On fast Fourier transform-based decoding of Reed-Solomon codes. (12th March 2021)

• Record Type: Journal Article
• Authors: Han, Yunghsiang S.; Chen, Chao; Lin, Sian-Jheng; Bai, Baoming
• Is Part Of: International journal of ad hoc and ubiquitous computing. Volume 36:Number 3(2021)
• Page Start: 180
• Page End: 187
• Publication Date: 2021-03-12
• Subjects: coding -- decoding -- Reed-Solomon codes -- fast Fourier transform -- FFT; Ubiquitous computing -- Periodicals; Embedded computer systems -- Periodicals; Electronic data processing -- Distributed processing -- Periodicals; Wireless communication systems -- Periodicals; Computer architecture -- Periodicals; 004.2
• Languages: English
• ISSNs: 1743-8225

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 2 v + f < n − k + 1. The decoding complexity is with only O ( n log n + ( n − k ) log 2 ( n − k )).