Algebraic decoding of the (71, 36, 11) quadratic residue code

In this study, a new approach is developed to facilitate faster decoding of a binary systematic (71, 36, 11) quadratic residue (QR) code. In this decoder, it simplifies the step of calculating the condition and avoids calculating the unknown syndrome, thereby yielding a fast algebraic decoder for co...

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Bibliographic Details
Published in:IET communications Vol. 10; no. 6; pp. 734 - 738
Main Authors: Lin, Tsung-Ching, Chang, Hsin-Chiu, Li, Yong, Chang, Jack, Truong, Trieu-Kien
Format: Journal Article
Language:English
Published: The Institution of Engineering and Technology 14.04.2016
Subjects:
Algebra
algebraic codes
algebraic decoding algorithm
Algorithms
BCH codes
binary systematic quadratic residue code
channel measurement information
Computer programs
C‐language
Decoding
Error analysis
Error correction
Mathematical analysis
quadratic residue code
Residues
software simulation
software simulation
C-language
binary systematic quadratic residue code
quadratic residue code
channel measurement information
BCH codes
algebraic decoding algorithm
decoding
algebraic codes
ISSN:1751-8628, 1751-8636
Online Access:Get full text
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Summary:In this study, a new approach is developed to facilitate faster decoding of a binary systematic (71, 36, 11) quadratic residue (QR) code. In this decoder, it simplifies the step of calculating the condition and avoids calculating the unknown syndrome, thereby yielding a fast algebraic decoder for correcting four possible errors. Moreover, while using the proposed algorithm, if uses the channel measurement information proposed by Chase to sequentially invert the bits of the received word until one of the errors is cancelled for the five-error case and apply the new algebraic decoding algorithm mentioned above to correct the remaining four errors, the algorithm has been verified through a software simulation in C-language. The simulation shows that the decoding scheme developed here is more efficient than the previous decoding algorithm developed for the (71, 36, 11) QR code and it is naturally suitable for software implementation.
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ISSN:1751-8628
1751-8636
DOI:10.1049/iet-com.2015.0159