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Journal articles on the topic 'Expander codes decoding algorithm'

Author: Grafiati

Published: 9 October 2021

Last updated: 30 July 2025

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1

FUJITA, H. "Justesen-Type Modified Expander Codes and Their Decoding Algorithm." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E88-A, no. 10 (2005): 2708–14. http://dx.doi.org/10.1093/ietfec/e88-a.10.2708.

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2

Chan, A. M., and F. R. Kschischang. "A simple taboo-based soft-decision decoding algorithm for expander codes." IEEE Communications Letters 2, no. 7 (1998): 183–85. http://dx.doi.org/10.1109/4234.703905.

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3

Old, Josias, and Manuel Rispler. "Generalized Belief Propagation Algorithms for Decoding of Surface Codes." Quantum 7 (June 7, 2023): 1037. http://dx.doi.org/10.22331/q-2023-06-07-1037.

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Belief propagation (BP) is well-known as a low complexity decoding algorithm with a strong performance for important classes of quantum error correcting codes, e.g. notably for the quantum low-density parity check (LDPC) code class of random expander codes. However, it is also well-known that the performance of BP breaks down when facing topological codes such as the surface code, where naive BP fails entirely to reach a below-threshold regime, i.e. the regime where error correction becomes useful. Previous works have shown, that this can be remedied by resorting to post-processing decoders ou

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4

Dowling, Michael, and Shuhong Gao. "Fast Decoding of Expander Codes." IEEE Transactions on Information Theory 64, no. 2 (2018): 972–78. http://dx.doi.org/10.1109/tit.2017.2726064.

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5

Viderman, Michael. "Linear-time decoding of regular expander codes." ACM Transactions on Computation Theory 5, no. 3 (2013): 1–25. http://dx.doi.org/10.1145/2493252.2493255.

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6

Feltstrom, Alberto JimÉnez, Dmitri Truhachev, Michael Lentmaier, and Kamil Sh Zigangirov. "Braided Block Codes." IEEE Transactions on Information Theory 55, no. 6 (2009): 2640–58. http://dx.doi.org/10.1109/tit.2009.2018350.

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A new class of binary iteratively decodable codes with good decoding performance is presented. These codes, called braided block codes (BBCs), operate on continuous data streams and are constructed by interconnection of two component block codes. BBCs can be considered as convolutional (or sliding) version of either Elias' product codes or expander codes. In this paper, we define BBCs, describe methods of their construction, analyze code properties, and study asymptotic iterative decoding performance.

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7

Blaum, Mario, Veera Deenadhayalan, and Steven Hetzler. "Expanded Blaum–Roth Codes With Efficient Encoding and Decoding Algorithms." IEEE Communications Letters 23, no. 6 (2019): 954–57. http://dx.doi.org/10.1109/lcomm.2019.2911286.

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8

Ron-Zewi, Noga, Mary Wootters, and Gilles Zemor. "Linear-Time Erasure List-Decoding of Expander Codes." IEEE Transactions on Information Theory 67, no. 9 (2021): 5827–39. http://dx.doi.org/10.1109/tit.2021.3086805.

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9

Ashikhmin, Alexei, and Vitaly Skachek. "Decoding of Expander Codes at Rates Close to Capacity." IEEE Transactions on Information Theory 52, no. 12 (2006): 5475–85. http://dx.doi.org/10.1109/tit.2006.885510.

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10

Barg, Alexander, and Gilles Zémor. "Error Exponents of Expander Codes under Linear-Complexity Decoding." SIAM Journal on Discrete Mathematics 17, no. 3 (2004): 426–45. http://dx.doi.org/10.1137/s0895480102403799.

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11

Galvez, Lucky, and Jon-Lark Kim. "Projection Decoding of Some Binary Optimal Linear Codes of Lengths 36 and 40." Mathematics 8, no. 1 (2019): 15. http://dx.doi.org/10.3390/math8010015.

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Practically good error-correcting codes should have good parameters and efficient decoding algorithms. Some algebraically defined good codes, such as cyclic codes, Reed–Solomon codes, and Reed–Muller codes, have nice decoding algorithms. However, many optimal linear codes do not have an efficient decoding algorithm except for the general syndrome decoding which requires a lot of memory. Therefore, a natural question to ask is which optimal linear codes have an efficient decoding. We show that two binary optimal [ 36 , 19 , 8 ] linear codes and two binary optimal [ 40 , 22 , 8 ] codes have an e

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12

Wang, Li Na, and Wei Tang. "Decoding Improvement for LT Codes." Applied Mechanics and Materials 394 (September 2013): 499–504. http://dx.doi.org/10.4028/www.scientific.net/amm.394.499.

