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Peterson-Gorenstein-Zierler algorithm for differential convolutional codes

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 2021年第3期32卷 321-344页

作者： Gomez-Torrecillas, Jose Lobillo, F. J. Navarro, Gabriel Sanchez-Hernandez, Jose Patricio Univ Granada IEMath GR Granada 18071 Spain Univ Granada Dept Algebra Granada 18071 Spain Univ Granada CITIC Granada 18071 Spain Univ Granada Dept Comp Sci & Artificial Intelligence Granada 18071 Spain

Differential Convolutional Codes with designed Hamming distance are defined, and an algebraic decoding algorithm, inspired by Peterson-Gorenstein-Zierler's algorithm, is designed for them.

关键词： Differential convolutional code Cyclic convolutional code Differential Reed-Solomon codes algebraic decoding algorithm

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

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IET COMMUNICATIONS 2016年第6期10卷 734-738页

作者： Lin, Tsung-Ching Chang, Hsin-Chiu Li, Yong Chang, Jack Trieu-Kien Truong I Shou Univ Dept Informat Engn Kaohsiung 82001 Taiwan Chongqing Univ Posts & Telecommun Chongqing Key Lab Mobile Commun Technol Chongqing 400065 Peoples R China Intellectual Property Grp Baker Hosterler WA USA

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.

关键词： algebraic codes decoding BCH codes quadratic residue code binary systematic quadratic residue code channel measurement information algebraic decoding algorithm software simulation C-language

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algebraic decoding of the binary systematic (71,36,11) quadratic residue code

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JOURNAL OF THE CHINESE INSTITUTE OF ENGINEERS 2013年第3期36卷 399-404页

作者： Lee, Hung-Peng Chang, Hsin-Chiu Chu, Shao-I Fortune Inst Technol Dept Comp Sci & Informat Engn Kaohsiung 831 Taiwan Xiamen Univ Dept Commun Engn Xiamen Peoples R China I Shou Univ Dept Elect Engn Kaohsiung 840 Taiwan

A fast and efficient algebraic decoding algorithm (ADA) is proposed to correct up to five possible error patterns in the binary systematic (71, 36, 11) quadratic residue (QR) code. The technique required here is based on the ADA developed by He et al. [2001. decoding the (47, 24, 11) quadratic residue code. IEEE transactions on information theory, 47 (3), 1181-1186.] and the modification of the ADA developed by Lin et al. [2010. decoding of the (31, 16, 7) quadratic residue code. Journal of the Chinese institute of engineers, 33 (4), 573-580;2010. High speed decoding of the binary (47, 24, 11) quadratic residue code. Information sciences, 180 (20), 4060-4068]. The new proposed conditions and the error-locator polynomials for different numbers of errors in the received word are derived. Simulation results show that the decoding speed of the proposed ADA is faster than the other existing ADAs.

关键词： quadratic residue code syndrome algebraic decoding algorithm

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Fast algebraic decoding of the (17, 9, 5) quadratic residue code

Fast algebraic decoding of the (17, 9, 5) quadratic residue ...

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International Conference on Consumer Electronics, Communications and Networks

作者： Hung-Peng Lee Department of Computer Science and Information Engineering Fortune Institute of Technology

ISBN: (纸本)9781457714146

A fast algebraic decoding algorithm is proposed to correct all patterns of two or fewer errors in the binary (17, 9, 5) quadratic residue (QR) code. Computer simulations show that the average decoding time of the proposed decoding algorithm is about 2.88 times less execution time than the D3 algebraic decoding algorithm of Chang et al.

关键词： Quadratic residue code algebraic decoding algorithm Error pattern Syndrome

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Study on the algebraic decoding of the (89, 45, 17) quadratic residue code

Study on the algebraic decoding of the (89, 45, 17) quadrati...

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International Conference on Consumer Electronics, Communications and Networks

作者： Hung-Peng Lee Department of Computer Science and Information Engineering Fortune Institute of Technology

ISBN: (纸本)9781457714146

A study on the weight-5 error patterns of the algebraic decoding of the (89, 45, 17) quadratic residue (QR) code with reducible generator polynomial, proposed by Truong et al. (2008), is presented. For the QR codes with irreducible generator polynomial, S_1 = 0 means that the received word has no errors. For the (89, 45, 17) QR codes, some weight-5 error patterns will cause a zero value in syndrome S_1. However, these weight-5 error patterns do not cause a decoding failure while using the inverse-free Berlekamp-Massey (IFBM) algorithm to determine the error-locator polynomial. An example shows the facts.

