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

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)).