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In this paper the performance of LT codes is analyzed. And then, for the remaining part of information which can be decoded still exists when decoding failure, an improved message passing decoding algorithm which retains the original algorithm framework is proposed. The simulation results have shown that the improved message passing decoding algorithm improves the decoding rate and reduces decoding overhead on the premise of appropriately increasing decoding complexity.

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13

Ratseev, S. M., and O. I. Cherevatenko. "ON DECODING ALGORITHMS FOR GENERALIZED REED — SOLOMON CODES WITH ERRORS AND ERASURES." Vestnik of Samara University. Natural Science Series 26, no. 3 (2020): 17–29. http://dx.doi.org/10.18287/2541-7525-2020-26-3-17-29.

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The article is devoted to the decoding algorithms for generalized Reed Solomon codes with errorsand erasures. These algorithms are based on Gao algorithm, Sugiyama algorithm, Berlekamp Massey algorithm (Peterson Gorenstein Zierler algorithm). The first of these algorithms belongs to syndrome-free decoding algorithms, the others to syndrome decoding algorithms. The relevance of these algorithms is that they are applicable for decoding Goppa codes, which are the basis of some promising post-quantum cryptosystems. These algorithms are applicable for Goppa codes over an arbitrary field, as opposed

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14

Ge, Li, and Guiping Li. "Optimization and Improvement of BP Decoding Algorithm for Polar Codes Based on Deep Learning." International Journal of Advanced Network, Monitoring and Controls 8, no. 2 (2023): 61–71. http://dx.doi.org/10.2478/ijanmc-2023-0057.

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Abstract In order to solve the high latency problem of polar codes belief propagation decoding algorithm in the 5G and the dimension limitation problem of belief propagation decoding algorithm under deep learning, a multilayer perceptron belief propagation decoding (MLP-BP) algorithm based on partitioning idea is proposed. In this work, polar codes is decoded using neural networks in partitioning, and the right transfer message value of BP decoding algorithm is also set to complete the propagation process. Simulation results show that, compared with BP decoding algorithm, the proposed algorith

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15

Minja, Aleksandar, Dušan Dobromirov, and Vojin Šenk. "Bidirectional stack decoding of polar codes." Vojnotehnicki glasnik 69, no. 2 (2021): 405–15. http://dx.doi.org/10.5937/vojtehg69-29858.

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Introduction/purpose: The paper introduces a reduced latency stack decoding algorithm of polar codes, inspired by the bidirectional stack decoding of convolutional codes and based on the folding technique. Methods: The stack decoding algorithm (also known as stack search) that is useful for decoding tree codes, the list decoding technique introduced by Peter Elias and the folding technique for polar codes which is used to reduce the latency of the decoding algorithm. The simulation was done using the Monte Carlo procedure. Results: A new polar code decoding algorithm, suitable for parallel imp

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16

Kong, Lingjun, Haiyang Liu, Wentao Hou, and Bin Dai. "Improving Decodability of Polar Codes by Adding Noise." Symmetry 14, no. 6 (2022): 1156. http://dx.doi.org/10.3390/sym14061156.

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This paper presents an online perturbed and directed neural-evolutionary (Online-PDNE) decoding algorithm for polar codes, in which the perturbation noise and online directed neuro-evolutionary noise sequences are sequentially added to the received sequence for re-decoding if the standard polar decoding fails. The new decoding algorithm converts uncorrectable received sequences into error-correcting regions of their decoding space for correct decoding by adding specific noises. To reduce the decoding complexity and delay, the PDNE decoding algorithm and sole neural-evolutionary (SNE) decoding

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17

Wang, Li Na, and Xiao Liu. "Improved BP Decoding Algorithm for LDPC Codes." Advanced Materials Research 846-847 (November 2013): 925–28. http://dx.doi.org/10.4028/www.scientific.net/amr.846-847.925.

