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

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

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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

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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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Raussendorf, Robert. "Key ideas in quantum error correction." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1975 (September 28, 2012): 4541–65. http://dx.doi.org/10.1098/rsta.2011.0494.

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In this introductory article on the subject of quantum error correction and fault-tolerant quantum computation, we review three important ingredients that enter known constructions for fault-tolerant quantum computation, namely quantum codes, error discretization and transversal quantum gates. Taken together, they provide a ground on which the theory of quantum error correction can be developed and fault-tolerant quantum information protocols can be built.

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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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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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Magdalena de la Fuente, Julio Carlos, Nicolas Tarantino, and Jens Eisert. "Non-Pauli topological stabilizer codes from twisted quantum doubles." Quantum 5 (February 17, 2021): 398. http://dx.doi.org/10.22331/q-2021-02-17-398.

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It has long been known that long-ranged entangled topological phases can be exploited to protect quantum information against unwanted local errors. Indeed, conditions for intrinsic topological order are reminiscent of criteria for faithful quantum error correction. At the same time, the promise of using general topological orders for practical error correction remains largely unfulfilled to date. In this work, we significantly contribute to establishing such a connection by showing that Abelian twisted quantum double models can be used for quantum error correction. By exploiting the group cohomological data sitting at the heart of these lattice models, we transmute the terms of these Hamiltonians into full-rank, pairwise commuting operators, defining commuting stabilizers. The resulting codes are defined by non-Pauli commuting stabilizers, with local systems that can either be qubits or higher dimensional quantum systems. Thus, this work establishes a new connection between condensed matter physics and quantum information theory, and constructs tools to systematically devise new topological quantum error correcting codes beyond toric or surface code models.

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Arora, H. D., and Anjali Dhiman. "Comparative Study of Generalized Quantitative-Qualitative Inaccuracy Fuzzy Measures for Noiseless Coding Theorem and 1:1 Codes." International Journal of Mathematics and Mathematical Sciences 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/258675.

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In coding theory, we study various properties of codes for application in data compression, cryptography, error correction, and network coding. The study of codes is introduced in Information Theory, electrical engineering, mathematics, and computer sciences for the transmission of data through reliable and efficient methods. We have to consider how coding of messages can be done efficiently so that the maximum number of messages can be sent over a noiseless channel in a given time. Thus, the minimum value of mean codeword length subject to a given constraint on codeword lengths has to be founded. In this paper, we have introduced mean codeword length of orderαand typeβfor 1:1 codes and analyzed the relationship between average codeword length and fuzzy information measures for binary 1:1 codes. Further, noiseless coding theorem associated with fuzzy information measure has been established.

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Günlü, Onur, and Rafael Schaefer. "An Optimality Summary: Secret Key Agreement with Physical Unclonable Functions." Entropy 23, no. 1 (December 24, 2020): 16. http://dx.doi.org/10.3390/e23010016.

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We address security and privacy problems for digital devices and biometrics from an information-theoretic optimality perspective to conduct authentication, message encryption/decryption, identification or secure and private computations by using a secret key. A physical unclonable function (PUF) provides local security to digital devices and this review gives the most relevant summary for information theorists, coding theorists, and signal processing community members who are interested in optimal PUF constructions. Low-complexity signal processing methods are applied to simplify information-theoretic analyses. The best trade-offs between the privacy-leakage, secret-key, and storage rates are discussed. Proposed optimal constructions that jointly design the vector quantizer and error-correction code parameters are listed. These constructions include modern and algebraic codes such as polar codes and convolutional codes, both of which can achieve small block-error probabilities at short block lengths, corresponding to a small number of PUF circuits. Open problems in the PUF literature from signal processing, information theory, coding theory, and hardware complexity perspectives and their combinations are listed to stimulate further advancements in the research on local privacy and security.

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Weaver, Nik. "Quantum Graphs as Quantum Relations." Journal of Geometric Analysis 31, no. 9 (January 13, 2021): 9090–112. http://dx.doi.org/10.1007/s12220-020-00578-w.

