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decoding algorithms of Twisted GRS Codes and Twisted Goppa Codes

IEEE TRANSACTIONS ON INFORMATION THEORY 2025年第2期71卷 1018-1027页

作者： Sun, Huan Yue, Qin Jia, Xue Li, Chengju Nanjing Univ Aeronaut & Astronaut Dept Math Nanjing 211100 Peoples R China State Key Lab Cryptol Beijing 100878 Peoples R China East China Normal Univ Shanghai Key Lab Trustworthy Comp Shanghai 200062 Peoples R China

In this paper, we use extended Euclid's algorithm to propose new decoding algorithms for two classes of maximum distance separable (MDS) twisted generalized Reed-Solomon (TGRS) codes of parameters [ n , n - t , t + 1] over F (q) . For even t , the algorithms can correct (t) /(2) errors with time complexity O ( qn ). Moreover, we also give a new decoding algorithm for a class of twisted Goppa codes. For even degree t of a Goppa polynomial, it can also correct (t) /(2) errors, which generalizes a (sic)(t -1)/(2)(sic)-error-correcting decoding algorithm by Sui and Yue (2023).

关键词： Codes decoding Reed-Solomon codes Polynomials Codecs Technological innovation Sun Linear codes Public key cryptography Mathematics Twisted generalized Reed-Solomon code twisted Goppa code MDS code decoding algorithm

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decoding algorithms of monotone codes and azinv codes and their unified view

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DESIGNS CODES AND CRYPTOGRAPHY 2022年第12期90卷 2893-2922页

作者： Takahashi, Hokuto Hagiwara, Manabu Chiba Univ Grad Sch Sci & Engn Inage Ku 1-33 Yayoi Cho Chiba Chiba Japan Chiba Univ Grad Sch Sci Inage Ku 1-33 Yayoi Cho Chiba Chiba Japan

This paper investigates linear-time decoding algorithms for two classes of error-correcting codes. One of the classes is monotone codes which are known as single deletion error-correcting codes, although they are not known to be single substitution error-correcting codes. The other is azinv codes which are known as single balanced adjacent deletion error-correcting codes, although they are not known to be single balanced adjacent substitution error-correcting codes. As a result, this paper proposes generalizations of Levenshtein's decoding algorithm for Levenshtein's single deletion or single substitution error-correcting codes. This paper points out that it is possible to unify our new two decoding algorithms. Moreover, we provide Python implementations of these algorithms and the graphs of their computational costs at https://***/Hokuto496 decoding_algorithms_of_monotone_codes_and_azinv_codes.

关键词： Coding theory Insertion/deletion decoding algorithm Balanced adjacent deletion Error-correcting codes

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Bahl-Cocke-Jelinek-Raviv decoding algorithm applied to the three-user binary adder channel

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IET COMMUNICATIONS 2015年第7期9卷 897-902页

作者： Alcoforado, Maria de Lourdes M. G. Oliveira, Mariana C. C. da Rocha, Valdemar C., Jr. Univ Pernambuco UPE Commun Grp GCOM Telecommun Lab LABTEL BR-50750470 Recife PE Brazil Univ Fed Pernambuco Commun Res Grp CODEC Dept Elect & Syst BR-50740550 Recife PE Brazil

The Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is a well-known maximum a posteriori probability decoding algorithm which has been proposed earlier for point to point communication applications, employing block codes or convolutional codes and turbo codes. This study describes an application of the BCJR algorithm for decoding the output of a multiple-access channel called the noisy three-user binary adder channel, in the presence of additive white Gaussian noise. The computer simulation results are presented for the overall coding performance in terms of bit error rate against signal-to-noise ratio.

关键词： Multiple Access Channel Block codes AWGN COMMUNICATIONS APPLICATION adders Access Channels Worm gears Maximum a posteriori estimation a posteriori probability decoding algorithm Simulation results convolutional coding

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Efficient 3D Hilbert Curve Encoding and decoding algorithms

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Chinese Journal of Electronics 2022年第2期31卷 277-284页

作者： JIA Lianyin LIANG Binbin LI Mengjuan LIU Yong CHEN Yinong DING Jiaman Faculty of Information Engineering and Automation Kunming University of Science and Technology Yunnan Key Laboratory of Artificial Intelligence Kunming University of Science and Technology Library Yunnan Normal University School of Information Science and Engineering Guangxi University for Nationalities School of Computing Informatics and Decision Systems Arizona State University

Hilbert curve describes a one-to-one mapping between multidimensional space and 1 D *** traditional 3D Hilbert encoding and decoding algorithms work on order-wise manner and are not aware of the difference between different input data and spend equivalent computing costs on them, thus resulting in a low efficiency. To solve this problem, in this paper we design efficient 3D state views for fast encoding and decoding. Based on the state views designed, a new encoding algorithm(JFK-3HE) and a new decoding algorithm(JFK-3HD) are proposed. JFK-3HE and JFK-3HD can avoid executing iteratively encoding or decoding each order by skipping the first 0 s in input data, thus decreasing the complexity and improving the efficiency. Experimental results show that JFK-3HE and JFK-3HD outperform the state-of-the-arts algorithms for both uniform and skew-distributed data.

