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Journal articles on the topic 'Error correction coding'

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Published: 4 June 2021

Last updated: 26 January 2023

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1

Yasunaga, Kenji. "Error Correction by Structural Simplicity: Correcting Samplable Additive Errors." Computer Journal 62, no. 9 (October 5, 2018): 1265–76. http://dx.doi.org/10.1093/comjnl/bxy100.

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Abstract This paper explores the possibilities and limitations of error correction by the structural simplicity of error mechanisms. Specifically, we consider channel models, called samplable additive channels, in which (i) errors are efficiently sampled without the knowledge of the coding scheme or the transmitted codeword; (ii) the entropy of the error distribution is bounded; and (iii) the number of errors introduced by the channel is unbounded. For the channels, several negative and positive results are provided. Assuming the existence of one-way functions, there are samplable additive errors of entropy nε for ε∈(0,1) that are pseudorandom, and thus not correctable by efficient coding schemes. It is shown that there is an oracle algorithm that induces a samplable distribution over {0,1}n of entropy m=ω(logn) that is not pseudorandom, but is uncorrectable by efficient schemes of rate less than 1−m/n−o(1). The results indicate that restricting error mechanisms to be efficiently samplable and not pseudorandom is insufficient for error correction. As positive results, some conditions are provided under which efficient error correction is possible.

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2

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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3

Faure, E. V. "FACTORIAL CODING WITH ERROR CORRECTION." Radio Electronics, Computer Science, Control, no. 3 (November 30, 2017): 130–38. http://dx.doi.org/10.15588/1607-3274-2017-3-15.

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4

Saleem, Huda, Huda Albermany, and Husein Hadi. "Proposed Method to Generated Strong Keys by Fuzzy Extractor And Biometric." International Journal of Engineering & Technology 7, no. 3.27 (August 15, 2018): 129. http://dx.doi.org/10.14419/ijet.v7i3.27.17672.

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The typical scheme used to generated cryptographic key is a fuzzy extractor. The fuzzy extractor is the extraction of a stable data from biometric data or noisy data based on the error correction code (ECC) method. Forward error correction includes two ways are blocked and convolutional coding used for error control coding. “Bose_Chaudhuri_Hocquenghem” (BCH) is one of the error correcting codes employ to correct errors in noise data. In this paper use fuzzy extractor scheme to find strong key based on BCH coding, face recognition data used SVD method and hash function. Hash_512 converted a string with variable length into a string of fixed length, it aims to protect information against the threat of repudiation.

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5

Aseeri, Fatimah Mohammed M. "Written Corrective Feedback as Practiced by Instructors of Writing in English at Najran University." Journal of Education and Learning 8, no. 3 (May 10, 2019): 112. http://dx.doi.org/10.5539/jel.v8n3p112.

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The present study aimed to address the extent to which faulty members and students at the department of English language at Najran University practice using the ways of written corrective feedback. The questionnaire, as the main study instrument was used to collect data while the descriptive analytical approach was used to analyze these collected data. Findings revealed that the direct way of correction, i.e., the identification of student’s errors by underlining or circling and then telling them how to correct such errors without allowing them the chance to figure out what the corrections are, was the most practiced way of written corrective feedback. Using Arabic, as it was students’ mother tongue, to show them their errors and then explain to them how to correct these errors was the second practiced way. Indirect correction like for example correcting student’s errors through writing in the margin that there was an error without giving them the correct answer was the least used way, as indicated by faculty members. Nevertheless, correcting students’ errors by coding the exact error in the text without giving them the correct answer was the least used way from students’ viewpoint. Moreover, findings showed that both faculty members and students were in favor of the comprehensive not the selective way of correction.

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6

Semerenko, Vasyl, and Oleksandr Voinalovich. "The simplification of computationals in error correction coding." Technology audit and production reserves 3, no. 2(59) (June 30, 2021): 24–28. http://dx.doi.org/10.15587/2706-5448.2021.233656.

