Hardware complexities of algebraic soft-decision Reed-Solomon decoders and comparisons

Algebraic soft-decision (ASD) decoding of Reed-Solomon (RS) codes can achieve significant coding gain over hard-decision decoding. For practical implementation purpose, ASD algorithms with simple multiplicity assignment schemes are preferred. This paper answers the question of which practical ASD algorithm has lower hardware complexity. In addition, decoder complexity comparisons for an example (458, 410) RS code constructed over GF(2¹⁰) are presented. This paper also provides discussions on how the hardware complexities of ASD decoders change with codeword length, code rate and other parameters.