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Annual Allerton Conference on Communication, Control, and Computing

作者： Yi Lu Andrea Montanari Balaji Prabhakar Department of Electrical Engineering Stanford University Departments of Electrical Engineering and Statistics Stanford University

ISBN: (纸本)9781424429257

A novel counter architecture, called Counter Braids, has recently been proposed for per-flow counting on high-speed links. Counter Braids has a layered structure and compresses the flow sizes as it counts. It has been shown that with a Maximum Likelihood (ML) decoding algorithm, the number of bits needed to store the size of a flow matches the entropy lower bound. As ML decoding is too complex to implement, an efficient message passing decoding algorithm has been proposed for practical purposes. The layers of Counter Braids are decoded sequentially, from the most significant to the least significant bits. In each layer, the message passing decoder solves a sparse signal recovery problem. In this paper we analyze the threshold dimensionality reduction rate (d-rate) of the message passing algorithm, and prove that it is correctly predicted by density evolution. Given a signal in R_+~n with TIE non-vanishing entries, we prove that one layer of Counter Braids can reduce its dimensionality by a factor 2.08·εlog(l/ε) + O(ε). This essentially matches the rate for sparse signal recovery via L_1 minimization, while keeping the overall complexity linear in n.

关键词： decoding algorithm message passing BRAIDING Signal restoration Counters Drill bits Pheromone a-Factor one layer

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Fast decoding algorithm of [256, 252] RS extended code

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Dianzi Yu Xinxi Xuebao/Journal of Electronics and Information Technology 2005年第12期27卷 1947-1951页

作者： Zhang, Yu-Liang Chen, Xiao-Min Center for Space Science and Applied Research Chinese Academy of Sciences Beijing 100080 China Graduate School Chinese Academy of Sciences Beijing 100039 China

In this article, the main point is to describe the fast decoding algorithm of [256,252] RS extended code. In order to correct the error in the received data quickly, the algorithm gets the error type and error pattern through simple parameter-comparison, then adds the error pattern to the receive data. Compared to the algorithms in existence, this algorithm has the advantages of using less hardware resources and decoding time. When this algorithm implements in hardware, its throughput is more than 400Mbit/s.

关键词： decoding algorithm RS extended code

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decoding algorithms of Twisted GRS Codes and Twisted Goppa Codes

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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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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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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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Coding properties and automorphism groups of two classes of twisted generalized Reed-Solomon codes

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DESIGNS CODES AND CRYPTOGRAPHY 2025年 1-27页

作者： Jia, Xue Yue, Qin Sun, Huan Nanjing Univ Aeronaut & Astronaut Sch Math Nanjing 211100 Peoples R China Hubei Univ Hubei Key Lab Appl Math Wuhan 430071 Peoples R China Nanjing Univ Posts & Telecommun Coll Sci Nanjing 210023 Peoples R China

Twisted generalized Reed-Solomon (TGRS) codes as a generalization of generalized Reed-Solomon (GRS) codes have attracted a lot of attention from many researchers in recent years. In this paper, we investigate the conditions for the equality of two classes of TGRS codes with different parameters. Moreover, we construct the permutation automorphism groups of two classes of TGRS codes and show they are quasi-cyclic codes. Finally, building upon the Berlekamp-Massey algorithm for GRS codes, we show a decoding scheme for a class of MDS TGRS codes.

