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Academic literature on the topic 'Error correcting index codes'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Error correcting index codes"

1

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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Hawkins, John A., Stephen K. Jones, Ilya J. Finkelstein, and William H. Press. "Indel-correcting DNA barcodes for high-throughput sequencing." Proceedings of the National Academy of Sciences 115, no. 27 (June 20, 2018): E6217—E6226. http://dx.doi.org/10.1073/pnas.1802640115.

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Many large-scale, high-throughput experiments use DNA barcodes, short DNA sequences prepended to DNA libraries, for identification of individuals in pooled biomolecule populations. However, DNA synthesis and sequencing errors confound the correct interpretation of observed barcodes and can lead to significant data loss or spurious results. Widely used error-correcting codes borrowed from computer science (e.g., Hamming, Levenshtein codes) do not properly account for insertions and deletions (indels) in DNA barcodes, even though deletions are the most common type of synthesis error. Here, we present and experimentally validate filled/truncated right end edit (FREE) barcodes, which correct substitution, insertion, and deletion errors, even when these errors alter the barcode length. FREE barcodes are designed with experimental considerations in mind, including balanced guanine-cytosine (GC) content, minimal homopolymer runs, and reduced internal hairpin propensity. We generate and include lists of barcodes with different lengths and error correction levels that may be useful in diverse high-throughput applications, including >106 single-error–correcting 16-mers that strike a balance between decoding accuracy, barcode length, and library size. Moreover, concatenating two or more FREE codes into a single barcode increases the available barcode space combinatorially, generating lists with >1015 error-correcting barcodes. The included software for creating barcode libraries and decoding sequenced barcodes is efficient and designed to be user-friendly for the general biology community.

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Karat, Nujoom Sageer, Simon Samuel, and B. Sundar Rajan. "Optimal Error Correcting Index Codes for Some Generalized Index Coding Problems." IEEE Transactions on Communications 67, no. 2 (February 2019): 929–42. http://dx.doi.org/10.1109/tcomm.2018.2878566.

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Thomas, Anoop, and B. Sundar Rajan. "A Discrete Polymatroidal Framework for Differential Error-Correcting Index Codes." IEEE Transactions on Communications 67, no. 7 (July 2019): 4593–604. http://dx.doi.org/10.1109/tcomm.2019.2910266.

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Yao, Yu, Yuena Ma, Husheng Li, and Jingjie Lv. "An explicit construction of quantum codes from one-generator generalized quasi-cyclic codes." MATEC Web of Conferences 336 (2021): 04001. http://dx.doi.org/10.1051/matecconf/202133604001.

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In this paper, we take advantage of a class of one-generator generalized quasi-cyclic (GQC) codes of index 2 to construct quantum error-correcting codes. By studying the form of Hermitian dual codes and their algebraic structure, we propose a sufficient condition for self-orthogonality of GQC codes with Hermitian inner product. By comparison, the quantum codes we constructed have better parameters than known codes.

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Kadiev, I. P., P. A. Kadiev, and B. R. Kudaev. "INTERLEAVING BURST ERROR ELEMENTS IN INFORMATION ARRAYS USING THE METHOD OF INDEX STRUCTURISATION." Herald of Dagestan State Technical University. Technical Sciences 46, no. 4 (January 2, 2020): 84–90. http://dx.doi.org/10.21822/2073-6185-2019-46-4-84-90.

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Objectives. “Burst errors” representing groups of accidentally or intentionally distorted or “erased” characters in blocks of information arrays violate the integrity of their content. However, the use of special codes for detecting and correcting such errors significantly reduces the speed of information transfer due to the need to introduce redundancy in the form of a large number of control characters. Therefore, this study sets out to develop a method for correcting burst errors.Method. A possible approach for correcting burst errors consists in interleaving preliminary permutations of information array elements between different array blocks. After eliminating the results of element permutations, these procedures cause the interleaving of distorted elements occurring during the transfer or storage of the information array between its various blocks, causing single or minor fold errors.Result. For solving problems of this class, a new method of permuting elements of an nxnset of finite sets is proposed based on the index structuring of the formed configurations. These sets are interpreted as information arrays of the same configuration, and the permutation – interleaving – of their elements is carried out according to the method of configuration formed by the index structuring of their location.Conclusion. Three methods for interleaving elements of the original information in arrays are proposed: between rows, between columns and combined – between rows and columns. The proposed interleaving methods based on the preliminary conversion of information arrays by permuting elements according to given algorithms allow their distortions under the influence of burst errors to be corrected. Thus, the task of combating the burst errors leading to the destruction of individual groups of characters can be reduced to solving a simpler problem of minor fold error correction.

