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1

Belhamra, Mohamed Amine, and El Mamoun Souidi. "Error Correcting Network Codes." Computer Networks 197 (October 2021): 108277. http://dx.doi.org/10.1016/j.comnet.2021.108277.

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2

Vladimirov, Sergey, Alexey Gutovskiy, and Artem Fomin. "Linear network coding with forward error correction in wireless packet relaying system." Telecom IT 10, no. 1 (June 15, 2022): 21–33. http://dx.doi.org/10.31854/2307-1303-2022-10-1-21-33.

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Research subject. The paper presents the results of comparing three byte error-correcting codes according to their probabilistic characteristics in a system with network coding. Method. Simulation modeling has been carried out to determine the probabilistic characteristics of byte error-correcting codes for a transmission system with network coding. The principles of coding and decoding of the studied codes are considered. Core results. The probabilistic characteristics of byte error-correcting codes are determined and presented, and recommendations are developed for their use in a transmission system with network coding, depending on its purpose. Practical relevance. The application of the considered error-correcting codes for the construction of transmission systems with network coding is proposed. The applicability of these codes in the development of applied byte protocols that require the use of forward error correction mechanisms in communication channels is noted.
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Prasad, K., and B. Sundar Rajan. "Network-Error Correcting Codes using Small Fields." IEEE Transactions on Communications 62, no. 2 (February 2014): 423–33. http://dx.doi.org/10.1109/tcomm.2014.010414.130329.

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4

SHOOMAN, MARTIN L., and FRANK A. CASSARA. "RELIABILITY OF ERROR CORRECTING CODES ON WIRELESS INFORMATION NETWORKS." International Journal of Reliability, Quality and Safety Engineering 03, no. 04 (December 1996): 283–304. http://dx.doi.org/10.1142/s0218539396000193.

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Error correcting codes are well known techniques for improving bit error rate (BER) performance in digital communication systems and are particularly important in wireless information networks to help establish reliable communication links. This paper examines the effect of coder/decoder circuitry failures on the overall communication system performance. A system analysis of the error correction coding scheme performance must include an evaluation of the reliability of the coder/decoder circuitry because their failures also serve as a source of undetected errors. The parity bit code, Hamming single error correcting and detecting code, and the Reed–Solomon code are included in the study. Results reveal that for applications as described in the text that require low bit error rate and operate at low data rates, the reliability of the coding circuitry can play a significant role in determining overall system performance. In fact, for such error and data rates, a simpler coding scheme with higher circuit reliability may actually be more beneficial than a more complex coding scheme with enhanced error correcting ability but with a higher chip failure rate.
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5

Krishnan, Prasad, and B. Sundar Rajan. "A Matroidal Framework for Network-Error Correcting Codes." IEEE Transactions on Information Theory 61, no. 2 (February 2015): 836–72. http://dx.doi.org/10.1109/tit.2014.2375332.

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6

Razali, Samirah, Kamaruddin Mamat, and Nor Shahniza Kamal Bashah. "Multiple error correction towards optimisation of energy in sensor network." Indonesian Journal of Electrical Engineering and Computer Science 13, no. 3 (March 1, 2019): 1208. http://dx.doi.org/10.11591/ijeecs.v13.i3.pp1208-1220.

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<span>Hybrid ARQ (HARQ) is among the optimum error controls implemented in Wireless Sensor Network as it reduces the overhead from retransmission and error correcting codes. The advancement in WSN includes the usage of high number of nodes and the increase in traffic with large data transmitted among the nodes had concerned the need for a new approach in error control algorithm. This paper proposed the multiple error correction based on HARQ process to aid the changes in channel with proper error correction assignment towards optimising the performances of WSN in terms of bit error rates, remaining energy, and latency for different types of congestion and channel conditions. In this study, we have developed the channel adaptation algorithm that can adapt to sudden changes and demonstrated the optimal error correcting codes as well as adjustment on the transmit power for the given channel condition and congestion presented. From the result analysed, the optimisation between the remaining energy and Bit Error rates happened on the basis of adapting to these different channel condition and congestion to minimize redundancies appended. From the result obtained, we concluded that by using multiple error correction algorithm with the aid of adjustment on the transmit power, the remaining energy can be optimised together with Bit Error rates and the excessive redundancies can be reduced</span>
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7

Samadi-Khaftari, Vahid, Morteza Esmaeili, and Thomas Aaron Gulliver. "Construction of MDS Convolutional Error-Correcting Network Codes Over Cyclic Networks." IEEE Transactions on Communications 65, no. 6 (June 2017): 2305–18. http://dx.doi.org/10.1109/tcomm.2017.2680441.

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8

Manin, Yuri I. "Error-correcting codes and neural networks." Selecta Mathematica 24, no. 1 (October 19, 2016): 521–30. http://dx.doi.org/10.1007/s00029-016-0284-4.