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In this paper, an improved belief propagation decoding algorithm was proposed for low density parity check codes. In the proposed decoding process, error bits can be detected once again after hard-decision in the conventional BP decoding algorithm. The detection criterion is based on check matrix characteristics and D-value between prior probability and posterior probability. Simulation results demonstrate the performance of the improved BP decoding algorithm outperform that of the conventional BP decoding algorithm.

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18

Wang, Xiumin, Jinlong He, Jun Li, and Liang Shan. "Reinforcement Learning for Bit-Flipping Decoding of Polar Codes." Entropy 23, no. 2 (2021): 171. http://dx.doi.org/10.3390/e23020171.

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A traditional successive cancellation (SC) decoding algorithm produces error propagation in the decoding process. In order to improve the SC decoding performance, it is important to solve the error propagation. In this paper, we propose a new algorithm combining reinforcement learning and SC flip (SCF) decoding of polar codes, which is called a Q-learning-assisted SCF (QLSCF) decoding algorithm. The proposed QLSCF decoding algorithm uses reinforcement learning technology to select candidate bits for the SC flipping decoding. We establish a reinforcement learning model for selecting candidate b

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19

Nazarov, Lev E. "The Decoding Algorithms For Error-Correcting Product Codes Based On Project Geometry Low-Density Parity-Check Codes." Radioelectronics. Nanosystems. Information Technologies 12, no. 3 (2020): 399–406. http://dx.doi.org/10.17725/rensit.2020.12.399.

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The focus of this paper is directed towards the investigation of the characteristics of symbol-by-symbol iterative decoding algorithms for error-correcting block product-codes (block turbo-codes) which enable to reliable information transfer at relatively low received signal/noise and provide high power efficiency. Specific feature of investigated product codes is construction with usage of low-density parity-check codes (LDPC) and these code constructions are in the class of LDPC too. According to this fact the considered code constructions have symbol-by-symbol decoding algorithms developed

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20

V, Sudharsan, Vijay Karthik V, and Yamuna B. "Reliability Level List Based Iterative SISO Decoding Algorithm for Block Turbo Codes." TELKOMNIKA Telecommunication, Computing, Electronics and Control 16, no. 5 (2018): 2040–47. https://doi.org/10.12928/TELKOMNIKA.v16i5.7463.

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An iterative Reliability Level List (RLL) based soft-input soft-output (SISO) decoding algorithm has been proposed for Block Turbo Codes (BTCs). The algorithm ingeniously adapts the RLL based decoding algorithm for the constituent block codes, which is a soft-input hard-output algorithm. The extrinsic information is calculated using the reliability of these hard-output decisions and is passed as softinput to the iterative turbo decoding process. RLL based decoding of constituent codes estimate the optimal transmitted codeword through a directed minimal search. The proposed RLL based decoder fo

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21

Ratseev, S. M., and O. I. Cherevatenko. "ON DECODING ALGORITHMS FOR GENERALIZED REED — SOLOMON CODES WITH ERRORS AND ERASURES. II." Vestnik of Samara University. Natural Science Series 27, no. 2 (2022): 7–15. http://dx.doi.org/10.18287/2541-7525-2021-27-2-7-15.

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The article is a continuation of the authors work On decoding algorithms for generalized Reed Solomon codes with errors and erasures. In this work, another modification of the Gao algorithm and the Berlekamp Massey algorithm is given. The first of these algorithms is a syndrome-free decoding algorithm, the second is a syndrome decoding algorithm. The relevance of these algorithms is that they are applicable for decoding Goppa codes, which are the basis of some promising post-quantum cryptosystems.

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22

Sun, Zeng You, and Huan Huan Li. "Improvement of LDPC Codes Decoding Algorithm in the Application of the Rotational OFDM System." Advanced Materials Research 934 (May 2014): 235–38. http://dx.doi.org/10.4028/www.scientific.net/amr.934.235.

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Because the performance of LDPC codes is better than Turbo codes, convolution codes, etc., so the combination of LDPC codes and the OFDM technology has higher effectiveness. Traditional LDPC decoding algorithm (BP algorithm) exists large amounts of multiplication, division and index calculation, and when decoding cycle, its computational cost will increase exponentially, which not only increases the complexity, and makes the numerical stability of the algorithm deteriorates, therefore, in this paper, we propose an improved decoding algorithm, namely the combination algorithm of Offset-BP-base

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23

HERNANDO, FERNANDO, and DIEGO RUANO. "DECODING OF MATRIX-PRODUCT CODES." Journal of Algebra and Its Applications 12, no. 04 (2013): 1250185. http://dx.doi.org/10.1142/s021949881250185x.

