized architecture for Reed-Solomon decoding. Through algorithm transformations on a modified Euclidean algorithm by Berlekamp et al., the REA is derived, featuring free of inversion operations. It has a fixed number 2$t$ of iterations (t is the error-correction capability), and owns a very simple description. By generalizing the Horiguchi-Koetter formula and exploring the early termination mechanism, we present the optimized reformulated Euclidean algorithm (OREA). The derivative architecture is a systolic one, consisting of 2t + 1 processing elements (PEs) with the critical path of one multiplier and one adder. Complexity comparisons show that the proposed OREA saves 30% resources over sDCMEA, the state-of-art architecture based on Euclidean algorithm, and has almost the same (actually slight lower) complexity as ePIBMA, the state-of-art architecture based on Berlekamp-Massey algorithm. Thus this work fills an important gap for the hardware implementation between two RS decoding algorithms.