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9

Zhuang, Zhuojun, A. J. Han Vinck, Yuan Luo, and Bin Dai. "Secure error-correcting network codes with side information leakage." IET Communications 9, no. 8 (May 21, 2015): 1068–75. http://dx.doi.org/10.1049/iet-com.2014.0870.

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10

Li, Aoqing, Fan Li, Qidi Gan, and Hongyang Ma. "Convolutional-Neural-Network-Based Hexagonal Quantum Error Correction Decoder." Applied Sciences 13, no. 17 (August 27, 2023): 9689. http://dx.doi.org/10.3390/app13179689.

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Topological quantum error-correcting codes are an important tool for realizing fault-tolerant quantum computers. Heavy hexagonal coding is a new class of quantum error-correcting coding that assigns physical and auxiliary qubits to the vertices and edges of a low-degree graph. The layout of heavy hexagonal codes is particularly suitable for superconducting qubit architectures to reduce frequency conflicts and crosstalk. Although various topological code decoders have been proposed, constructing the optimal decoder remains challenging. Machine learning is an effective decoding scheme for topological codes, and in this paper, we propose a machine learning heavy hexagonal decoder based on a convolutional neural network (CNN) to obtain the decoding threshold. We test our method on heavy hexagonal codes with code distance of three, five, and seven, and increase it to five, seven, and nine by optimizing the RestNet network architecture. Our results show that the decoder thresholding accuracies are about 0.57% and 0.65%, respectively, which are about 25% higher than the conventional decoding scheme under the depolarizing noise model. The proposed decoding architecture is also applicable to other topological code families.
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11

Hillar, Christopher, Tenzin Chan, Rachel Taubman, and David Rolnick. "Hidden Hypergraphs, Error-Correcting Codes, and Critical Learning in Hopfield Networks." Entropy 23, no. 11 (November 11, 2021): 1494. http://dx.doi.org/10.3390/e23111494.

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In 1943, McCulloch and Pitts introduced a discrete recurrent neural network as a model for computation in brains. The work inspired breakthroughs such as the first computer design and the theory of finite automata. We focus on learning in Hopfield networks, a special case with symmetric weights and fixed-point attractor dynamics. Specifically, we explore minimum energy flow (MEF) as a scalable convex objective for determining network parameters. We catalog various properties of MEF, such as biological plausibility, and then compare to classical approaches in the theory of learning. Trained Hopfield networks can perform unsupervised clustering and define novel error-correcting coding schemes. They also efficiently find hidden structures (cliques) in graph theory. We extend this known connection from graphs to hypergraphs and discover n-node networks with robust storage of 2Ω(n1−ϵ) memories for any ϵ>0. In the case of graphs, we also determine a critical ratio of training samples at which networks generalize completely.
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12

Durcek, Viktor, Michal Kuba, and Milan Dado. "Channel Coding in Optical Communication Systems." Transport and Communications 4, no. 2 (2016): 1–5. http://dx.doi.org/10.26552/tac.c.2016.2.1.

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In this paper, an overview of various types of error-correcting codes is present. Three generations of forward error correction methods used in optical communication systems are listed and described. Forward error correction schemes proposed for use in future high-speed optical networks can be found in the third generation of codes.
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13

Berger, Thierry, and Todor Todorov. "Improving the Watermarking Process with Usage of Block Error-Correcting Codes." Serdica Journal of Computing 2, no. 2 (July 24, 2008): 163–80. http://dx.doi.org/10.55630/sjc.2008.2.163-180.

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The emergence of digital imaging and of digital networks has made duplication of original artwork easier. Watermarking techniques, also referred to as digital signature, sign images by introducing changes that are imperceptible to the human eye but easily recoverable by a computer program. Usage of error correcting codes is one of the good choices in order to correct possible errors when extracting the signature. In this paper, we present a scheme of error correction based on a combination of Reed-Solomon codes and another optimal linear code as inner code. We have investigated the strength of the noise that this scheme is steady to for a fixed capacity of the image and various lengths of the signature. Finally, we compare our results with other error correcting techniques that are used in watermarking. We have also created a computer program for image watermarking that uses the newly presented scheme for error correction.
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14

Mei, Fan, Hong Chen, and Yingke Lei. "Blind Recognition of Forward Error Correction Codes Based on Recurrent Neural Network." Sensors 21, no. 11 (June 4, 2021): 3884. http://dx.doi.org/10.3390/s21113884.

