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Relevant bibliographies by topics / Error-correcting codes (Information theory)

Academic literature on the topic 'Error-correcting codes (Information theory)'

Author: Grafiati

Published: 4 June 2021

Last updated: 27 July 2024

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Journal articles on the topic "Error-correcting codes (Information theory)"

1

Conway, J., and N. Sloane. "Lexicographic codes: Error-correcting codes from game theory." IEEE Transactions on Information Theory 32, no. 3 (May 1986): 337–48. http://dx.doi.org/10.1109/tit.1986.1057187.

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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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Wang, Li-Na, Hongxu Wei, Yuchen Zheng, Junyu Dong, and Guoqiang Zhong. "Deep Error-Correcting Output Codes." Algorithms 16, no. 12 (December 4, 2023): 555. http://dx.doi.org/10.3390/a16120555.

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Ensemble learning, online learning and deep learning are very effective and versatile in a wide spectrum of problem domains, such as feature extraction, multi-class classification and retrieval. In this paper, combining the ideas of ensemble learning, online learning and deep learning, we propose a novel deep learning method called deep error-correcting output codes (DeepECOCs). DeepECOCs are composed of multiple layers of the ECOC module, which combines several incremental support vector machines (incremental SVMs) as base classifiers. In this novel deep architecture, each ECOC module can be considered as two successive layers of the network, while the incremental SVMs can be viewed as weighted links between two successive layers. In the pre-training procedure, supervisory information, i.e., class labels, can be used during the network initialization. The incremental SVMs lead this procedure to be very efficient, especially for large-scale applications. We have conducted extensive experiments to compare DeepECOCs with traditional ECOC, feature learning and deep learning algorithms. The results demonstrate that DeepECOCs perform, not only better than existing ECOC and feature learning algorithms, but also related to deep learning ones in most cases.

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Cazorla García, Pedro-José. "Perfect Codes over Non-Prime Power Alphabets: An Approach Based on Diophantine Equations." Mathematics 12, no. 11 (May 23, 2024): 1642. http://dx.doi.org/10.3390/math12111642.

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Perfect error-correcting codes allow for an optimal transmission of information while guaranteeing error correction. For this reason, proving their existence has been a classical problem in both pure mathematics and information theory. Indeed, the classification of the parameters of e-error correcting perfect codes over q-ary alphabets was a very active topic of research in the late 20th century. Consequently, all parameters of perfect e-error-correcting codes were found if e≥3, and it was conjectured that no perfect 2-error-correcting codes exist over any q-ary alphabet, where q>3. In the 1970s, this was proved for q a prime power, for q=2r3s and for only seven other values of q. Almost 50 years later, it is surprising to note that there have been no new results in this regard and the classification of 2-error-correcting codes over non-prime power alphabets remains an open problem. In this paper, we use techniques from the resolution of the generalised Ramanujan–Nagell equation and from modern computational number theory to show that perfect 2-error-correcting codes do not exist for 172 new values of q which are not prime powers, substantially increasing the values of q which are now classified. In addition, we prove that, for any fixed value of q, there can be at most finitely many perfect 2-error-correcting codes over an alphabet of size q.

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Huang, Pengfei, Yi Liu, Xiaojie Zhang, Paul H. Siegel, and Erich F. Haratsch. "Syndrome-Coupled Rate-Compatible Error-Correcting Codes: Theory and Application." IEEE Transactions on Information Theory 66, no. 4 (April 2020): 2311–30. http://dx.doi.org/10.1109/tit.2020.2966439.

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Sajjad, Muhammad, Tariq Shah, Qin Xin, and Bander Almutairi. "Eisenstein field BCH codes construction and decoding." AIMS Mathematics 8, no. 12 (2023): 29453–73. http://dx.doi.org/10.3934/math.20231508.