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AbstractThe “noncommutative graphs” which arise in quantum error correction are a special case of the quantum relations introduced in Weaver (Quantum relations. Mem Am Math Soc 215(v–vi):81–140, 2012). We use this perspective to interpret the Knill–Laflamme error-correction conditions (Knill and Laflamme in Theory of quantum error-correcting codes. Phys Rev A 55:900-911, 1997) in terms of graph-theoretic independence, to give intrinsic characterizations of Stahlke’s noncommutative graph homomorphisms (Stahlke in Quantum zero-error source-channel coding and non-commutative graph theory. IEEE Trans Inf Theory 62:554–577, 2016) and Duan, Severini, and Winter’s noncommutative bipartite graphs (Duan et al., op. cit. in Zero-error communication via quantum channels, noncommutative graphs, and a quantum Lovász number. IEEE Trans Inf Theory 59:1164–1174, 2013), and to realize the noncommutative confusability graph associated to a quantum channel (Duan et al., op. cit. in Zero-error communication via quantum channels, noncommutative graphs, and a quantum Lovász number. IEEE Trans Inf Theory 59:1164–1174, 2013) as the pullback of a diagonal relation. Our framework includes as special cases not only purely classical and purely quantum information theory, but also the “mixed” setting which arises in quantum systems obeying superselection rules. Thus we are able to define noncommutative confusability graphs, give error correction conditions, and so on, for such systems. This could have practical value, as superselection constraints on information encoding can be physically realistic.

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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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Sah, Dhaneshwar. "Iterative Decoding of Turbo Codes." Journal of Advanced College of Engineering and Management 3 (January 10, 2018): 15. http://dx.doi.org/10.3126/jacem.v3i0.18810.

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<p><strong> </strong>This paper presents a Thesis which consists of a study of turbo codes as an error-control Code and the software implementation of two different decoders, namely the Maximum a Posteriori (MAP), and soft- Output Viterbi Algorithm (SOVA) decoders. Turbo codes were introduced in 1993 by berrouet at [2] and are perhaps the most exciting and potentially important development in coding theory in recent years. They achieve near- Shannon-Limit error correction performance with relatively simple component codes and large interleavers. They can be constructed by concatenating at least two component codes in a parallel fashion, separated by an interleaver. The convolutional codes can achieve very good results. In order of a concatenated scheme such as a turbo codes to work properly, the decoding algorithm must affect an exchange of soft information between component decoders. The concept behind turbo decoding is to pass soft information from the output of one decoder to the input of the succeeding one, and to iterate this process several times to produce better decisions. Turbo codes are still in the process of standardization but future applications will include mobile communication systems, deep space communications, telemetry and multimedia. Finally, we will compare these two algorithms which have less complexity and which can produce better performance.</p><p><strong>Journal of Advanced College of Engineering and Management</strong>, Vol.3, 2017, Page: 15-30</p>

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

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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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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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Tezeren, Serdar U. "Reed-Muller codes in error correction in wireless adhoc networks." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2004. http://library.nps.navy.mil/uhtbin/hyperion/04Mar%5FTezeren.pdf.

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Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, March 2004.
Thesis advisor(s): Murali Tummala, Roberto Cristi. Includes bibliographical references (p. 133-134). Also available online.

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Hillier, Caleb Pedro. "A system on chip based error detection and correction implementation for nanosatellites." Thesis, Cape Peninsula University of Technology, 2018. http://hdl.handle.net/20.500.11838/2841.