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Forward error correction coding is the most common way of channel coding and the key point of error correction coding. Therefore, the recognition of which coding type is an important issue in non-cooperative communication. At present, the recognition of FEC codes is mainly concentrated in the field of semi-blind identification with known types of codes. However, the receiver cannot know the types of channel coding previously in non-cooperative systems such as cognitive radio and remote sensing of communication. Therefore, it is important to recognize the error-correcting encoding type with no prior information. In the paper, we come up with a neoteric method to identify the types of FEC codes based on Recurrent Neural Network (RNN) under the condition of non-cooperative communication. The algorithm classifies the input data into Bose-Chaudhuri-Hocquenghem (BCH) codes, Low-density Parity-check (LDPC) codes, Turbo codes and convolutional codes. So as to train the RNN model with better performance, the weight initialization method is optimized and the network performance is improved. The experimental result indicates that the average recognition rate of this model is 99% when the signal-to-noise ratio (SNR) ranges from 0 dB to 10 dB, which is in line with the requirements of engineering practice under the condition of non-cooperative communication. Moreover, the comparison of different parameters and models show the effectiveness and practicability of the algorithm proposed.
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15

Zhou, Hang, and Guangjun Liu. "Matroidal error correction networks and linear network error correction MDS codes." Wuhan University Journal of Natural Sciences 18, no. 6 (December 2013): 477–83. http://dx.doi.org/10.1007/s11859-013-0960-6.

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16

Chen, Siguang, Meng Wu, and Weifeng Lu. "Compressed error and erasure correcting codes via rank-metric codes in random network coding." International Journal of Communication Systems 25, no. 11 (August 16, 2011): 1398–414. http://dx.doi.org/10.1002/dac.1316.

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17

Zhang, Zhen. "Linear Network Error Correction Codes in Packet Networks." IEEE Transactions on Information Theory 54, no. 1 (January 2008): 209–18. http://dx.doi.org/10.1109/tit.2007.909139.

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18

Pedrosa, Valéria G., and Max H. M. Costa. "Index Coding with Multiple Interpretations." Entropy 24, no. 8 (August 18, 2022): 1149. http://dx.doi.org/10.3390/e24081149.

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The index coding problem consists of a system with a server and multiple receivers with different side information and demand sets, connected by a noiseless broadcast channel. The server knows the side information available to the receivers. The objective is to design an encoding scheme that enables all receivers to decode their demanded messages with a minimum number of transmissions, referred to as an index code length. The problem of finding the minimum length index code that enables all receivers to correct a specific number of errors has also been studied. This work establishes a connection between index coding and error-correcting codes with multiple interpretations from the tree construction of nested cyclic codes. The notion of multiple interpretations using nested codes is as follows: different data packets are independently encoded, and then combined by addition and transmitted as a single codeword, minimizing the number of channel uses and offering error protection. The resulting packet can be decoded and interpreted in different ways, increasing the error correction capability, depending on the amount of side information available at each receiver. Motivating applications are network downlink transmissions, information retrieval from datacenters, cache management, and sensor networks.
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19

Jose Raj, M., and Dr Sharmini Enoch. "Performance analysis of highly improved hybrid turbo codes for 4G wireless networks." International Journal of Engineering & Technology 8, no. 4 (October 19, 2019): 398. http://dx.doi.org/10.14419/ijet.v8i4.20841.

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Efficient error correcting codes are essential in modern digital communication systems. Highly Improved Hybrid Turbo Code (HIHTC) is a low complex error and efficient error correcting code with excellentBit Error Rate (BER) which is comparable to Low Complexity Hybrid Turbo Codes (LCHTC), Improved Low Complexity Hybrid Turbo Codes (ILCHTC) and other Hybrid Turbo Codes. Rate 1/3 HIHTC shows a BER of 10-5 for E b/No of 1.7 dB which is closer to the E b/No of Improved Low Complexity Hybrid Turbo Codes. In this paper we analyze the performance of HIHTC in comparison with otherLow Complexity Hybrid Turbo Codes, for their performance in 4G and 5G wireless networks
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20

Esposito, Anna, Salvatore Rampone, and Roberto Tagliaferri. "A neural network for error correcting decoding of binary linear codes." Neural Networks 7, no. 1 (January 1994): 195–202. http://dx.doi.org/10.1016/0893-6080(94)90068-x.

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21

MATSUMOTO, R. "Construction Algorithm for Network Error-Correcting Codes Attaining the Singleton Bound." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E90-A, no. 9 (September 1, 2007): 1729–35. http://dx.doi.org/10.1093/ietfec/e90-a.9.1729.

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22

Zhang, Guangzhi, Shaobin Cai, and Dongqiu Zhang. "The Nonlinear Network Coding and Its Application in Error-Correcting Codes." Wireless Personal Communications 102, no. 2 (December 19, 2017): 831–60. http://dx.doi.org/10.1007/s11277-017-5109-z.