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Sageer Karat, Nujoom, Anoop Thomas, and Balaji Sundar Rajan. "Optimal Linear Error Correcting Delivery Schemes for Two Optimal Coded Caching Schemes." Entropy 22, no. 7 (July 13, 2020): 766. http://dx.doi.org/10.3390/e22070766.

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For coded caching problems with small buffer sizes and the number of users no less than the amount of files in the server, an optimal delivery scheme was proposed by Chen, Fan, and Letaief in 2016. This scheme is referred to as the CFL scheme. In this paper, an extension to the coded caching problem where the link between the server and the users is error prone, is considered. The closed form expressions for average rate and peak rate of error correcting delivery scheme are found for the CFL prefetching scheme using techniques from index coding. Using results from error correcting index coding, an optimal linear error correcting delivery scheme for caching problems employing the CFL prefetching is proposed. Another scheme that has lower sub-packetization requirement as compared to CFL scheme for the same cache memory size was considered by J. Gomez-Vilardebo in 2018. An optimal linear error correcting delivery scheme is also proposed for this scheme.

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LIU, TAILIN, FENGTONG WEN, and QIAOYAN WEN. "ON THE AUTOMORPHISM GROUPS OF A FAMILY OF BINARY QUANTUM ERROR-CORRECTING CODES." International Journal of Quantum Information 04, no. 06 (December 2006): 1013–22. http://dx.doi.org/10.1142/s0219749906002377.

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Based on the classical binary simplex code [Formula: see text] and any fixed-point-free element f of [Formula: see text], Calderbank et al. constructed a binary quantum error-correcting code [Formula: see text]. They proved that [Formula: see text] has a normal subgroup H, which is a semidirect product group of the centralizer Z(f) of f in GLm(2) with [Formula: see text], and the index [Formula: see text] is the number of elements of Ff = {f, 1 - f, 1/f, 1 - 1/f, 1/(1 - f), f/(1 - f)} that are conjugate to f. In this paper, a theorem to describe the relationship between the quotient group [Formula: see text] and the set Ff is presented, and a way to find the elements of Ff that are conjugate to f is proposed. Then we prove that [Formula: see text] is isomorphic to S3 and H is a semidirect product group of [Formula: see text] with [Formula: see text] in the linear case. Finally, we generalize a result due to Calderbank et al.

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Indoonundon, Deevya, Tulsi Pawan Fowdur, and Sunjiv Soyjaudah. "A Concealment Aware UEP scheme for H.264 using RS Codes." Indonesian Journal of Electrical Engineering and Computer Science 6, no. 3 (June 1, 2017): 671. http://dx.doi.org/10.11591/ijeecs.v6.i3.pp671-681.

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<p>H.264/AVC is currently the most widely adopted video coding standard due to its high compression capability and flexibility. However, compressed videos are highly vulnerable to channel errors which may result in severe quality degradation of a video. This paper presents a concealment aware Unequal Error Protection (UEP) scheme for H.264 video compression using Reed Solomon (RS) codes. The proposed UEP technique assigns a code rate to each Macroblock (MB) based on the type of concealment and a Concealment Dependent Index (CDI). Two interleaving techniques, namely Frame Level Interleaving (FLI) and Group Level Interleaving (GLI) have also been employed. Finally, prioritised concealment is applied in cases where error correction is beyond the capability of the RS decoder. Simulation results have demonstrated that the proposed framework provides an average gain of 2.96 dB over a scheme that used Equal Error Protection (EEP).</p>

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Haeupler, Bernhard, and Amirbehshad Shahrasbi. "Synchronization Strings: Codes for Insertions and Deletions Approaching the Singleton Bound." Journal of the ACM 68, no. 5 (October 31, 2021): 1–39. http://dx.doi.org/10.1145/3468265.