关键词： order-wise manner multidimensional space encoding state-of-the-arts algorithms encoding algorithm parallel algorithms JFK-3HE statistical distributions decoding solid modelling design efficient 3D JFK-3HD traditional 3D Hilbert encoding equivalent computing costs different input data decoding algorithm Hilbert curve state views iterative methods

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Progressive-Proximity Bit-Flipping for decoding Surface Codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2025年第3期73卷 1419-1430页

作者： Pacenti, Michele Flanagan, Mark F. Chytas, Dimitris Vasic, Bane Univ Arizona Dept Elect & Comp Engn Tucson AZ 85721 USA Univ Coll Dublin Sch Elect & Elect Engn Dublin 4 Ireland

Topological quantum codes, such as toric and surface codes, are excellent candidates for hardware implementation due to their robustness against errors and their local interactions between qubits. However, decoding these codes efficiently remains a challenge: existing decoders often fall short of meeting requirements such as having low computational complexity (ideally linear in the code's blocklength), low decoding latency, and low power consumption. In this paper we propose a novel bit-flipping (BF) decoder tailored for toric and surface codes. We introduce the proximity vector as a heuristic metric for flipping bits, and we develop a new subroutine for correcting degenerate multiple errors on adjacent qubits. Our algorithm has quadratic complexity growth and it can be efficiently implemented as it does not require operations on dynamic memories, as do state-of-art decoding algorithms such as minimum weight perfect matching or union find. The proposed decoder shows a decoding threshold of 7.5% for the 2D toric code and 7% for the rotated planar code over the binary symmetric channel.

关键词： Codes Maximum likelihood decoding Vectors Qubit Iterative decoding Hardware Transmission line matrix methods Surface codes topological codes bit flipping decoding algorithm quantum error correction

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A decoding algorithm for Cyclic Codes over Symbol-Pair Read Channels

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2015年第12期E98A卷 2415-2422页

作者： Takita, Makoto Hirotomo, Masanori Morii, Masakatu Kobe Univ Grad Sch Engn Kobe Hyogo 6578501 Japan Saga Univ Grad Sch Sci & Engn Saga 8408502 Japan

Cassuto and Blaum presented a new coding framework for channels whose outputs are overlapping pairs of symbols in storage applications. Such channels are called symbol-pair read channels. Pair distance and pair error are used in symbol-pair read channels. Yaakobi et al. proved a lower bound on the minimum pair distance of cyclic codes. Furthermore, they provided a decoding algorithm for correcting pair errors using a decoder for cyclic codes, and showed the number of pair errors that can be corrected by their algorithm. However, their algorithm cannot correct all pair error vectors within half of the minimum pair distance. In this paper, we propose an efficient decoding algorithm for cyclic codes over symbol-pair read channels. It is based on the relationship between pair errors and syndromes. In addition, we show that the proposed algorithm can correct more pair errors than Yaakobi's algorithm.

关键词： symbol-pair read channel cyclic code pair error decoding algorithm

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Designing quantum circuits for decoding binary linear codes

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2025年第1期58卷 015302-015302页

作者： Yoo, Hyungkee Choi, Whan-Hyuk Lee, Yoonjin Sunchon Natl Univ Dept Math Educ Sunchon 57922 South Korea Kangwon Natl Univ Dept Math Chunchon 24341 South Korea Kangwon Natl Univ Kangwon Res Inst Math Sci Chunchon 24341 South Korea Ewha Womans Univ Dept Math Seoul 03760 South Korea

In the coding theory, it is one of the most important research problems to find an efficient algorithm for the decoding process. A quantum computer is an innovative computing device that performs calculations using the principles of quantum mechanics. In this paper, we find a decoding algorithm for binary linear codes using quantum circuits;this is the first time that quantum circuits are used as a main tool for decoding binary linear codes. Our decoding algorithm is mainly based on Grover's search algorithm. In detail, we study the process of implementing the exhaustive search using quantum circuits for decoding binary linear codes. For our purpose, we design a modified Grover's algorithm (algorithm 1) using three tools: the matrix multiplier, the Hamming weight counter, and the state indicator. We present algorithm 2, which is a quantum decoding algorithm for binary linear codes. We illustrate algorithm 1 using the [7, 4, 3] Hamming code, and algorithm 2 is implemented by IBM Quantum Composer.