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23

Jorge Fernandez-Mayoralas and Raouia Masmoudi Ghodhbane. "Performance of a parallel Hamming coding in short-frame OFDM sensor's network." ITU Journal on Future and Evolving Technologies 2, no. 1 (April 12, 2021): 77–88. http://dx.doi.org/10.52953/tdhg1720.

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In this paper, we focus on the most relevant Error Correcting Codes (ECCs): the Hamming code and the Reed-Solomon code in order to meet the trade-off between the low implementation complexity and the high error correction capacity in a short-frame OFDM communication system. Moreover, we discuss and validate via simulations this trade-off between complexity (Hamming is the easiest to code) and error correction capability (Reed-Solomon being the most effective). Therefore, we have to either improve the correction capacity of the Hamming code, or decrease the complexity cost for the Reed-Solomon code. Based on this analysis, we propose a new design of parallel Hamming coding. On the one hand, we validate this new model of parallel Hamming coding with numerical results using MATLAB-Simulink tools and BERTool Application which makes easier the Bit Error Rate (BER) performance simulations. On the other hand, we implement the design of this new model on an FPGA mock-up and we show that this solution of a parallel Hamming encoder/decoder uses a few resources (LUTs) and has a higher capability of correcting when compared to the simple Hamming code.
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24

Yang, Xiao-Lin, Yu-Mei Chen, and Bin Zhou. "Constructing Error Correcting Codes for Wireless Sensor Networks." Information Technology Journal 9, no. 8 (November 1, 2010): 1758–60. http://dx.doi.org/10.3923/itj.2010.1758.1760.

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25

Kadel, Rajan, Krishna Paudel, Deepani B. Guruge, and Sharly J. Halder. "Opportunities and Challenges for Error Control Schemes for Wireless Sensor Networks: A Review." Electronics 9, no. 3 (March 19, 2020): 504. http://dx.doi.org/10.3390/electronics9030504.

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Error Correction Schemes (ECSs) significantly contribute to enhancing reliability and energy efficiency of Wireless Sensor Networks (WSNs). This review paper offers an overview of the different types of ECS used in communication systems and a synopsis of the standards for WSN. We also discuss channels and network models for WSN as they are crucial for efficient ECS design and implementation. The literature review conducted on the proposed energy consumption and efficiency models for WSN indicates that existing research work has not considered Single Hop Asymmetric Structure (SHAS) with high performing Error Correcting Codes (ECCs). We present a review on proposed ECS for WSN based on three criteria: Forward Error Correction (FEC), adaptive error correction techniques, and other techniques. Based on our review work, we found that there are limited works on ECS design on a realistic network model i.e., a modified multi-hop WSN model. Finally, we offer future research challenges and opportunities on ECS design and implementation for WSN.
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26

Chen, Si Guang, Meng Wu, and Wei Feng Lu. "Secret Error-Correcting Network Coding against Eavesdropping and Pollution Attacks." Advanced Materials Research 457-458 (January 2012): 1499–507. http://dx.doi.org/10.4028/www.scientific.net/amr.457-458.1499.

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In this work we consider the problem of designing a secret error-correcting network coding scheme against an adversary that can re-select the tapping links in different time slot and inject z erroneous packets into network. We first derive a necessary condition for keeping the transmitted information secret from the adversary, while the network is only subject to the eavesdropping attack. We then design an error-correcting scheme by combining the rank-metric codes with shared secret model, which can decode the transmitted information correctly provided a sufficiently large q. With that, a secret error-correcting network coding is proposed by combining this error-correcting scheme with secret communication. We show that under the requirement of communication can achieve a rate of packets. Moreover, it ensures that the communicated information is reliable and information-theoretic security from the adversary. In particular, the requirement of packet length is not as large as the required in [12]. Finally, the security and performance analyses illustrate the characteristics of our scheme.
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27

Xue, Yun-Jia, Hao-Wen Wang, Yan-Bing Tian, Yi-Nuo Wang, Yu-Xuan Wang, and Shu-Mei Wang. "Quantum Information Protection Scheme Based on Reinforcement Learning for Periodic Surface Codes." Quantum Engineering 2022 (July 18, 2022): 1–9. http://dx.doi.org/10.1155/2022/7643871.