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The object of research is the processes of error correction transformation of information in automated systems. The research is aimed at reducing the complexity of decoding cyclic codes by combining modern mathematical models and practical tools. The main prerequisite for the complication of computations in deterministic linear error-correcting codes is the use of the algebraic representation as the main mathematical apparatus for these types of codes. Despite the universalism of the algebraic approach, its main drawback is the impossibility of taking into account the characteristic features of all subclasses of linear codes. In particular, the cyclic property is not taken into account at all for cyclic codes. Taking this property into account, one can go to a fundamentally different mathematical representation of cyclic codes – the theory of linear automata in Galois fields (linear finite-state machine). For the automaton representation of cyclic codes, it is proved that the problem of syndromic decoding of these codes in the general case is an NP-complete problem. However, if to use the proposed hierarchical approach to problems of complexity, then on its basis it is possible to carry out a more accurate analysis of the growth of computational complexity. Correction of single errors during one time interval (one iteration) of decoding has a linear decoding complexity on the length of the codeword, and error correction during m iterations of permutations of codeword bits has a polynomial complexity. According to three subclasses of cyclic codes, depending on the complexity of their decoding: easy decoding (linear complexity), iteratively decoded (polynomial complexity), complicate decoding (exponential complexity). Practical ways to reduce the complexity of computations are considered: alternate use of probabilistic and deterministic linear codes, simplification of software and hardware implementation by increasing the decoding time, use of interleaving. A method of interleaving is proposed, which makes it possible to simultaneously generate the burst errors and replace them with single errors. The mathematical apparatus of linear automata allows solving together the indicated problems of error correction coding.

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7

Chouksey, Sagar, Mayur Ghadle, Abdul Rasheed, and Shaikh Khursheed Mohd Murtaza. "PERFORMANCE AND ANALYSIS OF REED-SOLOMAN CODES FOR EFFICIENT COMMUNICATION SYSTE." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 10, no. 1 (July 25, 2013): 1249–54. http://dx.doi.org/10.24297/ijct.v10i1.3327.

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In wireless communication systems reducing bit/frame/symbol error rate is critical. If bit error rates are high then in wireless communication system our aim is to minimize error by employing various coding methods on the data transferred. Various channel coding for error detection and correction helps the communication system designers to reduce the effects of a noisy data transmission channel. In this paper our focus is to study and analysis of the performance of Reed-Solomon code that is used to encode the data stream in digital communication. The performances were evaluated by applying to different phase sift keying (PSK) modulation scheme in Noisy channel. Reed-Solomon codes are one of the best for correcting burst errors and find wide range of applications in digital communications and data storage. Reed-Solomon codes are good coding technique for error correcting, in which redundant information is added to data so that it can be recovered reliably despite errors in transmission or retrieval. The error correction system used is based on a Reed-Solomon code. These codes are also used on satellite and other communications systems.Â

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8

Curto, Carina, Vladimir Itskov, Katherine Morrison, Zachary Roth, and Judy L. Walker. "Combinatorial Neural Codes from a Mathematical Coding Theory Perspective." Neural Computation 25, no. 7 (July 2013): 1891–925. http://dx.doi.org/10.1162/neco_a_00459.

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Shannon's seminal 1948 work gave rise to two distinct areas of research: information theory and mathematical coding theory. While information theory has had a strong influence on theoretical neuroscience, ideas from mathematical coding theory have received considerably less attention. Here we take a new look at combinatorial neural codes from a mathematical coding theory perspective, examining the error correction capabilities of familiar receptive field codes (RF codes). We find, perhaps surprisingly, that the high levels of redundancy present in these codes do not support accurate error correction, although the error-correcting performance of receptive field codes catches up to that of random comparison codes when a small tolerance to error is introduced. However, receptive field codes are good at reflecting distances between represented stimuli, while the random comparison codes are not. We suggest that a compromise in error-correcting capability may be a necessary price to pay for a neural code whose structure serves not only error correction, but must also reflect relationships between stimuli.

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9

Kalmykov, Igor Anatolyevich, Vladimir Petrovich Pashintsev, Kamil Talyatovich Tyncherov, Aleksandr Anatolyevich Olenev, and Nikita Konstantinovich Chistousov. "Error-Correction Coding Using Polynomial Residue Number System." Applied Sciences 12, no. 7 (March 25, 2022): 3365. http://dx.doi.org/10.3390/app12073365.