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We propose a decoding algorithm for the (u | u + v)-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two different ways. In some cases, one can decode beyond the error-correction capability of the code.

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24

Martín Sánchez, Sandra, and Francisco J. Plaza Martín. "A Decoding Algorithm for Convolutional Codes." Mathematics 10, no. 9 (2022): 1573. http://dx.doi.org/10.3390/math10091573.

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It is shown how the decoding algorithms of Pellikaan and Rosenthal can be coupled to produce a decoding algorithm for convolutional codes. Bounds for the computational cost per decoded codeword are also computed. As a case study, our results are applied to a family of convolutional codes constructed by Rosenthal–Schumacher–York and, in this situation, the previous bounds turn out to be polynomial on the degree of the code.

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25

Ju, Suming, and Guangguo Bi. "Fast decoding algorithm for RS codes." Electronics Letters 33, no. 17 (1997): 1452. http://dx.doi.org/10.1049/el:19971005.

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26

Lu, Erl-Huei, Chiou-Yng Lee, and Ron-Lon Tsai. "Decoding algorithm for DEC RS codes." Electronics Letters 36, no. 6 (2000): 546. http://dx.doi.org/10.1049/el:20000436.

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27

Azouaoui, Ahmed, Mostafa Belkasmi, and Abderrazak Farchane. "Efficient Dual Domain Decoding of Linear Block Codes Using Genetic Algorithms." Journal of Electrical and Computer Engineering 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/503834.

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A computationally efficient algorithm for decoding block codes is developed using a genetic algorithm (GA). The proposed algorithm uses the dual code in contrast to the existing genetic decoders in the literature that use the code itself. Hence, this new approach reduces the complexity of decoding the codes of high rates. We simulated our algorithm in various transmission channels. The performance of this algorithm is investigated and compared with competitor decoding algorithms including Maini and Shakeel ones. The results show that the proposed algorithm gives large gains over the Chase-2 de

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28

Xu, Jin, Ying Zhao, and Shu Qiang Duan. "Research and Realization by FPGA of Turbo Codes." Advanced Materials Research 588-589 (November 2012): 765–68. http://dx.doi.org/10.4028/www.scientific.net/amr.588-589.765.

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Turbo Code is a channel coding with excellent error-correcting performance in the condition of low noise-signal ratio.It has a superior decoding performance approaching the Shannon limit by adopting the random coding and decoding. This paper focuses on Turbo code and its implementation with FPGA and deeply analyzes the decoding theory and algorithm of Turbo code. Firstly, it analyzes the decoding theory of Turbo code. Then, it discusses key issues in the process of implementation with the most excellent and complicated Max—log—MAP algorithm. At last, it ends up with the Turbo encoder and decod

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29

Wang, Xiumin, Jinlong He, Jun Li, Zhuoting Wu, Liang Shan, and Bo Hong. "Improved Adaptive Successive Cancellation List Decoding of Polar Codes." Entropy 21, no. 9 (2019): 899. http://dx.doi.org/10.3390/e21090899.

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Although the adaptive successive cancellation list (AD-SCL) algorithm and the segmented-CRC adaptive successive cancellation list (SCAD-SCL) algorithm based on the cyclic redundancy check (CRC) can greatly reduce the computational complexity of the successive cancellation list (SCL) algorithm, these two algorithms discard the previous decoding result and re-decode by increasing L, where L is the size of list. When CRC fails, these two algorithms waste useful information from the previous decoding. In this paper, a simplified adaptive successive cancellation list (SAD-SCL) is proposed. Before t

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30

Ratseev, S. M., A. D. Lavrinenko, and E. A. Stepanova. "ON THE BERLEKAMP — MASSEY ALGORITHM AND ITS APPLICATION FOR DECODING ALGORITHMS." Vestnik of Samara University. Natural Science Series 27, no. 1 (2021): 44–61. http://dx.doi.org/10.18287/2541-7525-2021-27-1-44-61.