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Quantum information transfer is an information processing technology with high speed and high entanglement with the help of quantum mechanics principles. To solve the problem of quantum information getting easily lost during transmission, we choose topological quantum error correction codes as the best candidate codes to improve the fidelity of quantum information. The stability of topological error correction codes brings great convenience to error correction. The quantum error correction codes represented by surface codes have produced very good effects in the error correction mechanism. In order to solve the problem of strong spatial correlation and optimal decoding of surface codes, we introduced a reinforcement learning decoder that can effectively characterize the spatial correlation of error correction codes. At the same time, we use a double-layer convolutional neural network model in the confrontation network to find a better error correction chain, and the generation network can approach the best correction model, to ensure that the discriminant network corrects more nontrivial errors. To improve the efficiency of error correction, we introduced a double-Q algorithm and ResNet network to increase the error correction success rate and training speed of the surface code. Compared with the previous MWPM 0.005 decoder threshold, the success rate has slightly improved, which can reach up to 0.0068 decoder threshold. By using the residual neural network architecture, we saved one-third of the training time and increased the training accuracy to about 96.6%. Using a better training model, we have successfully increased the decoder threshold from 0.0068 to 0.0085, and the depolarized noise model being used does not require a priori basic noise, so that the error correction efficiency of the entire model has slightly improved. Finally, the fidelity of the quantum information has successfully improved from 0.2423 to 0.7423 by using the error correction protection schemes.
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28

Bassalygo, L. A. "Nonbinary Error-Correcting Codes with One-Time Error-Free Feedback." Problems of Information Transmission 41, no. 2 (April 2005): 125–29. http://dx.doi.org/10.1007/s11122-005-0017-3.

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29

Guang, Xuan, Fang-Wei Fu, and Zhen Zhang. "Construction of Network Error Correction Codes in Packet Networks." IEEE Transactions on Information Theory 59, no. 2 (February 2013): 1030–47. http://dx.doi.org/10.1109/tit.2012.2222344.

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30

Magzoub, Mohammed Ahmed, Azlan Abd Aziz, Mohammed Ahmed Salem, Hadhrami Ab Ghani, Azlina Abdul Aziz, and Azwan Mahmud. "Physical layer security and energy efficiency over different error correcting codes in wireless sensor networks." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 6 (December 1, 2020): 6673. http://dx.doi.org/10.11591/ijece.v10i6.pp6673-6681.

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Despite the rapid growth in the market demanding for wireless sensor networks (WSNs), they are far from being secured or efficient. WSNs are vulnerable to malicious attacks and utilize too much power. At the same time, there is a significant increment of the security threats due to the growth of the several applications that employ wireless sensor networks. Therefore, introducing physical layer security is considered to be a promising solution to mitigate the threats. This paper evaluates popular coding techniques like Reed solomon (RS) techniques and scrambled error correcting codes specifically in terms of security gap. The difference between the signal to nose ratio (SNR) of the eavesdropper and the legitimate receiver nodes is defined as the security gap. We investigate the security gap, energy efficiency, and bit error rate between RS and scrambled t-error correcting codes for wireless sensor networks. Lastly, energy efficiency in RS and Bose-Chaudhuri-Hocquenghem (BCH) is also studied. The results of the simulation emphasize that RS technique achieves similar security gap as scrambled error correcting codes. However, the analysis concludes that the computational complexities of the RS is less compared to the scrambled error correcting codes. We also found that BCH code is more energy-efficient than RS.
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31

Partala, Juha. "Semantically Secure Symmetric Encryption with Error Correction for Distributed Storage." Security and Communication Networks 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/4321296.

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A distributed storage system (DSS) is a fundamental building block in many distributed applications. It applies linear network coding to achieve an optimal tradeoff between storage and repair bandwidth when node failures occur. Additively homomorphic encryption is compatible with linear network coding. The homomorphic property ensures that a linear combination of ciphertext messages decrypts to the same linear combination of the corresponding plaintext messages. In this paper, we construct a linearly homomorphic symmetric encryption scheme that is designed for a DSS. Our proposal provides simultaneous encryption and error correction by applying linear error correcting codes. We show its IND-CPA security for a limited number of messages based on binary Goppa codes and the following assumption: when dividing a scrambled generator matrix G^ into two parts G1^ and G2^, it is infeasible to distinguish G2^ from random and to find a statistical connection between G1^ and G2^. Our infeasibility assumptions are closely related to those underlying the McEliece public key cryptosystem but are considerably weaker. We believe that the proposed problem has independent cryptographic interest.
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32

Zigangirov, K. Sh, A. E. Pusane, D. K. Zigangirov, and D. J. Costello. "On the error-correcting capability of LDPC codes." Problems of Information Transmission 44, no. 3 (September 2008): 214–25. http://dx.doi.org/10.1134/s0032946008030046.

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33

Sansoda, Buncha, and Somsak Choomchuay. "Performance Evaluation of Concatenate Coding for Body Area Network Applications." Advanced Materials Research 931-932 (May 2014): 932–36. http://dx.doi.org/10.4028/www.scientific.net/amr.931-932.932.