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There has been a tendency to use the theory of finite Galois fields, or GF(2n), in cryptographic ciphers (AES, Kuznyechik) and digital signal processing (DSP) systems. It is advisable to use modular codes of the polynomial residue number system (PRNS). Modular codes of PRNS are arithmetic codes in which addition, subtraction and multiplication operations are performed in parallel on the bases of the code, which are irreducible polynomials. In this case, the operands are small-bit residues. However, the independence of calculations on the bases of the code and the lack of data exchange between the residues can serve as the basis for constructing codes of PRNS capable of detecting and correcting errors that occur during calculations. The article will consider the principles of constructing redundant codes of the polynomial residue number system. The results of the study of codes of PRNS with minimal redundancy are presented. It is shown that these codes are only able to detect an error in the code combination of PRNS. It is proposed to use two control bases, the use of which allows us to correct an error in any residue of the code combination, in order to increase the error-correction abilities of the code of the polynomial residue number system. Therefore, the development of an algorithm for detecting and correcting errors in the code of the polynomial residue number system, which allows for performing this procedure based on modular operations that are effectively implemented in codes of PRNS, is an urgent task.

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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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11

Ahamed Z, Ghouse, and Anuj Jain. "Literature Review on High Definition Image Error Concealment." International Journal of Engineering & Technology 7, no. 3.12 (July 20, 2018): 165. http://dx.doi.org/10.14419/ijet.v7i3.12.15910.

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This paper is give us a overview of Error control method used in image or video transmission. Data in transmission is lost due to link failure or due to congestion and loss in packets, so the aim of this method is to protect data from these errors. Error detection coding and Error correction coding are two types of error control mechanism. Some of the error control mechanisms are Retransmission, Forward error correction, error concealment and error resilience. We are discussing a summary of three methods and Error Concealment in details.

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12

Guo, Wangmei, Dan He, and Ning Cai. "On Capacity of Network Error Correction Coding With Random Errors." IEEE Communications Letters 22, no. 4 (April 2018): 696–99. http://dx.doi.org/10.1109/lcomm.2018.2795598.

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13

Liebowitz, Suzanne, and David Casasent. "Error-correction coding in an associative processor." Applied Optics 26, no. 6 (March 15, 1987): 999. http://dx.doi.org/10.1364/ao.26.000999.

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14

Roth, Ron M., and Pascal O. Vontobel. "Coding for Combined Block–Symbol Error Correction." IEEE Transactions on Information Theory 60, no. 5 (May 2014): 2697–713. http://dx.doi.org/10.1109/tit.2014.2310479.

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15

Lundqvist, H., and G. Karlsson. "On error-correction coding for CDMA PON." Journal of Lightwave Technology 23, no. 8 (August 2005): 2342–51. http://dx.doi.org/10.1109/jlt.2005.850776.

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16

Kadum, Asaad Chlab, Wameedh Nazar Flayyih, and Fakhrul Zaman Rokhani. "Reliability Analysis of Multibit Error Correcting Coding and Comparison to Hamming Product Code for On-Chip Interconnect." Journal of Engineering 26, no. 6 (June 1, 2020): 94–106. http://dx.doi.org/10.31026/j.eng.2020.06.08.

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Error control schemes became a necessity in network-on-chip (NoC) to improve reliability as the on-chip interconnect errors increase with the continuous shrinking of geometry. Accordingly, many researchers are trying to present multi-bit error correction coding schemes that perform a high error correction capability with the simplest design possible to minimize area and power consumption. A recent work, Multi-bit Error Correcting Coding with Reduced Link Bandwidth (MECCRLB), showed a huge reduction in area and power consumption compared to a well-known scheme, namely, Hamming product code (HPC) with Type-II HARQ. Moreover, the authors showed that the proposed scheme can correct 11 random errors which is considered a high number of errors to be corrected by any scheme used in NoC. The high correction capability with moderate number of check bits along with the reduction in power and area requires further investigation in the accuracy of the reliability model. In this paper, reliability analysis is performed by modeling the residual error probability Presidual which represents the probability of decoder error or failure. New model to estimate Presidual of MECCRLB is derived, validated against simulation, and compared to HPC to assess the capability of MECCRLB. The results show that HPC outperforms MECCRLB from reliability perspective. The former corrects all single and double errors, and fails in 5.18% cases of the triple errors, whereas the latter is found to correct all single errors but fails in 32.5% of double errors and 38.97% of triple errors.