关键词： Quadratic residue code algebraic decoding algorithm Error pattern Syndrome

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decoding the Binary (71,36,11) Quadratic Residue Code

Decoding the Binary (71,36,11) Quadratic Residue Code

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International Conference on Computer Science and Education (CSE 2011)

作者： Lee, Hung-Peng Chang, Hsin-Chiu Fortune Inst Technol Dept Comp Sci & Informat Engn Kaohsiung 831 Taiwan

ISBN: (纸本)9783642224171

In this paper, an efficient algebraic decoding algorithm (ADA) is proposed to correct all patterns of five errors or less in the binary systematic (71. 36, 11) quadratic residue (QR) code. The method is based on the modification of the ADAs developed by Reed et al and Lin et al. The proposed conditions and the error-locator polynomials for decoding this code will be derived. Simulation result shows that the average decoding time of the proposed ADA is faster than the ADA proposed by Chang et al.

关键词： syndrome QR code error pattern algebraic decoding algorithm

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An improvement on decoding of the binary systematic (47,24,11) quadratic residue code

An improvement on decoding of the binary systematic (47,24,1...

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2011 International Conference on Business Management and Electronic Information(BMEI 2011)

作者： Hung-Peng Lee Hsin-Chiu Chang Department of Computer Science and Information Engineering Fortune Institute of Technology Kaohsiung City 831 Taiwan Department of Communication Engineering Xiamen University Xiamen China

ISBN: (纸本)9781612841083

An improved algebraic decoding algorithm (ADA) is presented to decode up to five possible errors in a binary systematic (47,24,11) quadratic residue (QR) *** main idea of the improved ADA is to find out the new conditions in four-error and five-error cases and the smallest degree of the unknown syndrome polynomial in five-error ***,the computational complexity in the finite field can be reduced.A simulation result shows that the decoding speed of the proposed ADA is faster than other existing ADAs.

关键词： algebraic decoding algorithm quadratic residue codes error locator polynomial syndrome

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decoding the Binary(71,36,11) Quadratic Residue Code

Decoding the Binary(71,36,11) Quadratic Residue Code

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Advances in Information Technology and Education

作者： Hung-Peng Lee Hsin-Chiu Chang Department of Computer Science and Information Engineering Fortune Institute of Technology

In this paper, an efficient algebraic decoding algorithm(ADA) is proposed to correct all patterns of five errors or less in the binary systematic(71, 36, 11) quadratic residue(QR) code. The method is based on the modification of the ADAs developed by Reed et al and Lin et al. The proposed conditions and the error-locator polynomials for decoding this code will be derived. Simulation result shows that the average decoding time of the proposed ADA is faster than the ADA proposed by Chang et al.

关键词： syndrome QR code error pattern algebraic decoding algorithm

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

Improvement on decoding of the (71, 36, 11)quadratic residue...

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The 6th International Conference on Computer Science & Education(第六届国际计算机新科技与教育学术会议 ICCSE 2011)

作者： Hung-Peng Lee Hsin-Chiu Chang Dept.of Computer Science and Information Engineering Fortune Institute of Technology Kaohsiung City 831 Taiwan

In this paper, a fast algebraic decoding algorithm (ADA) is proposed to correct all patterns of five errors or less in the binary systematic (71, 36, 11) quadratic residue (QR) code. The method is based on the modification of the ADAs developed by Reed et al and Lin et al. The new conditions and the errorlocator polynomials for decoding this code will be derived. Besides, a computer search shows that the minimum degree of the unknown syndrome polynomial f(S7) in the five-error case is 2. Hence, the computational complexity can be reduced in finite field. Simulation result shows that the average decoding time of the proposed ADA is superior to the ADA given by Chang et al.

关键词： quadratic residue code algebraic decoding algorithm error-locator polynomial syndrome

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decoding THE (24,12,8) GOLAY CODE

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IEE PROCEEDINGS-E COMPUTERS AND DIGITAL TECHNIQUES 1990年第3期137卷 202-206页

作者： REED, IS YIN, X TRUONG, TK HOLMES, JK CALTECH JET PROP LABCOMMUN SYST RES SECTPASADENACA 91109

A simplified procedure, called the shift-search method, is developed to decode the three possible errors in a (23,12,7) Golay codeword. The algebraic decoding algorithm developed recently by Elia is compared with this algorithm. A computer simulation shows that both algorithms are modular, regular and naturally suitable for either VLSI or software implementation. Both of these algorithms decode efficiently the 1/2-rate (24,12) Golay code for correcting three errors and detecting four errors. The algebraic technique is a slightly faster algorithm in software than the shift-search procedure.

关键词： algebraic technique Golay code decoding software implementation VLSI computer simulation Codes shift-search method Information theory algebraic decoding algorithm codes decoding

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