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In digital communications, since it is of importance that the receiving data is identical to the transmitted data, the error correcting code is one good solution to maintaining the information accuracy between the transmitter and the receiver. This research paper proposes the application of the error correcting code to Wireless Body Area Network (WBAN). The error correcting code in this research work is the concatenate code of the Reed-Solomon code (RS) and the convolutional code (CC). Information data in WBAN with the Rician channel condition is modulated with the Binary Phase Shift Keying (BPSK) scheme. In addition, the path loss of WBAN is examined. The Additive White Gaussian Noise (AWGN) and Rayleigh fading channels are employed for comparison purposes to illustrate the effects on bit error performance of different channel environments. The RS code is an outer code while the convolutional code an inner code. The findings show that the concatenate code performs better than the single codes, i.e. RS and CC. At BER 10-3, the concatenate code {RS(255,223)+CC(171,133)} is better than either RS(255,223) at 5dB or CC(171,133) at 1.5dB. If the inner code is changed to CC(7,5) at BER 10-3, the performance is reduced by approximately 0.6dB. Thus, the coding complexity can be tailored according to the desired error correcting capability.
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34

Beeharry, Yogesh, Tulsi P. Fowdur, and Krishnaraj M. S. Soyjaudah. "Performance of Hybrid Binary and Non-Binary Turbo Decoding Schemes for LTE and DVB-RCS Standards." ECTI Transactions on Electrical Engineering, Electronics, and Communications 17, no. 1 (September 9, 2019): 1–13. http://dx.doi.org/10.37936/ecti-eec.2019171.215363.

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Binary and Non-Binary Turbo codes have been deployed in several digital communication standards to perform error correction. In order to enhance their error performance, several schemes such as Joint Source Channel Decoding (JSCD), extrinsic information scaling mechanisms, and prioritized QAM constellation mapping have been proposed for improving the error performance of error correcting codes. In this paper, hybrid schemes comprising of JSCD, regression based extrinsic information scaling, and prioritized 16-Quadrature Amplitude Modulation (QAM) with binary and non-binary Turbo codes have been presented. Significant improvement in error performance has been observed with the proposed scheme as compared to the conventional one. The hybrid scheme in the case of binary symmetric and asymmetric LTE Turbo codes, and triple binary Turbo codes outperform the conventional scheme by 0.8 dB on average. With duo-binary Turbo codes for the DVB-RCS standard, the hybrid scheme outperforms the conventional one with an average gain of 0.9 dB in BER performance.
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35

Noori Ghanim, Zainab, and Fadia Noori Hummadi Al-Nuaimy. "Variable length error correcting code for image in OFDM and PAPR reduction." Indonesian Journal of Electrical Engineering and Computer Science 27, no. 2 (August 1, 2022): 859. http://dx.doi.org/10.11591/ijeecs.v27.i2.pp859-866.

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Data <span>transmission in orthogonal frequency division multiplexing (OFDM) system needs source and channel coding, the transmitted data suffers from the bad effect of large peak to average power ratio (PAPR). Source code and channel codes can be joined using different joined codes. Variable length error correcting code (VLEC) is one of these joined codes. VLEC is used in mat lab simulation for image transmission in OFDM system, different VLEC code length is used and compared to find that the PAPR decreased with increasing the code length. Several techniques are used and compared for PAPR reduction. The PAPR of OFDM signal is measured for image coding with VLEC and compared with image coded by Huffman source coding and Bose-Chaudhuri-Hochquenghem (BCH) channel coding, the VLEC code decreases the data transmitted size and keep the same level of PAPR reduction with respect to data coded by Huffman and BCH code when using PAPR reduction methods.</span>
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36

Abed, Hamdan Kadhim, and Wameedh Nazar Flayyih. "Comparative Reliability Analysis between Horizontal-Vertical-Diagonal Code and Code with Crosstalk Avoidance and Error Correction for NoC Interconnects." Journal of Engineering 29, no. 7 (July 1, 2023): 120–36. http://dx.doi.org/10.31026/j.eng.2023.07.08.

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Ensuring reliable data transmission in Network on Chip (NoC) is one of the most challenging tasks, especially in noisy environments. As crosstalk, interference, and radiation were increased with manufacturers' increasing tendency to reduce the area, increase the frequencies, and reduce the voltages. So many Error Control Codes (ECC) were proposed with different error detection and correction capacities and various degrees of complexity. Code with Crosstalk Avoidance and Error Correction (CCAEC) for network-on-chip interconnects uses simple parity check bits as the main technique to get high error correction capacity. Per this work, this coding scheme corrects up to 12 random errors, representing a high correction capacity compared with many other code schemes. This candidate has high correction capability but with a high codeword size. In this work, the CCAEC code is compared to another well-known code scheme called Horizontal-Vertical-Diagonal (HVD) error detecting and correcting code through reliability analysis by deriving a new accurate mathematical model for the probability of residual error Pres for both code schemes and confirming it by simulation results for both schemes. The results showed that the HVD code could correct all single, double, and triple errors and failed to correct only 3.3 % of states of quadric errors. In comparison, the CCAEC code can correct a single error and fails in 1.5%, 7.2%, and 16.4% cases of double, triple, and quadric errors, respectively. As a result, the HVD has better reliability than CCAEC and has lower overhead; making it a promising coding scheme to handle the reliability issues for NoC.
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37

Schlingemann, D. "Logical network implementation for graph codes and cluster states." Quantum Information and Computation 3, no. 5 (2003): 431–49. http://dx.doi.org/10.26421/qic3.5-4.

