Fast Encoding Algorithms for Reed-Solomon Codes With Between Four and Seven Parity Symbols

This article describes a fast Reed-Solomon encoding algorithm with four and seven parity symbols in between. First, we show that the syndrome of Reed-Solomon codes can be computed via the Reed-Muller transform. Based on this result, the fast encoding algorithm is then derived. Analysis shows that th...

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Published in:	IEEE transactions on computers Vol. 69; no. 5; pp. 699 - 705
Main Authors:	Yu, Leilei, Lin, Zhichang, Lin, Sian-Jheng, Han, Yunghsiang S., Yu, Nenghai
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.05.2020 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms Arrays coding algorithm Complexity theory Computer simulation Cutting speed Decoding Encoding Parity Reed–Muller transform Reed–Solomon code Sparse matrices Symbols Systematics Transforms
ISSN:	0018-9340, 1557-9956
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Abstract	This article describes a fast Reed-Solomon encoding algorithm with four and seven parity symbols in between. First, we show that the syndrome of Reed-Solomon codes can be computed via the Reed-Muller transform. Based on this result, the fast encoding algorithm is then derived. Analysis shows that the proposed approach asymptotically requires 3 XORs per data bit, representing an improvement over previous algorithms. The simulation demonstrates that the performance of the proposed approach improves with the increase of code length and is superior to other methods. In particular, when the parity number is 5, the proposed approach is about two times faster than other cutting-edge methods.
AbstractList	This article describes a fast Reed–Solomon encoding algorithm with four and seven parity symbols in between. First, we show that the syndrome of Reed–Solomon codes can be computed via the Reed–Muller transform. Based on this result, the fast encoding algorithm is then derived. Analysis shows that the proposed approach asymptotically requires 3 XORs per data bit, representing an improvement over previous algorithms. The simulation demonstrates that the performance of the proposed approach improves with the increase of code length and is superior to other methods. In particular, when the parity number is 5, the proposed approach is about two times faster than other cutting-edge methods.
Author	Lin, Zhichang Yu, Nenghai Yu, Leilei Lin, Sian-Jheng Han, Yunghsiang S.
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Snippet	This article describes a fast Reed-Solomon encoding algorithm with four and seven parity symbols in between. First, we show that the syndrome of Reed-Solomon... This article describes a fast Reed–Solomon encoding algorithm with four and seven parity symbols in between. First, we show that the syndrome of Reed–Solomon...
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SubjectTerms	Algorithms Arrays coding algorithm Complexity theory Computer simulation Cutting speed Decoding Encoding Parity Reed–Muller transform Reed–Solomon code Sparse matrices Symbols Systematics Transforms
Title	Fast Encoding Algorithms for Reed-Solomon Codes With Between Four and Seven Parity Symbols
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