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17

Cao, Yue, Zaixin Liu, and Longyu Wu. "Bluetooth Low Energy Error Correction Based on Convolutional Coding." Journal of Physics: Conference Series 2093, no. 1 (November 1, 2021): 012033. http://dx.doi.org/10.1088/1742-6596/2093/1/012033.

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Abstract Contemporarily, the Internet of Things (IoT) is recently a newly emerging technology for connecting small devices into a platform; the IoT has been an increasingly demanded front-edge technology in terms of connecting different devices using information transmission and storage technology. To adapt to the small capacities of device batteries, Bluetooth Low Energy is adopted as the protocol of communication. However, the existing standards do not have a suitable and specific error correction method. As there is no ideal information transmission channel, there must be errors that occurred during message transmission. The performance and capacity of error correction become decisive factors in evaluating how efficient the IoT communication system performs. This article uses convolutional coding—a better-performing coding scheme than block coding—to correct errors in information transmission and reception on Internet of Things devices. It is better competent to control and correct bit errors in information transmission. To achieve this goal, convolutional coding algorithms devised by Dr Justin Coon at the University of Oxford have been referred to. By simulation using MATLAB, it has been found that the error rate is enhanced significantly for high Signal-to-Noise Ratio (SNR) in convolutional codes compared to uncoded messages.

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18

Kaneko, Toshinobu. ""Introduction to coding theory. (2): Error detection and error correction"." Journal of the Institute of Television Engineers of Japan 44, no. 8 (1990): 1014–21. http://dx.doi.org/10.3169/itej1978.44.1014.

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19

Taubin, Feliks, and Andrey Trofimov. "Concatenated Coding for Multilevel Flash Memory with Low Error Correction Capabilities in Outer Stage." SPIIRAS Proceedings 18, no. 5 (September 19, 2019): 1149–81. http://dx.doi.org/10.15622/sp.2019.18.5.1149-1181.

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One of the approaches to organization of error correcting coding for multilevel flash memory is based on concatenated construction, in particular, on multidimensional lattices for inner coding. A characteristic feature of such structures is the dominance of the complexity of the outer decoder in the total decoder complexity. Therefore the concatenated construction with low-complexity outer decoder may be attractive since in practical applications the decoder complexity is the crucial limitation for the usage of the error correction coding. We consider a concatenated coding scheme for multilevel flash memory with the Barnes-Wall lattice based codes as an inner code and the Reed-Solomon code with correction up to 4…5 errors as an outer one. Performance analysis is fulfilled for a model characterizing the basic physical features of a flash memory cell with non-uniform target voltage levels and noise variance dependent on the recorded value (input-dependent additive Gaussian noise, ID-AGN). For this model we develop a modification of our approach for evaluation the error probability for the inner code. This modification uses the parallel structure of the inner code trellis which significantly reduces the computational complexity of the performance estimation. We present numerical examples of achievable recording density for the Reed-Solomon codes with correction up to four errors as the outer code for wide range of the retention time and number of write/read cycles.

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Liang, Hsin Ying, Chia Hsin Cheng, Cheng Ying Yang, and Kun Fu Zhang. "A Modified Least Significant Bit Embedding with Error Correction." Applied Mechanics and Materials 284-287 (January 2013): 3256–59. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.3256.

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This paper proposes a modified Least significant bit (LSB) embedding capable of both a high embedding payload and error correction. The method proposed in this paper combines the techniques of both LSB embedding and multilevel coding to produce stego images with error correction capability and high embedding payloads. The proposed method divides cover work into multiple blocks, and each LSB for all the pixels in each block is considered a layer. Reed-Muller codes are used to encode cipher and embed data into every layer. LSB embedding has no inherent capability to correct errors in cipher extraction, but the proposed method can correct some errors according to the error correction capability of multilevel coding. Compared with LSB embedding, simulation results show that the proposed method has a similar peak signal noise ratio (PSNR) and embedding payload. The peak signal noise ratio (PSNR) exceeds 40 dB by using our proposed method. Additionally, our proposed method offers significantly superior embedding payloads and error correction capabilities.

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21

Lin, Qiuzhen, Kwok-Wo Wong, Ming Li, and Jianyong Chen. "An Effective Error Correction Scheme for Arithmetic Coding." Mathematical Problems in Engineering 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/861093.