关键词： Twisted generalized Reed-Solomon codes Code equivalence Automorphism group decoding algorithm

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Magnetic Linear Encoder Based on Fuzzy Transition algorithm

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2025年 74卷

作者： Kang, Jian Dai, Yong Li, Huan Zhao, Jiarui Zhao, Yitao Hao, Shuanghui Harbin Inst Technol Sch Mechatron Engn Lab Intelligent Equipment Technol Harbin 150001 Peoples R China Shandong Taizhan Electromech Technol Co Ltd Zibo 255130 Peoples R China Shanxi Mech & Elect Design & Res Inst Co Ltd Taiyuan 030009 Peoples R China

In the research into linear displacement sensors, the main research targets are optical grating and magnetic grating-based displacement sensors. However, magnetic grating and optical grating techniques are horizontal measurement methods, which basically require a sliding substrate, a read head, and other components. The resulting magnetic grating or optical grating-based displacement sensors are large in size and cannot realize displacement measurements in small space or vertical measurement scenarios. In this article, a novel and highly accurate linear displacement sensor is designed for use in small space and vertical measurements that uses a completely different structure to conventional magnetic grating or optical grating-based displacement sensors. The proposed magnetic linear displacement sensor consists of two components: a moving shaft with nested magnets and a printed circuit board (PCB) that does not need a moving substrate or a sliding guide. The proposed sensor offers a simple structure, small size, high measurement stability, and high environmental adaptability. The sensor has a completely new structure, and no similar structural design has been reported in the current literature. A permanent magnet ring, an anti-oscillation interference structure, and a system circuit are designed in this article, and the possible oscillating interference, deterministic error, and random interference error characteristics of the sensor are analyzed. A linear displacement sensor decoding algorithm based on fuzzy transitions is designed based on the anti-oscillation structure: the corresponding anti-interference algorithm is added to it, and the effectiveness of the fuzzy transition decoding algorithm is then verified. Finally, an experimental platform is designed for nonlinear error calibration and swing error validation, and the performance specifications of the proposed displacement sensor are verified using this platform. The effect of oscillation error suppression i

关键词： Sensors Magnetic sensors Optical sensors Displacement measurement Gratings Optical variables measurement Oscillators Interference Adaptive optics Sensor phenomena and characterization decoding algorithm fuzzy transition linear encoder magnetic grating

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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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An Efficient Weighted Bit-Flipping algorithm for decoding LDPC Codes Based on Log-Likelihood Ratio of Bit Error Probability

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IEICE TRANSACTIONS ON COMMUNICATIONS 2017年第12期E100B卷 2095-2103页

作者： Chen, Tso-Cho Lu, Erl-Huei Li, Chia-Jung Huang, Kuo-Tsang China Univ Sci & Technol Dept Avion Hsinchu Taiwan Chang Gung Univ Dept Elect Engn Taoyuan Taiwan

In this paper, a weighted multiple bit flipping (WMBF) algorithman for decoding low-density parity-check (LDPC) codes is proposed first. Then the improved WMBF algorithm which we call the efficient weighted bit-flipping (EWBF) algorithm is developed. The EWBF algorithm can dynamically choose either multiple bit-flipping or single bit-flipping in each iteration according to the log-likelihood ratio of the error probability of the received bits. Thus, it can efficiently increase the convergence speed of decoding and prevent the decoding process from falling into loop traps. Compared with the parallel weighted bit-flipping (PWBF) algorithm, the EWBF algorithm can achieve significantly lower computational complexity without performance degradation when the Euclidean geometry (EG)-LDPC codes are decoded. Furthermore, the flipping criterion does not require any parameter adjustment.

关键词： low-density parity-check codes weighted bit-flipping multiple bit-flipping decoding algorithm log-likelihood ratio convergence speed

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MODIFIED TIME-DOMAIN algorithm FOR decoding REED-SOLOMON CODES

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IEEE TRANSACTIONS ON COMMUNICATIONS 1993年第7期41卷 1036-1038页

作者： SHAYAN, YR LENGOC, T CONCORDIA UNIV DEPT ELECT & COMP ENGNMONTREAL H3G 1M8QUEBECCANADA

A technique to reduce the number of inversions in the time-domain decoding algorithm based on an algebraic decoder (Blahut's decoder) is introduced. It is proved that the modified algorithm is equivalent to the or... 详细信息

关键词： Reed-Solomon codes decoders Inversion decoding algorithm algorithms decoding Modified Equivalent

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