Low hardware complexity key equation solver chip for Reed-Solomon decoders

Abstract

This paper proposes a new simplified degree computationless modified Euclid's algorithm (S-DCME) and its architecture for Reed-Solomon decoders. The proposed S-DCME algorithm reformulates the existing modified Euclid's (ME) algorithm and uses new initial conditions to remove unnecessary hardware components and to use simple data paths. Thus, it requires two less multipliers and t + 2 less multiplexers compared with the reformulated inversionless Berlekamp-Massey (RiBM) algorithm which has shown the best performance so far. The critical path delay of S-DCME is 7.92 ns, i.e., TMul + TADD + TMUX, that is equal to that of RiBM. The gate count of the implemented chip using the MagnaChip HSI 0.25 mum standard cell library is 17,800.