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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Veröffentlicht in:IEEE transactions on computers Jg. 69; H. 5; S. 699 - 705
Hauptverfasser: Yu, Leilei, Lin, Zhichang, Lin, Sian-Jheng, Han, Yunghsiang S., Yu, Nenghai
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.05.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
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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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2019.2963827