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The paper is devoted to the Berlekamp Masssey algorithm and its equivalent version based on the extended Euclidean algorithm. An optimized Berlekamp Massey algorithm is also given for the case ofa field of characteristic 2. The Berlekamp Massey algorithm has a quadratic complexity and is used, for example, to solve systems of linear equations in which the matrix of the system is the Toeplitz matrix. In particular, such systems of equations appear in algorithms for the syndrome decoding of BCH codes, Reed Solomon codes, generalized Reed Solomon codes, and Goppa codes. Algorithms for decoding th

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31

Zhong, Fei, and Shu Xu Guo. "Study on a New Joint Source-Channel Decoder Design." Applied Mechanics and Materials 340 (July 2013): 471–75. http://dx.doi.org/10.4028/www.scientific.net/amm.340.471.

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To improve upon the Low-Density Parity-Check (LDPC) codes , incorporating compressed sensing (CS) and information redundancy, a new joint decoding algorithm frame is presented. The proposed system exploits the information redundancy by CS reconstruction during the iterative decoding process to correct decoding of LDPC codes. The simulation results show that the algorithm presented can improve system decoding performance and obviously make bit error ratio (BER) lower then traditional LDPC codes. In addition, a relatively short argument is given on different CS reconstructed algorithms in propos

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32

Zhang, Yingxian, Aijun Liu, Xiaofei Pan, Shi He, and Chao Gong. "A Generalization Belief Propagation Decoding Algorithm for Polar Codes Based on Particle Swarm Optimization." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/606913.

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We propose a generalization belief propagation (BP) decoding algorithm based on particle swarm optimization (PSO) to improve the performance of the polar codes. Through the analysis of the existing BP decoding algorithm, we first introduce a probability modifying factor to each node of the BP decoder, so as to enhance the error correcting capacity of the decoding. Then, we generalize the BP decoding algorithm based on these modifying factors and drive the probability update equations for the proposed decoding. Based on the new probability update equations, we show the intrinsic relationship of

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33

Dinh, Hai Q., Bac T. Nguyen, and Songsak Sriboonchitta. "Skew Constacyclic Codes over Finite Fields and Finite Chain Rings." Mathematical Problems in Engineering 2016 (2016): 1–17. http://dx.doi.org/10.1155/2016/3965789.

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This paper overviews the study of skewΘ-λ-constacyclic codes over finite fields and finite commutative chain rings. The structure of skewΘ-λ-constacyclic codes and their duals are provided. Among other results, we also consider the Euclidean and Hermitian dual codes of skewΘ-cyclic and skewΘ-negacyclic codes over finite chain rings in general and overFpm+uFpmin particular. Moreover, general decoding procedure for decoding skew BCH codes with designed distance and an algorithm for decoding skew BCH codes are discussed.

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34

Li, Shuang, Shicheng Zhang, Zhenxing Chen, and Seog Geun Kang. "A hybrid decoding of Reed–Muller codes." International Journal of Distributed Sensor Networks 13, no. 2 (2017): 155014771668340. http://dx.doi.org/10.1177/1550147716683406.

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In this article, a hybrid decoding algorithm for Reed–Muller codes is presented. Unlike the conventional algorithm, the presented algorithm ends recursive decomposition when [Formula: see text] and [Formula: see text] appeared. A simplified maximum-likelihood algorithm based on fast Hadamard transform is also exploited to decode the systematic code through its special structure. As a result, the presented hybrid decoding algorithm reduces the number of floating-point multiplications significantly as compared with the conventional algorithms. In addition, the new algorithm has better error perf

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35

Zhang, Ji, Anmin Chen, Ying Zhang, Baofeng Ji, Huaan Li, and Hengzhou Xu. "Low-Density Parity-Check Decoding Algorithm Based on Symmetric Alternating Direction Method of Multipliers." Entropy 27, no. 4 (2025): 404. https://doi.org/10.3390/e27040404.

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The Alternating Direction Method of Multipliers (ADMM) has proven to be an efficient approach for implementing linear programming (LP) decoding of low-density parity-check (LDPC) codes. By introducing penalty terms into the LP decoding model’s objective function, ADMM-based variable node penalized decoding effectively mitigates non-integral solutions, thereby improving frame error rate (FER) performance, especially in the low signal-to-noise ratio (SNR) region. In this paper, we leverage the ADMM framework to derive explicit iterative steps for solving the LP decoding problem for LDPC codes wi

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36

Chen, Weigang, Tian Zhao, and Changcai Han. "Soft Decision Decoding with Cyclic Information Set and the Decoder Architecture for Cyclic Codes." Electronics 12, no. 12 (2023): 2693. http://dx.doi.org/10.3390/electronics12122693.

