A novel polynomial selection scheme for low-complexity chase algebraic soft-decision reed-solomon decoding

Abstract

Algebraic soft-decision decoding (ASD) of Reed-Solomon (RS) codes can achieve substantial coding gain with polynomial complexity. Particularly, the low-complexity Chase (LCC) ASD decoding has better performance-complexity tradeoff. In the LCC decoding, 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">η</sup> test vectors need to be interpolated over, and a polynomial selection scheme needs to be employed to select one interpolation output to send to the rest decoding steps. The polynomial selection can account for a significant proportion of the overall LCC decoder area, especially in the case of long RS codes and large η. In this paper, a novel low-complexity polynomial selection scheme is proposed and efficiently incorporated into the LCC decoder. By sacrificing one single message symbol and modifying the encoder slightly, the polynomial selection is done using simple computations. For a (458, 410) RS code over GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sup> ), the encoder and LCC decoder with η = 8 employing the proposed scheme requires 34% less area without changing the encoding or decoding throughput.