关键词： decoding algorithm quantum circuit Grover's algorithm binary linear code exhaustive search

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New Constructions of q-Ary MDS Array Codes With Multiple Parities and Their Effective decoding

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IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第11期69卷 7082-7098页

作者： Lv, Jingjie Fang, Weijun Chen, Xiangyu Yang, Jing Xia, Shu-Tao Tsinghua Univ Tsinghua Shenzhen Int Grad Sch Shenzhen 518055 Peoples R China Shandong Univ Key Lab Cryptol Technol & Informat Secur Minist Educ Qingdao 266237 Peoples R China Shandong Univ Sch Cyber Sci & Technol Qingdao 266237 Peoples R China Huawei Technol Co Ltd Shenzhen 518055 Guangdong Peoples R China

From the perspective of parity-check matrices, we present new constructions of q -ary maximum distance separable (MDS) array codes with multiple parities. Applying these constructions, some new types of MDS array codes with array numbers m-tau can be derived, where gcd(m,q)=1 . Moreover, an explicit construction of binary MDS array codes is also presented. Compared to the existing MDS array codes, one important characteristic of these codes is that their available code lengths are much longer, which is suitable for large-scale storage systems. In some particular cases, the maximum code lengths of these codes and their extension can be up to 2(m-tau) and 2(m-tau)+1 (or 2(m-tau)+2 ), respectively. Moreover, to demonstrate the applicability of our constructed MDS array codes, we present an effective generic decoding method for the erased errors. In particular, when there are no more than three erasures occurring, a scheduled algorithm for the syndrome computation of our explicit construction is further proposed, whose computational complexity is asymptotically optimal. Furthermore, this algorithm can be directly applied to the encoding procedure of their extended form. The simulation shows that our new MDS array codes have better encoding and decoding performances than the corresponding extended RS codes coupled with different algorithms.

关键词： Codes decoding Redundancy Encoding Arrays Computational complexity Symbols Array codes maximum-distance separable codes quasi-cyclic codes Blaum-Roth codes Reed-Solomon codes decoding algorithm syndrome computation

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Two-staged Weighted Bit Flipping (WBF) decoding algorithm for LDPC codes

Two-staged Weighted Bit Flipping (WBF) decoding algorithm fo...

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IEEE International Workshop on Anti-counterfeiting, Security, Identification, ASID

作者： Kexiang Ma Jing Jin Wei Li Peng Zhang China Academy of Electronics and Information Technology Beijing China Beijing Institute of Astronautical Systems Engineering Beijing China Beijing Institute of Nearspace Vehicle's Systems Engineering Beijing China Northwest Regional Air Traffic Management Bureau of CAAC Xi'an China

In this paper, a two-staged decoding strategy which can be used for the Weighted Bit Flipping (WBF) based decoding algorithm for LDPC codes is presented. At the two stages, a parallel WBF and bit-flipping (BF) algorithms are adopted separately. Correspondingly, by the study of the iterative decoding process of the PWBF algorithm, a simple function is introduced to dynamically implement the switch of two decoding stages. The proposed algorithm can noticeably lower the error floor of PWBF algorithm with a modest increase in computation complexity and hardware cost. The validation of the proposed algorithm is verified by simulation.

关键词： LDPC error floor weighted bit flipping low density parity check codes error floor decoding algorithm bit flipping

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decoding algorithm of LDPC codes for Cascaded BSC-AWGN channels

Decoding Algorithm of LDPC codes for Cascaded BSC-AWGN chann...

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Annual Summit and Conference of Asia-Pacific-Signal-and-Information-Processing-Association (APSIPA)

作者： Phakphisut, Watid Supnithi, Pornchai King Mongkuts Inst Technol Ladkrabang Fac Engn Bangkok 10520 Thailand

ISBN: (纸本)9786163618238

The written-in errors in bit patterned media (BPM) recording systems cause the erroneous bits during the writing process, leading to performance degradation. In previous works, the BPM read/write channel is modeled as a binary symmetric channel (BSC) with an additive white Gaussian noise (AWGN) channel or the cascaded BSC-AWGN channels. The initial channel information including the written-in errors probability has been proposed for low-density parity check (LDPC) decoder. However, the decoding algorithm remains the same as in the case of AWGN channels. In this work, we show that the crossover probability of BSC channels will affect the check node processing of LDPC codes. Therefore, we modify the check node computation that takes into account of the crossover probability of BSC channels. The simulation results show that the proposed LDPC decoder outperforms the ones with the conventional and modified likelihood function in terms of the bit error rate performance.

关键词： AWGN channels error statistics parity check codes probability LDPC codes additive white Gaussian noise binary symmetric channel bit error rate bit patterned media recording systems cascaded BSC-AWGN channels channel information crossover probability decoding algorithm erroneous bits low-density parity check decoder modified likelihood function written-in errors Decision support systems decoding Degradation Error probability Media Parity check codes Writing

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