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Thesis (Master of Engineering in Electrical Engineering)--Cape Peninsula University of Technology, 2018.
This thesis will focus on preventing and overcoming the effects of radiation in RAM on board the ZA cube 2 nanosatellite. The main objective is to design, implement and test an effective error detection and correction (EDAC) system for nanosatellite applications using a SoC development board. By conducting an in-depth literature review, all aspects of single-event effects are investigated, from space radiation right up to the implementation of an EDAC system. During this study, Hamming code was identified as a suitable EDAC scheme for the prevention of single-event effects. During the course of this thesis, a detailed radiation study of ZA cube 2’s space environment is conducted. This provides insight into the environment to which the satellite will be exposed to during orbit. It also provides insight which will allow accurate testing should accelerator tests with protons and heavy ions be necessary. In order to understand space radiation, a radiation study using ZA cube 2’s orbital parameters was conducted using OMERE and TRIM software. This study included earth’s radiation belts, galactic cosmic radiation, solar particle events and shielding. The results confirm that there is a need for mitigation techniques that are capable of EDAC. A detailed look at different EDAC schemes, together with a code comparison study was conducted. There are two types of error correction codes, namely error detection codes and error correction codes. For protection against radiation, nanosatellites use error correction codes like Hamming, Hadamard, Repetition, Four Dimensional Parity, Golay, BCH and Reed Solomon codes. Using detection capabilities, correction capabilities, code rate and bit overhead each EDAC scheme is evaluated and compared. This study provides the reader with a good understanding of all common EDAC schemes. The field of nanosatellites is constantly evolving and growing at a very fast speed. This creates a growing demand for more advanced and reliable EDAC systems that are capable of protecting all memory aspects of satellites. Hamming codes are extensively studied and implemented using different approaches, languages and software. After testing three variations of Hamming codes, in both Matlab and VHDL, the final and most effective version was Hamming [16, 11, 4]2. This code guarantees single error correction and double error detection. All developed Hamming codes are suited for FPGA implementation, for which they are tested thoroughly using simulation software and optimised.

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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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Du, Toit F. J. "A fountain code forward error correction strategy for SensLAB applications." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/86399.

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Thesis (MScEng)--Stellenbosch University, 2014.
ENGLISH ABSTRACT: The discovery of sparse graph codes, used in forward error correction strate- gies, has had an unrivaled impact on Information theory over the past decade. A recent advancement in this field, called Fountain codes, have gained much attention due to its intelligent rate adaptivity, and lend itself to applications such as multicasting and broadcasting networks. These particular properties can be considered valuable in a wireless sensor network setting as it is capable of providing forward error correction, and the added conceptual network protocol related extensions. A wireless sensor network testbed in France, called SensLAB, provides an experimental facility for researchers to develop and evaluate sensor network protocols, aside from a simulation environment. Tremendous value can be added to the SensLAB community if an appropriate forward error correction design, such as Fountain codes, is deemed feasible for use on such a platform. This thesis investigates the use of Fountain codes, in a binary erasure channel environment, as a forward error correction strategy for the distribution of reliable data content over the SensLAB platform. A short message length LT code using two different decoding mechanisms were developed and evaluated for possible implementation. Furthermore, a short message length Raptor code was developed by using supplementary theory and optimisation techniques that permit scalability in terms of the message size. The results favoured the Raptor code design as it performs close to near optimal while still satisfying the rateless- and universality property, at low computational complexity.
AFRIKAANSE OPSOMMING: Die ontdekking van yl-grafiekkodes, van toepassing op foutkorreksie strategieë, het onlangs 'n ongeewenaarde impak op Informasieteorie gehad. In 'n onlangse vooruitgang in hierdie veld, genoem Fonteinkodes, word daar meer fokus geplaas op die intelligente tempo aanpassingsvermoë van hierdie kodes, wat nuttige toepassing kan inhou in multi-saai- en uitsaai netwerke. Hierdie eienskappe kan moontlik as waardevol beskou word in draadlose sensor netwerke weens die fout regstellingsvermoë en die bykomende konseptuele netwerk protokol verwante uitbreidings. 'n Draadlose sensor netwerk toetsplatvorm in Frankryk, genoem die SensLAB, bied navorsers die geleentheid om eksperimentele sensor netwerk protokolle te ontwikkel en te toets buite 'n tipiese simulasie-omgewing. Groot waarde kan bygevoeg word aan die SensLAB gemeenskap indien 'n geskikte foutkorreksie strategie ontwikkel word, soos Fonteinkodes, en as geskik beskou kan word vir hierdie platvorm. In hierdie tesis word Fonteinkodes saam met die SensLAB platvorm ondersoek, binne die raamwerk van 'n binêre verlieskanaal, om vir foutkorreksie oor die verspreiding van betroubare data in SensLAB op te tree. 'n Kort boodskap LT kode word voorgestel deur van twee verskillende dekoderings meganismes gebruik te maak. 'n Alternatief, genaamd Raptorkode, was ook ondersoek. 'n Raptorkode. 'n Kort boodskap Raptor kode, wat ontwikkel is met bykomende teorie en optimeringstegnieke, word ook voorgestel. Die bykomende tegnieke bied 'n skaleerbare boodskap lengte terwyl dit tempoloos en universeel bly, en lae kompleksiteit bied.