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We propose an effective error correction technique for arithmetic coding with forbidden symbol. By predicting the occurrence of the subsequent forbidden symbols, the forbidden region is actually expanded and theoretically, a better error correction performance can be achieved. Moreover, a generalized stack algorithm is exploited to detect the forbidden symbol beforehand. The proposed approach is combined with themaximum a posteriori(MAP) metric to keep the highly probable decoding paths in the stack. Simulation results justify that our scheme performs better than the existing MAP methods on the error correction performance, especially at a low coding rate.

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22

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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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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Abdulhamid, Mohanad, and Mbugua Thairu. "Performance Analysis of Turbo Codes Over AWGN Channel." Scientific Bulletin of Electrical Engineering Faculty 19, no. 1 (April 1, 2019): 43–48. http://dx.doi.org/10.1515/sbeef-2019-0009.

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AbstractTurbo coding is a very powerful error correction technique that has made a tremendous impact on channel coding in the past two decades. It outperforms most known coding schemes by achieving near Shannon limit error correction using simple component codes and large interleavers. This paper investigates the turbo coder in detail. It presents a design and a working model of the error correction technique using Simulink, a companion softwareto MATLAB. Finally, graphical and tabular results are presented to show that the designed turbo coder works as expected.

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25

Zhu, H., W. A. Clarke, and H. C. Ferreira. "Watermarking for jpeg images using error correction coding." SAIEE Africa Research Journal 99, no. 4 (December 2008): 98–102. http://dx.doi.org/10.23919/saiee.2008.9485360.

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26

Huang, Lingchen, Huazi Zhang, Rong Li, Yiqun Ge, and Jun Wang. "AI Coding: Learning to Construct Error Correction Codes." IEEE Transactions on Communications 68, no. 1 (January 2020): 26–39. http://dx.doi.org/10.1109/tcomm.2019.2951403.

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Silva, Danilo, and Frank R. Kschischang. "On Metrics for Error Correction in Network Coding." IEEE Transactions on Information Theory 55, no. 12 (December 2009): 5479–90. http://dx.doi.org/10.1109/tit.2009.2032817.

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Dau, Son Hoang, Vitaly Skachek, and Yeow Meng Chee. "Error Correction for Index Coding With Side Information." IEEE Transactions on Information Theory 59, no. 3 (March 2013): 1517–31. http://dx.doi.org/10.1109/tit.2012.2227674.

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Kak. "Encryption and Error-Correction Coding Using D Sequences." IEEE Transactions on Computers C-34, no. 9 (September 1985): 803–9. http://dx.doi.org/10.1109/tc.1985.1676636.

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Bakos, Jason D., Donald M. Chiarulli, and Steven P. Levitan. "Lightweight Error Correction Coding for System-Level Interconnects." IEEE Transactions on Computers 56, no. 3 (March 2007): 289–304. http://dx.doi.org/10.1109/tc.2007.49.

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Zhen Zhang. "Theory and Applications of Network Error Correction Coding." Proceedings of the IEEE 99, no. 3 (March 2011): 406–20. http://dx.doi.org/10.1109/jproc.2010.2093551.

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32

Miller, S. L., and L. B. Milstein. "Error correction coding for a meteor burst channel." IEEE Transactions on Communications 38, no. 9 (1990): 1520–29. http://dx.doi.org/10.1109/26.61393.

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Popplewell, A., and J. J. O'Reilly. "Manchester-like coding with single error correction and double error detection." Electronics Letters 29, no. 6 (1993): 524. http://dx.doi.org/10.1049/el:19930350.

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WEN, KAI, and GUI LU LONG. "ONE-PARTY QUANTUM-ERROR-CORRECTING CODES FOR UNBALANCED ERRORS: PRINCIPLES AND APPLICATION TO QUANTUM DENSE CODING AND QUANTUM SECURE DIRECT COMMUNICATION." International Journal of Quantum Information 08, no. 04 (June 2010): 697–719. http://dx.doi.org/10.1142/s0219749910006289.