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<abstract> <p>First, we will go through the theory behind the Eisenstein field (EF) and its extension field. In contrast, we provide a detailed framework for building BCH codes over the EF in the second stage. BCH codes over the EF are decoded using the Berlekamp-Massey algorithm (BMA) in this article. We investigate the error-correcting capabilities of these codes and provide expressions for minimal distance. We provide researchers and engineers creating and implementing robust error-correcting codes for digital communication systems with detailed information on building, decoding and performance assessment.</p> </abstract>

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Ben-Gal, Irad, and Lev B. Levitin. "An application of information theory and error-correcting codes to fractional factorial experiments." Journal of Statistical Planning and Inference 92, no. 1-2 (January 2001): 267–82. http://dx.doi.org/10.1016/s0378-3758(00)00165-8.

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Namba, Kazuteru, and Eiji Fujiwara. "Nonbinary single-symbol error correcting, adjacent two-symbol transposition error correcting codes over integer rings." Systems and Computers in Japan 38, no. 8 (2007): 54–60. http://dx.doi.org/10.1002/scj.10516.

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Çalkavur, Selda. "Public-Key Cryptosystems and Bounded Distance Decoding of Linear Codes." Entropy 24, no. 4 (April 1, 2022): 498. http://dx.doi.org/10.3390/e24040498.

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Error-correcting codes form an important topic in information theory. They are used to correct errors that occur during transmission on a noisy channel. An important method for correcting errors is bounded distance decoding. The public-key cryptosystem is a cryptographic protocol that has two different keys. One of them is a public-key that can be known by everyone, and the other is the private-key only known to the user of the system. The data encrypted with the public-key of a given user can only be decrypted by this user with his or her private-key. In this paper, we propose a public-key cryptosystem based on the error-correcting codes. The decryption is performed by using the bounded distance decoding of the code. For a given code length, dimension, and error-correcting capacity, the new system allows dealing with larger plaintext than other code based public-key cryptosystems.

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Khalifa, Othman O., Nur Amirah bt Sharif, Rashid A. Saeed, S. Abdel-Khalek, Abdulaziz N. Alharbi, and Ali A. Alkathiri. "Digital System Design for Quantum Error Correction Codes." Contrast Media & Molecular Imaging 2021 (December 15, 2021): 1–8. http://dx.doi.org/10.1155/2021/1101911.

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Quantum computing is a computer development technology that uses quantum mechanics to perform the operations of data and information. It is an advanced technology, yet the quantum channel is used to transmit the quantum information which is sensitive to the environment interaction. Quantum error correction is a hybrid between quantum mechanics and the classical theory of error-correcting codes that are concerned with the fundamental problem of communication, and/or information storage, in the presence of noise. The interruption made by the interaction makes transmission error during the quantum channel qubit. Hence, a quantum error correction code is needed to protect the qubit from errors that can be caused by decoherence and other quantum noise. In this paper, the digital system design of the quantum error correction code is discussed. Three designs used qubit codes, and nine-qubit codes were explained. The systems were designed and configured for encoding and decoding nine-qubit error correction codes. For comparison, a modified circuit is also designed by adding Hadamard gates.

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Dissertations / Theses on the topic "Error-correcting codes (Information theory)"

1

Wang, Xuesong. "Cartesian authentication codes from error correcting codes /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?COMP%202004%20WANGX.

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Rudra, Atri. "List decoding and property testing of error correcting codes /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/6929.

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Nenno, Robert B. "An introduction to the theory of nonlinear error-correcting codes /." Online version of thesis, 1987. http://hdl.handle.net/1850/10350.

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Palaniappan, Karthik. "Propagation of updates to replicas using error correcting codes." Morgantown, W. Va. : [West Virginia University Libraries], 2001. http://etd.wvu.edu/templates/showETD.cfm?recnum=1915.

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Thesis (M.S.)--West Virginia University, 2001.
Title from document title page. Document formatted into pages; contains vi, 68 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 67-68).

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Alabbadi, Mohssen. "Intergration of error correction, encryption, and signature based on linear error-correcting block codes." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/14959.

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Shen, Bingxin. "Application of Error Correction Codes in Wireless Sensor Networks." Fogler Library, University of Maine, 2007. http://www.library.umaine.edu/theses/pdf/ShenB2007.pdf.

