Novel Interpolation and Polynomial Selection for Low-Complexity Chase 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 interpolation and polynomial selection can account for a significant part of the LCC decoder area, especially in the case of long RS codes and large η . In this paper, simplifications are first proposed for a low-complexity polynomial selection scheme. Then a novel interpolation scheme is developed by making use of the simplified polynomial selection. Instead of interpolating over each vector, our scheme first generates information necessary for the polynomial selection. Then only the selected vectors are interpolated over. The proposed interpolation and polynomial selection schemes can lead to 162% higher efficiency in terms of throughput-over-area ratio for an example LCC decoder with η = 8 for a (458, 410) RS code over <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GF</i> (2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sup> ).