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The soft decision decoding algorithm for cyclic codes, especially the maximum likelihood (ML) decoding algorithm, can obtain significant performance superior to that of algebraic decoding, but the complexity is much higher. To deal with this problem, an improved soft decision decoding algorithm based on a cyclic information set and its efficient implementation architecture are proposed. This algorithm employs the property of the cyclic codes to generate a series of cyclic information sequences by circularly shifting, constructing the cyclic information set. Then, a limited number of candidate

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37

Dong, Jie, Yong Li, Rui Liu, Taolin Guo, and Francis C. M. Lau. "Efficient Decoder for Turbo Product Codes Based on Quadratic Residue Codes." Electronics 11, no. 21 (2022): 3598. http://dx.doi.org/10.3390/electronics11213598.

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In this letter, we study turbo product codes with quadratic residue codes (called QR-TPCs) as the component codes. We propose an efficient decoder based on Chase-II algorithm with two convergence conditions for the iterative decoding of QR-TPCs. For each row and column, the Chase-II decoder will stop immediately when one of the conditions is met. The simulation results show that the proposed algorithm has a lower computational complexity compared with existing decoding methods. Moreover, a comparison with 5G low-density parity-check codes shows that the proposed turbo product codes have better

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38

Poulin, D., and Y. Chung. "On the iterative decoding of sparse quantum codes." Quantum Information and Computation 8, no. 10 (2008): 986–1000. http://dx.doi.org/10.26421/qic.10-8.

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We address the problem of decoding sparse quantum error correction codes. For Pauli channels, this task can be accomplished by a version of the belief propagation algorithm used for decoding sparse classical codes. Quantum codes pose two new challenges however. Firstly, their Tanner graph unavoidably contain small loops which typically undermines the performance of belief propagation. Secondly, sparse quantum codes are by definition highly degenerate. The standard belief propagation algorithm does not exploit this feature, but rather it is impaired by it. We propose heuristic methods to improv

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39

Poulin, D., and Y. Chung. "On the iterative decoding of sparse quantum codes." Quantum Information and Computation 8, no. 10 (2008): 986–1000. http://dx.doi.org/10.26421/qic8.10-8.

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We address the problem of decoding sparse quantum error correction codes. For Pauli channels, this task can be accomplished by a version of the belief propagation algorithm used for decoding sparse classical codes. Quantum codes pose two new challenges however. Firstly, their Tanner graph unavoidably contain small loops which typically undermines the performance of belief propagation. Secondly, sparse quantum codes are by definition highly degenerate. The standard belief propagation algorithm does not exploit this feature, but rather it is impaired by it. We propose heuristic methods to improv

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40

Askali, Mohamed, Fouad Ayoub, Idriss Chana, and Mostafa Belkasmi. "Iterative Soft Permutation Decoding of Product Codes." Computer and Information Science 9, no. 1 (2016): 128. http://dx.doi.org/10.5539/cis.v9n1p128.

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<p>In this paper the performance of product codes based on quadratic residue codes is investigated. Our Proposed<br />Iterative decoding SISO based on a soft permutation decoding algorithm (SPDA) as a component decoder.<br />Numerical result for the proposed algorithm over Additive White Gaussian Noise (AWGN) channel is provided.<br />Results show that the turbo effect of the proposed decoder algorithm is established for this family of quadratic<br />residue codes.</p>

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41

A. Zikry, Abdel Halim, Ashraf Y. Hassan, Wageda I. Shaban, and Sahar F. Abdel-Momen. "Performance Analysis of LDPC Decoding Techniques." International Journal of Recent Technology and Engineering 9, no. 5 (2021): 17–26. http://dx.doi.org/10.35940/ijrte.e5067.019521.