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El, Rifai Ahmed Mahmoud. "Applications of linear block codes to the McEliece cryptosystem." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/16604.

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Corazza, Federico Augusto. "Analysis of graph-based quantum error-correcting codes." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23801/.

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With the advent of quantum computers, there has been a growing interest in the practicality of this device. Due to the delicate conditions that surround physical qubits, one could wonder whether any useful computation could be implemented on such devices. As we describe in this work, it is possible to exploit concepts from classical information theory and employ quantum error-correcting techniques. Thanks to the Threshold Theorem, if the error probability of physical qubits is below a given threshold, then the logical error probability corresponding to the encoded data qubit can be arbitrarily low. To this end, we describe decoherence which is the phenomenon that quantum bits are subject to and is the main source of errors in quantum memories. From the cause of error of a single qubit, we then introduce the error models that can be used to analyze quantum error-correcting codes as a whole. The main type of code that we studied comes from the family of topological codes and is called surface code. Of these codes, we consider both the toric and planar structures. We then introduce a variation of the standard planar surface code which better captures the symmetries of the code architecture. Once the main properties of surface codes have been discussed, we give an overview of the working principles of the algorithm used to decode this type of topological code: the minimum weight perfect matching. Finally, we show the performance of the surface codes that we introduced, comparing them based on their architecture and properties. These simulations have been performed with different error channel models to give a more thorough description of their performance in several situations showing relevant results.

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Luna, Amjad A. "The design and implementation of trellis-based soft decision decoders for block codes." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/15818.

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Blanchard, Bart. "Quantization effects and implementation considerations for turbo decoders." [Gainesville, Fla.] : University of Florida, 2002. http://purl.fcla.edu/fcla/etd/UFE1000107.

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Thesis (M.S.)--University of Florida, 2002.
Title from title page of source document. Document formatted into pages; contains xiii, 91 p.; also contains graphics. Includes vita. Includes bibliographical references.

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Books on the topic "Error-correcting codes (Information theory)"

1

Poli, Alain. Error correcting codes: Theory and applications. Hemel Hempstead: Prentice Hall, 1992.

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2

Error-correcting codes and finite fields. Oxford: Clarendon Press, 1992.

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3

Purser, Michael. Introduction to error-correcting codes. Boston: Artech House, 1995.

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4

1942-, Costello Daniel J., ed. Error control coding: Fundamentals and applications. 2nd ed. Upper Saddle River, N.J: Pearson-Prentice Hall, 2004.

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5

Papini, Odile. Algèbre discrète et codes correcteurs. Berlin: Springer, 1995.

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6

Pless, Vera. Introduction to the theory of error-correcting codes. 3rd ed. New York: Wiley, 1998.

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Pless, Vera. Introduction to the theory of error-correcting codes. 2nd ed. New York: Wiley, 1989.

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8

United States. National Aeronautics and Space Administration. Scientific and Technical Information Program, ed. Introduction to forward-error-correcting coding. Cleveland, Ohio: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1996.

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United States. National Aeronautics and Space Administration. Scientific and Technical Information Program, ed. Introduction to forward-error-correcting coding. Cleveland, Ohio: National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program, 1996.

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10

Guy, Farrell Patrick, ed. Essentials of error-control coding. West Sussex, England: John Wiley & Sons, 2006.

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Book chapters on the topic "Error-correcting codes (Information theory)"

1

Guimarães, Dayan Adionel. "Notions of Information Theory and Error-Correcting Codes." In Digital Transmission, 689–840. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01359-1_8.

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Battail, Gérard. "An Overview of Information Theory and Error-Correcting Codes." In An Outline of Informational Genetics, 13–36. Cham: Springer International Publishing, 2008. http://dx.doi.org/10.1007/978-3-031-01629-5_3.

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van Lint, Jacobus H., and Gerard van der Geer. "Error-correcting codes." In Introduction to Coding Theory and Algebraic Geometry, 13–14. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-9286-5_2.

