Hardware complexities of low-complexity Chase Reed Solomon decoders and comparisons

Reed-Solomon (RS) codes are widely used in digital communication and storage systems. Algebraic soft-decision decoding (ASD) of RS codes can achieve significant coding gain over the hard-decision decoding (HDD). Compared with other ASD algorithms, the low-complexity Chase (LCC) decoding algorithm needs less computation complexity with similar or higher coding gain. Several techniques have been applied to reduce the decoding complexity and made the LCC decoding algorithm easier to be implemented by hardware. This paper answers the question that which practical LCC decoder is the most efficient. In addition, decoder complexity comparisons for an example (255, 239) RS code constructed over GF(2⁸) are presented. This paper also provides discussions on how the hardware complexities of LCC decoders change with the decoding parameter and code rate.