New Cost-Effective Simplified Euclid’s Algorithm for Reed-Solomon Decoders

This paper proposes a cost-effective simplified Euclid’s (SE) algorithm for Reed-Solomon decoders, which can replace the existing modified Euclid’s (ME) algorithm. The new proposed SE algorithm, using new initial conditions and polynomials, can significantly reduce the computation complexity compared with the existing ME and reformulated inversionless Berlekamp-Massey (RiBM) algorithms, since it has the least number of coefficients in the new initial conditions. Thus, the proposed SE architecture, consisting of only 3t basic cells, has the smallest area among the existing key solver blocks, where t means the error correction capability. In addition, the SE architecture requires only the latency of 2t clock cycles to solve the key equation without initial latency. The proposed RS decoder has been synthesized using the 0.18 μm Samsung cell library, and the gate count of the RS decoder, excluding FIFO memory, is only 40,136 for the (255, 239, 8) RS code.