Title: On fast Fourier transform-based decoding of Reed-Solomon codes

Authors: Yunghsiang S. Han; Chao Chen; Sian-Jheng Lin; Baoming Bai

Addresses: The State Key Laboratory of ISN, Xidian University, Xi'an, China; School of Electrical Engineering and Intelligentization, Dongguan University of Technology, Dongguan, China ' The State Key Laboratory of ISN, Xidian University, Xi'an, China ' School of Information Science and Technology, University of Science and Technology of China, Hefei, China ' The State Key Laboratory of ISN, Xidian University, Xi'an, China

Abstract: Reed-Solomon (RS) codes is a popular class of codes that have been implemented in many practical systems. Recently, a fast approach to the error decoding of RS codes based on fast Fourier transform (FFT) was invented. In this work, we derive the key equation based on the Lagrange polynomial and then present erasure-and-error decoding of an (n; k) RS code. This decoding algorithm can simultaneously correct up to v errors and f erasures when 2v + f < n − k + 1. The decoding complexity is with only O(n log n + (n − k) log²(n − k)).

Keywords: coding; decoding; Reed-Solomon codes; fast Fourier transform; FFT.

DOI: 10.1504/IJAHUC.2021.113877

International Journal of Ad Hoc and Ubiquitous Computing, 2021 Vol.36 No.3, pp.180 - 187

Received: 31 Oct 2020
Accepted: 31 Oct 2020
Published online: 31 Mar 2021 *

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