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Zhang, Liren. "Recovery of cell loss in ATM networks using forward error correction coding techniques /." Title page, contents and summary only, 1992. http://web4.library.adelaide.edu.au/theses/09PH/09phz6332.pdf.

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Thesis (Ph. D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, 1993.
Copies of author's previously published articles inserted. Includes bibliographical references (leaves 179-186).

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Daniel, J. S. "Synthesis and decoding of array error control codes." Thesis, University of Manchester, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.374587.

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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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Jeffery, Casey Miles. "Performance analysis of dynamic sparing and error correction techniques for fault tolerance in nanoscale memory structures." [Gainesville, Fla.] : University of Florida, 2004. http://purl.fcla.edu/fcla/etd/UFE0007163.

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

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Moon, Todd K. Error Correction Coding. New York: John Wiley & Sons, Ltd., 2005.

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Glover, Neal. Practical error correction design for engineers. 2nd ed. Broomfield, Colo: Data Systems Technology, Corp., 1988.

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Geisel, William A. Tutorial on Reed-Solomon error correction coding. Houston, Texas: National Aeronautics and Space Administration, Lyndon B. Johnson Space Center, 1990.

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Geisel, William A. Tutorial on Reed-Solomon error correction coding. Houston, Texas: National Aeronautics and Space Administration, Lyndon B. Johnson Space Center, 1990.

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Geisel, William A. Tutorial on Reed-Solomon error correction coding. Houston, Texas: National Aeronautics and Space Administration, Lyndon B. Johnson Space Center, 1990.

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A, Marelli, and Ravasio R, eds. Error correction codes for non-volatile memories. [Dordrecht]: Springer, 2008.

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Weldon, E. J. Jr, coaut, ed. Error-Correcting Codes. 2nd ed. Boston: Massachusetts Institute of Technology, 1988.

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MacWilliams, Florence Jessie. The theory of error correcting codes. 8th ed. Amsterdam: North-Holland Pub. Co., 1993.

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

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Vera, Pless, ed. Fundamentals of error-correcting codes. Cambridge: Cambridge University Press, 2010.

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

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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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Böhm, Christoph, and Maximilian Hofer. "Error Correction Codes." In Physical Unclonable Functions in Theory and Practice, 87–102. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-5040-5_5.

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Alber, G., M. Mussinger, and A. Delgado. "Quantum Information Processing and Error Correction with Jump Codes." In Quantum Information Processing, 14–27. Weinheim, FRG: Wiley-VCH Verlag GmbH & Co. KGaA, 2005. http://dx.doi.org/10.1002/3527606009.ch2.

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Alber, G., M. Mussinger, and A. Delgado. "Quantum Information Processing and Error Correction with Jump Codes." In Quantum Information Processing, 14–27. Weinheim, FRG: Wiley-VCH Verlag GmbH & Co. KGaA, 2005. http://dx.doi.org/10.1002/3527603549.ch2.

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Djordjevic, Ivan B. "Classical and Quantum Error-Correction Coding in Genetics." In Quantum Biological Information Theory, 237–69. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-22816-7_6.