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In this article, we present unbalanced-quantum-error-correcting codes (one-party QECCs) — a novel idea for correcting unbalanced quantum errors. In some quantum communication tasks using entangled pairs, the error distributions between two parts of the pairs are unbalanced, and one party holds the whole entangled pairs at the final stage, and he or she is able to perform joint measurements on the pairs. In this situation the proposed one-party QECCs can improve error correction by allowing a higher-tolerated error rate. We have established the general correspondence between linear classical codes and the one-party QECCs, and we have given the general definition for these types of quantum-error-correcting codes. It has been shown that the one-party QECCs can correct errors as long as the error threshold is not larger than 0.5. They work even for fidelity less than 0.5 as long as it is larger than 0.25. We give several concrete examples of the one-party QECCs. We provide the applications of the one-party QECCs in quantum dense coding, so that it can function in noisy channels. As a result, a large number of quantum secure direct communication protocols based on dense coding are also able to be protected by this new type of one-party QECCs.

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Wei, Yan Kang, Da Ming Wang, and Wei Jia Cui. "“Soft Error” Correction Method Based on Low Complexity Coding and Encoding Algorithm." Applied Mechanics and Materials 556-562 (May 2014): 6344–49. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.6344.

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SEU is one of the major challenges affecting the reliability of computers on-board. In this paper, we design a kind of encoding and decoding algorithms with a low complexity based on the data correction method to resolve the data stream errors SEU may bring. Firstly, we use the theory of linear block codes to analyze various methods of data fault tolerance, and then from the encoding and decoding principle of linear block codes we design a kind of encoding and decoding algorithms with a low complexity of linear block code, The fault-tolerant coding method can effectively correct single-bit data errors caused by SEU, with low fault-tolerant overhead. Fault injection experiments show that: this method can effectively correct data errors caused by single event upset. Compared with other common error detection or correction methods, error correction performance of this method is superior, while its fault tolerance cost is less.

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Vosoughi, Arash, Vanessa Testoni, Pamela C. Cosman, and Laurence B. Milstein. "Multiview coding and error correction coding for 3D video over noisy channels." Signal Processing: Image Communication 30 (January 2015): 107–20. http://dx.doi.org/10.1016/j.image.2014.10.006.

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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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Nicolas Bailon, Daniel, Johann-Philipp Thiers, and Jürgen Freudenberger. "Error Correction for TLC and QLC NAND Flash Memories Using Cell-Wise Encoding." Electronics 11, no. 10 (May 16, 2022): 1585. http://dx.doi.org/10.3390/electronics11101585.

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The growing error rates of triple-level cell (TLC) and quadruple-level cell (QLC) NAND flash memories have led to the application of error correction coding with soft-input decoding techniques in flash-based storage systems. Typically, flash memory is organized in pages where the individual bits per cell are assigned to different pages and different codewords of the error-correcting code. This page-wise encoding minimizes the read latency with hard-input decoding. To increase the decoding capability, soft-input decoding is used eventually due to the aging of the cells. This soft-decoding requires multiple read operations. Hence, the soft-read operations reduce the achievable throughput, and increase the read latency and power consumption. In this work, we investigate a different encoding and decoding approach that improves the error correction performance without increasing the number of reference voltages. We consider TLC and QLC flashes where all bits are jointly encoded using a Gray labeling. This cell-wise encoding improves the achievable channel capacity compared with independent page-wise encoding. Errors with cell-wise read operations typically result in a single erroneous bit per cell. We present a coding approach based on generalized concatenated codes that utilizes this property.

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Comar, Bradley. "Method of Combining Cryptography and LDPC Coding for Enhanced Privacy." International Journal of Interdisciplinary Telecommunications and Networking 13, no. 4 (October 2021): 51–70. http://dx.doi.org/10.4018/ijitn.2021100105.

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This paper describes a method of combining cryptographic encoding and low density parity check (LDPC) encoding for the purpose of enhancing privacy. This method uses pseudorandom number generators (PRNGs) to create parity check matrices that are constantly updated. The generated cyphertext is at least as private as a standard additive (XORing) cryptosystem, and also has error correcting capability. The eavesdropper, Eve, has the expanded burden of having to perform cryptanalysis and error correction simultaneously.

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Hayashi, Masahito. "Secure Physical Layer Network Coding versus Secure Network Coding." Entropy 24, no. 1 (December 27, 2021): 47. http://dx.doi.org/10.3390/e24010047.