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In a previous paper a straight forward construction method for quantum error correcting codes, based on graphs, has been presented. These graph codes are directly related to cluster states which have been introduced by Briegel and Raussendorf. We show that the preparation of a cluster state as well as the coding operation for a graph code, can be implemented by a logical network by only using one type of two-qubit gate, e.g. CNOT or controlled Phase, and one type of one-qubit gate, e.g. the Hadamard transform. Concerning the qubit case each vertex corresponds to an Hadamard gate and each edge corresponds to a controlled not gate.
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38

KENDZIORRA, ANDREAS, and STEFAN E. SCHMIDT. "NETWORK CODING WITH MODULAR LATTICES." Journal of Algebra and Its Applications 10, no. 06 (December 2011): 1319–42. http://dx.doi.org/10.1142/s0219498811005208.

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Kötter and Kschischang presented in 2008 a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this alphabet is the map d : (U, V) ↦ dim (U+V)- dim (U∩V). In this paper we generalize this model to arbitrary modular lattices, i.e. we consider codes, which are subsets of modular lattices. The used metric in this general case is the map d : (u, v) ↦ h(u ∨ v) - h(u ∧ v), where h is the height function of the lattice. We apply this model to submodule lattices. Moreover, we show a method to compute the size of spheres in certain modular lattices and present a sphere packing bound, a sphere covering bound, and a Singleton bound for codes, which are subsets of modular lattices.
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39

Tyncherov, Kamil T., Vyacheslav Sh Mukhametshin, Victor A. Krasnobaev, and Maria V. Selivanova. "Error Control Coding Algorithms in High Reliability Telemetry Systems." Symmetry 14, no. 7 (July 1, 2022): 1363. http://dx.doi.org/10.3390/sym14071363.

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In the oil and gas industry, in the process of drilling support (geosteering) and well telemetry, there is a problem of transmitting reliable information via wireless communication channels. The quality of such communication, as a rule, suffers due to the presence of errors caused by interference. As the depth of the well increases, the problem becomes more extensive. In order to solve the problem, it is proposed to choose noise-resistant coding in the system of residual classes. This system parallelizes the execution of arithmetic operations, has corrective abilities and organically adapts to the neural network basis of intelligent field management. At the same time, there are constraining factors for the mass application of the RNS; for example, difficulties in implementing non-modular procedures, forward and reverse coding, and some difficulties in identifying and correcting errors. That is why the task of improving the RNS seems relevant not only for oil and gas complexes, but also for any digital signal processing applications focused on intelligent neural network management on the basis of non-positional computing. The material of the article is limited to the study of the noise immunity of linear codes of the deduction system and the development of algorithms for detecting and correcting errors.
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40

Wang, Qiwen, and Sidharth Jaggi. "End-to-End Error-Correcting Codes on Networks With Worst-Case Bit Errors." IEEE Transactions on Information Theory 64, no. 6 (June 2018): 4467–79. http://dx.doi.org/10.1109/tit.2018.2817801.

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41

Vempaty, Aditya, Yunghsiang S. Han, and Pramod K. Varshney. "Target Localization in Wireless Sensor Networks Using Error Correcting Codes." IEEE Transactions on Information Theory 60, no. 1 (January 2014): 697–712. http://dx.doi.org/10.1109/tit.2013.2289859.

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42

Van Wonterghem, Johannes, Amira Alloum, Joseph Jean Boutros, and Marc Moeneclaey. "On short-length error-correcting codes for 5G-NR." Ad Hoc Networks 79 (October 2018): 53–62. http://dx.doi.org/10.1016/j.adhoc.2018.06.005.

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43

Goto, Munehiro. "Examples of single-error-correcting perfect BCD-AN codes." Electronics and Communications in Japan (Part I: Communications) 70, no. 4 (1987): 55–62. http://dx.doi.org/10.1002/ecja.4410700406.

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44

Cao, Qian, Hao-Wen Wang, Ying-Jie Qu, Yun-Jia Xue, and Shu-Mei Wang. "Quantum Teleportation Error Suppression Algorithm Based on Convolutional Neural Networks and Quantum Topological Semion Codes." Quantum Engineering 2022 (November 24, 2022): 1–10. http://dx.doi.org/10.1155/2022/6245336.