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4

Baylis, John. "Number theory — arithmetic for codes." In Error-correcting Codes, 25–47. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4899-3276-1_3.

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Zeng, Bei, Xie Chen, Duan-Lu Zhou, and Xiao-Gang Wen. "Quantum Error-Correcting Codes." In Quantum Information Meets Quantum Matter, 63–82. New York, NY: Springer New York, 2019. http://dx.doi.org/10.1007/978-1-4939-9084-9_3.

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6

Langford, John, and Alina Beygelzimer. "Sensitive Error Correcting Output Codes." In Learning Theory, 158–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11503415_11.

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Cancellieri, Giovanni. "Turbo Codes." In Polynomial Theory of Error Correcting Codes, 473–502. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-01727-3_9.

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Cancellieri, Giovanni. "LDPC Convolutional Codes." In Polynomial Theory of Error Correcting Codes, 581–622. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-01727-3_12.

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9

Spielman, Daniel A. "The complexity of error-correcting codes." In Fundamentals of Computation Theory, 67–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0036172.

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Trevisan, Luca. "Error-Correcting Codes in Complexity Theory." In Lecture Notes in Computer Science, 4. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-44849-7_4.

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Conference papers on the topic "Error-correcting codes (Information theory)"

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Roth, Ron M. "Analog Error-Correcting Codes." In 2019 IEEE International Symposium on Information Theory (ISIT). IEEE, 2019. http://dx.doi.org/10.1109/isit.2019.8849843.

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Wang, Qiwen, Sidharth Jaggi, and Shuo-Yen Robert Li. "Binary error correcting network codes." In 2011 IEEE Information Theory Workshop (ITW). IEEE, 2011. http://dx.doi.org/10.1109/itw.2011.6089511.

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Yaakobi, Eitan, Paul H. Siegel, Alexander Vardy, and Jack K. Wolf. "Multiple error-correcting WOM-codes." In 2010 IEEE International Symposium on Information Theory - ISIT. IEEE, 2010. http://dx.doi.org/10.1109/isit.2010.5513373.

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Yaakobi, Eitan, and Tuvi Etzion. "High dimensional error-correcting codes." In 2010 IEEE International Symposium on Information Theory - ISIT. IEEE, 2010. http://dx.doi.org/10.1109/isit.2010.5513662.

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Buzaglo, Sarit, Eitan Yaakobi, Tuvi Etzion, and Jehoshua Bruck. "Error-correcting codes for multipermutations." In 2013 IEEE International Symposium on Information Theory (ISIT). IEEE, 2013. http://dx.doi.org/10.1109/isit.2013.6620321.

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Klove, Torleiv, Bella Bose, and Noha Elarief. "Systematic single limited magnitude asymmetric error correcting codes." In 2010 IEEE Information Theory Workshop on Information Theory (ITW). IEEE, 2010. http://dx.doi.org/10.1109/itwksps.2010.5503196.

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Huang, Qin, Shu Lin, and Khaled Abdel-Ghaffar. "Error-correcting codes for flash coding." In 2011 Information Theory and Applications Workshop (ITA). IEEE, 2011. http://dx.doi.org/10.1109/ita.2011.5743580.

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Roy, Shounak, and Shayan Srinivasa Garani. "Two Dimensional Algebraic Error Correcting Codes." In 2018 Information Theory and Applications Workshop (ITA). IEEE, 2018. http://dx.doi.org/10.1109/ita.2018.8502956.

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Ngai, Chi Kin, and Shenghao Yang. "Deterministic Secure Error-Correcting (SEC) Network Codes." In 2007 IEEE Information Theory Workshop. IEEE, 2007. http://dx.doi.org/10.1109/itw.2007.4313056.

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Tallini, Luca G., Noha Elarief, and Bella Bose. "On efficient repetition error correcting codes." In 2010 IEEE International Symposium on Information Theory - ISIT. IEEE, 2010. http://dx.doi.org/10.1109/isit.2010.5513741.

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