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When a network has relay nodes, there is a risk that a part of the information is leaked to an untrusted relay. Secure network coding (secure NC) is known as a method to resolve this problem, which enables the secrecy of the message when the message is transmitted over a noiseless network and a part of the edges or a part of the intermediate (untrusted) nodes are eavesdropped. If the channels on the network are noisy, the error correction is applied to noisy channels before the application of secure NC on an upper layer. In contrast, secure physical layer network coding (secure PLNC) is a method to securely transmit a message by a combination of coding operation on nodes when the network is composed of set of noisy channels. Since secure NC is a protocol on an upper layer, secure PLNC can be considered as a cross-layer protocol. In this paper, we compare secure PLNC with a simple combination of secure NC and error correction over several typical network models studied in secure NC.

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Klesse, Rochus. "A Random Coding Based Proof for the Quantum Coding Theorem." Open Systems & Information Dynamics 15, no. 01 (March 2008): 21–45. http://dx.doi.org/10.1142/s1230161208000055.

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We present a proof for the quantum channel coding theorem which relies on the fact that a randomly chosen code space typically is highly suitable for quantum error correction. In this sense, the proof is close to Shannon's original treatment of information transmission via a noisy classical channel.

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INOUE, Masato, and Haruhiko KANEKO. "Adaptive Marker Coding for Insertion/Deletion/Substitution Error Correction." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E97.A, no. 2 (2014): 642–51. http://dx.doi.org/10.1587/transfun.e97.a.642.

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Balevi, Eren, and Jeffrey G. Andrews. "Autoencoder-Based Error Correction Coding for One-Bit Quantization." IEEE Transactions on Communications 68, no. 6 (June 2020): 3440–51. http://dx.doi.org/10.1109/tcomm.2020.2977280.

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Chi, K. K., and X. M. Wang. "Analysis of network error correction based on network coding." IEE Proceedings - Communications 152, no. 4 (2005): 393. http://dx.doi.org/10.1049/ip-com:20045307.

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Byrne, Eimear, and Marco Calderini. "Error Correction for Index Coding With Coded Side Information." IEEE Transactions on Information Theory 63, no. 6 (June 2017): 3712–28. http://dx.doi.org/10.1109/tit.2017.2687933.

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Braunstein, Samuel L., and John A. Smolin. "Perfect quantum-error-correction coding in 24 laser pulses." Physical Review A 55, no. 2 (February 1, 1997): 945–50. http://dx.doi.org/10.1103/physreva.55.945.

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Kawakami, W., and K. I. Kitayama. "Optical error-correction coding encoder and decoder: design considerations." Applied Optics 34, no. 23 (August 10, 1995): 5064. http://dx.doi.org/10.1364/ao.34.005064.

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Zhang, Xue, Jianbin Liu, and Yanfeng Jiang. "STT-MRAM error correction technology based on LDPC coding." AIP Advances 10, no. 1 (January 1, 2020): 015205. http://dx.doi.org/10.1063/1.5130007.

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Smith, L. J. M., and G. D. Burton. "Punctured coding for forward error correction in satellite communications." Journal of the Institution of Electronic and Radio Engineers 58, no. 3 (1988): 125. http://dx.doi.org/10.1049/jiere.1988.0022.

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Gao, Xiao Rong, Pei Wang, Jian Qiang Guo, Jin Long Li, Kai Yang, and Ti Kui Wang. "Error Correction Based on LDPC Codes in Wireless Optical Communication." Applied Mechanics and Materials 380-384 (August 2013): 3811–14. http://dx.doi.org/10.4028/www.scientific.net/amm.380-384.3811.

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Complex atmospheric environment seriously affect the quality of wireless of information transmission. In order to improve the wireless optical communication quality, and reduce the influence of attenuation, flicker, angle misalignment caused by atmospheric scattering, absorption, turbulence, beam expander, mismatch, atmospheric channel model is established while coding techniques for error control in wireless optical communication was researched into.The improvement result of error rate by error correction coding in different SNR situations was obtained. The results showed that the LDPC coding can significantly reduce the BER. For Gaussian channel, SNR can be reduced 8 dB when BER is 10-6; For wireless optical communication , LDPC codes can make the error rate reduced by 4-5 orders of magnitude.

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