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Quantum error correction (QEC) is a key technique for building scalable quantum computers that can be used to mitigate the effects of errors on physical quantum bits. Since quantum states are more or less affected by noise, errors are inevitable. Traditional QEC codes face huge challenges. Therefore, designing an error suppression algorithm based on neural networks (NN) and quantum topological error correction (QTEC) codes is particularly important for quantum teleportation. In this paper, QTEC codes: semion codes—a greater than 2 dimensional (2D) error correction code based on the double semion model—are used to suppress errors during quantum teleportation, using a NN to build a decoder based on semion codes and to simulate the quantum information error suppression process and the suppression effect. The proposed convolutional neural network (CNN) decoder is suitable for small distance topological semion codes. The aim is to optimize the NN for better decoder performance while deriving the relationship between decoder performance and slope and pseudothreshold during training and calculate the thresholds for different noise areas when the code distances are the same, P t h r e s h o l d = 0.082 for A r e a < 0.007 d B and P t h r e s h o l d = 0.096 for A r e a < 0.01 d B . This paper demonstrates the ability of CNNs to suppress errors in quantum transmission information and the great potential of NNs in the field of quantum computing.
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Li, Chao, Zhiyong Feng, and Chao Xu. "Error-correcting output codes for multi-label emotion classification." Multimedia Tools and Applications 75, no. 22 (May 28, 2016): 14399–416. http://dx.doi.org/10.1007/s11042-016-3608-7.

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46

Guang, Xuan, Fang-Wei Fu, and Zhen Zhang. "Variable-Rate Linear Network Error Correction MDS Codes." IEEE Transactions on Information Theory 62, no. 6 (June 2016): 3147–64. http://dx.doi.org/10.1109/tit.2016.2550522.

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47

Schaathun, Hans Georg. "On error-correcting fingerprinting codes for use with watermarking." Multimedia Systems 13, no. 5-6 (September 19, 2007): 331–44. http://dx.doi.org/10.1007/s00530-007-0096-7.

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48

Wang, Jiao, Jianqing Li, Hao Huang, and Hong Wang. "Fine-grained recognition of error correcting codes based on 1-D convolutional neural network." Digital Signal Processing 99 (April 2020): 102668. http://dx.doi.org/10.1016/j.dsp.2020.102668.

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49

Chopra, Shakti Raj, Akhil Gupta, Sudeep Tanwar, Calin Ovidiu Safirescu, Traian Candin Mihaltan, and Ravi Sharma. "Multi-User Massive MIMO System with Adaptive Antenna Grouping for Beyond 5G Communication Network." Mathematics 10, no. 19 (October 3, 2022): 3621. http://dx.doi.org/10.3390/math10193621.

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Error-correcting codes with limited errors and higher spectral efficiency are the main concern for wireless communications. In the current situation, research is increasing daily to satisfy the growing demand for users with improved QoS. Adaptive Antenna Grouping (AAG) with a multilevel space–time trellis coding scheme in the Multi-User Massive MIMO system is the better option to provide flexible data transfer speeds, encoding gains, and gain in diversity with improved spectral efficiency and low decoding complexity, including the power optimization by reduced SNR at the same Symbol Error Rate/Frame Error Rate (SER/FER). The prior aim of maintaining spectral efficiency is achieved by using Massive MIMO. This paper presents the AAG according to the channel state information in the Massive MIMO scenario. The impact of the proposed model on standard ITU-R M.2135 scenarios is also demonstrated in this paper.
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50

Song, Yang, Qiyu Kang, and Wee Peng Tay. "Error-Correcting Output Codes with Ensemble Diversity for Robust Learning in Neural Networks." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 11 (May 18, 2021): 9722–29. http://dx.doi.org/10.1609/aaai.v35i11.17169.

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Though deep learning has been applied successfully in many scenarios, malicious inputs with human-imperceptible perturbations can make it vulnerable in real applications. This paper proposes an error-correcting neural network (ECNN) that combines a set of binary classifiers to combat adversarial examples in the multi-class classification problem. To build an ECNN, we propose to design a code matrix so that the minimum Hamming distance between any two rows (i.e., two codewords) and the minimum shared information distance between any two columns (i.e., two partitions of class labels) are simultaneously maximized. Maximizing row distances can increase the system fault tolerance while maximizing column distances helps increase the diversity between binary classifiers. We propose an end-to-end training method for our ECNN, which allows further improvement of the diversity between binary classifiers. The end-to-end training renders our proposed ECNN different from the traditional error-correcting output code (ECOC) based methods that train binary classifiers independently. ECNN is complementary to other existing defense approaches such as adversarial training and can be applied in conjunction with them. We empirically demonstrate that our proposed ECNN is effective against the state-of-the-art white-box and black-box attacks on several datasets while maintaining good classification accuracy on normal examples.
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