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Low density parity checking codes (LDPC) are one of the most important issues in coding theory at present. LDPC-code are a type of linear-block LDPC-codes. Channel coding might be considered as the finest conversant and most potent components of cellular communications systems, that was employed for transmitting errors corrections imposed by noise, fading and interfering. LDPC-codes are advanced coding gain, i.e., new area in coding. the performances of LDPC-code are similar to the Shannon-limiting, this led to the usage of decoding in several applications in digital communications systems, li

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42

Abdel, Halim A. Zikry, Y. Hassan Ashraf, I. Shaban Wageda, and F. Abdel-Momen Sahar. "Performance Analysis of LDPC Decoding Techniques." International Journal of Recent Technology and Engineering (IJRTE) 9, no. 5 (2021): 17–26. https://doi.org/10.35940/ijrte.E5067.019521.

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<strong>Abstract:</strong> Low density parity checking codes (LDPC) are one of the most important issues in coding theory at present. LDPC-code are a type of linear-block LDPC-codes. Channel coding might be considered as the finest conversant and most potent components of cellular communications systems, that was employed for transmitting errors corrections imposed by noise, fading and interfering. LDPC-codes are advanced coding gain, i.e., new area in coding. the performances of LDPC-code are similar to the Shannon-limiting, this led to the usage of decoding in several applications in digital

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43

Malygina, Ekaterian S., Artem A. Kuninets, Vyacheslav L. Ratochka, Alexandr G. Duplenko, and Daniil Ya Neiman. "Algebraic-geometry codes and decoding by error-correcting pairs." Prikladnaya Diskretnaya Matematika, no. 62 (2023): 83–105. http://dx.doi.org/10.17223/20710410/62/7.

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We consider the basic theory of algebraic curves and their function fields necessary for constructing algebraic geometry codes and a pair of codes forming an error-correction pair which is used in a precomputation step of the decoding algorithm for the algebraic geometry codes. Also, we consider the decoding algorithm and give the necessary theory to prove its correctness. As a result, we consider elliptic curves, Hermitian curves and Klein quartics and construct the algebraic geometry codes associated with these families of curves, and also explicitly define the error-correcting pairs for the

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44

Benedetto, S., D. Divsalar, G. Montorsi, and F. Pollara. "Algorithm for continuous decoding of turbo codes." Electronics Letters 32, no. 4 (1996): 314. http://dx.doi.org/10.1049/el:19960217.

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Shankar, Priti. "Decoding Reed-Solomon codes using Euclid’s algorithm." Resonance 12, no. 4 (2007): 37–51. http://dx.doi.org/10.1007/s12045-007-0037-y.

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46

Raphaeli, D., and A. Gurevitz. "Investigation into decoding algorithm for turbo codes." Electronics Letters 36, no. 9 (2000): 809. http://dx.doi.org/10.1049/el:20000613.

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Puchinger, Sven, Sven Müelich, David Mödinger, Johan Rosenkilde né Nielsen, and Martin Bossert. "Decoding Interleaved Gabidulin Codes using Alekhnovich's Algorithm." Electronic Notes in Discrete Mathematics 57 (March 2017): 175–80. http://dx.doi.org/10.1016/j.endm.2017.02.029.

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Martínez, Consuelo, and Fabián Molina. "The syndromes decoding algorithm in group codes." Finite Fields and Their Applications 89 (August 2023): 102206. http://dx.doi.org/10.1016/j.ffa.2023.102206.

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49

Ivanov, Yu Yu, B. O. Bodnarenko, D. V. Borysiuk, and O. S. Shchyrov. "Modified Algorithm for Decoding Convolutional Turbo-Codes." Visnyk of Vinnytsia Politechnical Institute 178, no. 1 (2025): 86–91. https://doi.org/10.31649/1997-9266-2025-178-1-86-91.

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Wang, Zhong Xun, Fang Qiang Zhu, Li Liu, and Juan Wang. "Loop Detection Based on Bit-Flipping Decoding Algorithm for LDPC Codes." Advanced Materials Research 271-273 (July 2011): 452–57. http://dx.doi.org/10.4028/www.scientific.net/amr.271-273.452.

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Abstract:

In this paper, we introduce a new bit-flipping decoding algorithm for low-density parity-check codes based on loop detection mechanism, which is an extension to soft-decision decoding. This decoding algorithm's performance has been significantly improved by introducing a loop detection mechanism for the failed flipping bit and leading into the soft-decision about the reliability measure of the received symbols. Theoretical analysis shows that the complexity of this algorithm is lower. Some simulation results are given, which show that compared with other known kinds of bit-flipping decoding al

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