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Nguyen, Duc Manh, and Sunghwan Kim. "Application of Classical Codes over GF(4) on Quantum Error Correction Codes." In Frontiers in Intelligent Computing: Theory and Applications, 116–22. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-32-9186-7_13.

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Golomb, Solomon W., Robert E. Peile, and Robert A. Scholtz. "Error Correction II: The Information-Theoretic Viewpoint." In Basic Concepts in Information Theory and Coding, 309–68. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4757-2319-9_6.

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Chow, Yang-Wai, Willy Susilo, Guomin Yang, James G. Phillips, Ilung Pranata, and Ari Moesriami Barmawi. "Exploiting the Error Correction Mechanism in QR Codes for Secret Sharing." In Information Security and Privacy, 409–25. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-40253-6_25.

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Golomb, Solomon W., Robert E. Peile, and Robert A. Scholtz. "Error Correction I: Distance Concepts and Bounds." In Basic Concepts in Information Theory and Coding, 243–308. Boston, MA: Springer US, 1994. http://dx.doi.org/10.1007/978-1-4757-2319-9_5.

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Jürgensen, H., and S. Konstantinidis. "Error correction for channels with substitutions, insertions, and deletions." In Information Theory and Applications II, 149–63. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0025142.

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

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Balli, Huseyin, Xijin Yan, and Zhen Zhang. "Error Correction Capability of Random Network Error Correction Codes." In 2007 IEEE International Symposium on Information Theory. IEEE, 2007. http://dx.doi.org/10.1109/isit.2007.4557447.

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Mazumdar, Arya, Gregory W. Wornell, and Venkat Chandar. "Update efficient codes for error correction." In 2012 IEEE International Symposium on Information Theory - ISIT. IEEE, 2012. http://dx.doi.org/10.1109/isit.2012.6283534.

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Helleseth, T., T. Klove, and V. I. Levenshtein. "Error-correction capability of binary linear codes." In IEEE International Symposium on Information Theory, 2003. Proceedings. IEEE, 2003. http://dx.doi.org/10.1109/isit.2003.1228480.

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Chilappagari, S. K., B. Vasic, and M. W. Marcellin. "Guaranteed error correction capability of codes on graphs." In 2009 Information Theory and Applications Workshop (ITA). IEEE, 2009. http://dx.doi.org/10.1109/ita.2009.5044922.

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Chowdhury, Arijit, and B. Sundar Rajan. "Quantum error correction via codes over GF(2)." In 2009 IEEE International Symposium on Information Theory - ISIT. IEEE, 2009. http://dx.doi.org/10.1109/isit.2009.5205646.

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Yang, Hengjie, and Wangmei Guo. "Distributed decoding of convolutional network error correction codes." In 2017 IEEE International Symposium on Information Theory (ISIT). IEEE, 2017. http://dx.doi.org/10.1109/isit.2017.8006958.

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Pattabiraman, Srilakshmi, Ryan Gabrys, and Olgica Milenkovic. "Reconstruction and Error-Correction Codes for Polymer-Based Data Storage." In 2019 IEEE Information Theory Workshop (ITW). IEEE, 2019. http://dx.doi.org/10.1109/itw44776.2019.8989171.

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Liu, Xishuo, and Stark C. Draper. "ADMM decoding of error correction codes: From geometries to algorithms." In 2015 IEEE Information Theory Workshop (ITW). IEEE, 2015. http://dx.doi.org/10.1109/itw.2015.7133156.

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Prakash, N., Govinda M. Kamath, V. Lalitha, and P. Vijay Kumar. "Optimal linear codes with a local-error-correction property." In 2012 IEEE International Symposium on Information Theory - ISIT. IEEE, 2012. http://dx.doi.org/10.1109/isit.2012.6284028.

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Barg, Alexander, and Arya Mazumdar. "Codes in permutations and error correction for rank modulation." In 2010 IEEE International Symposium on Information Theory - ISIT. IEEE, 2010. http://dx.doi.org/10.1109/isit.2010.5513604.

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