Fast Encoding and Decoding Algorithms for Arbitrary (n,k) Reed-Solomon Codes Over \mathbb

Recently, a new polynomial basis over finite fields was proposed such that the computational complexity of the fast Fourier transform (FFT) is <inline-formula> <tex-math notation="LaTeX">O(n\log n) </tex-math></inline-formula>. Based on FFTs, the encoding and decodi...

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Bibliographic Details
Published in:IEEE communications letters Vol. 24; no. 4; pp. 716 - 719
Main Authors: Tang, Nianqi, Lin, Yun
Format: Journal Article
Language:English
Published: IEEE 01.04.2020
Subjects:
Complexity theory
Decoding
decoding algorithm
Encoding
fast fourier transform
Indexes
Laplace equations
Reed-Solomon codes
Transforms
ISSN:1089-7798, 1558-2558
Online Access:Get full text
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Summary:Recently, a new polynomial basis over finite fields was proposed such that the computational complexity of the fast Fourier transform (FFT) is <inline-formula> <tex-math notation="LaTeX">O(n\log n) </tex-math></inline-formula>. Based on FFTs, the encoding and decoding algorithms for Reed-Solomon (RS) codes were proposed, which are shown to have the lowest computational complexity in the literature. However, these algorithms require that the code length and the number of parity symbols must be power of two. In this letter, we present the encoding and decoding algorithms for arbitrary RS codes based on FFTs. Furthermore, these new algorithms also reach the best known complexity bound.
ISSN:1089-7798
1558-2558
DOI:10.1109/LCOMM.2020.2965453