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We introduce synchronization strings , which provide a novel way to efficiently deal with synchronization errors , i.e., insertions and deletions. Synchronization errors are strictly more general and much harder to cope with than more commonly considered Hamming-type errors , i.e., symbol substitutions and erasures. For every ε > 0, synchronization strings allow us to index a sequence with an ε -O(1) -size alphabet, such that one can efficiently transform k synchronization errors into (1 + ε)k Hamming-type errors . This powerful new technique has many applications. In this article, we focus on designing insdel codes , i.e., error correcting block codes (ECCs) for insertion-deletion channels. While ECCs for both Hamming-type errors and synchronization errors have been intensely studied, the latter has largely resisted progress. As Mitzenmacher puts it in his 2009 survey [30]: “ Channels with synchronization errors...are simply not adequately understood by current theory. Given the near-complete knowledge, we have for channels with erasures and errors...our lack of understanding about channels with synchronization errors is truly remarkable. ” Indeed, it took until 1999 for the first insdel codes with constant rate, constant distance, and constant alphabet size to be constructed and only since 2016 are there constructions of constant rate insdel codes for asymptotically large noise rates. Even in the asymptotically large or small noise regimes, these codes are polynomially far from the optimal rate-distance tradeoff. This makes the understanding of insdel codes up to this work equivalent to what was known for regular ECCs after Forney introduced concatenated codes in his doctoral thesis 50 years ago. A straightforward application of our synchronization strings-based indexing method gives a simple black-box construction that transforms any ECC into an equally efficient insdel code with only a small increase in the alphabet size. This instantly transfers much of the highly developed understanding for regular ECCs into the realm of insdel codes. Most notably, for the complete noise spectrum, we obtain efficient “near-MDS” insdel codes, which get arbitrarily close to the optimal rate-distance tradeoff given by the Singleton bound. In particular, for any δ ∈ (0,1) and ε > 0, we give a family of insdel codes achieving a rate of 1 - δ - ε over a constant-size alphabet that efficiently corrects a δ fraction of insertions or deletions.

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Dissertations / Theses on the topic "Error correcting index codes"

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Kosek, Peter M. "Error Correcting Codes." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1417508067.

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Skoglund, Isabell. "Reed-Solomon Codes - Error Correcting Codes." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-97343.

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In the following pages an introduction of the error correcting codes known as Reed-Solomon codes will be presented together with different approaches for decoding. This is supplemented by a Mathematica program and a description of this program that gives an understanding in how the choice of decoding algorithms affect the time it takes to find errors in stored or transmitted information.

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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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Hessler, Martin. "Optimization, Matroids and Error-Correcting Codes." Doctoral thesis, Linköpings universitet, Tillämpad matematik, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-51722.

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The first subject we investigate in this thesis deals with optimization problems on graphs. The edges are given costs defined by the values of independent exponential random variables. We show how to calculate some or all moments of the distributions of the costs of some optimization problems on graphs. The second subject that we investigate is 1-error correcting perfect binary codes, perfect codes for short. In most work about perfect codes, two codes are considered equivalent if there is an isometric mapping between them. We call this isometric equivalence. Another type of equivalence is given if two codes can be mapped on each other using a non-singular linear map. We call this linear equivalence. A third type of equivalence is given if two codes can be mapped on each other using a composition of an isometric map and a non-singular linear map. We call this extended equivalence. In Paper 1 we give a new better bound on how much the cost of the matching problem with exponential edge costs varies from its mean. In Paper 2 we calculate the expected cost of an LP-relaxed version of the matching problem where some edges are given zero cost. A special case is when the vertices with probability 1 – p have a zero cost loop, for this problem we prove that the expected cost is given by a formula. In Paper 3 we define the polymatroid assignment problem and give a formula for calculating all moments of its cost. In Paper 4 we present a computer enumeration of the 197 isometric equivalence classes of the perfect codes of length 31 of rank 27 and with a kernel of dimension 24. In Paper 5 we investigate when it is possible to map two perfect codes on each other using a non-singular linear map. In Paper 6 we give an invariant for the equivalence classes of all perfect codes of all lengths when linear equivalence is considered. In Paper 7 we give an invariant for the equivalence classes of all perfect codes of all lengths when extended equivalence is considered. In Paper 8 we define a class of perfect codes that we call FRH-codes. It is shown that each FRH-code is linearly equivalent to a so called Phelps code and that this class contains Phelps codes as a proper subset.

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Fyn-Sydney, Betty Iboroma. "Phan geometries and error correcting codes." Thesis, University of Birmingham, 2013. http://etheses.bham.ac.uk//id/eprint/4433/.

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In this thesis, we define codes based on the Phan geometry of type An. We show that the action of the group SUn+1(q) is not irreducible on the code. In the rank two case, we prove that the code is spanned by those apartments which only consist of chambers belonging to the Phan geometry and obtain submodules for the code.

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Guruswami, Venkatesan 1976. "List decoding of error-correcting codes." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/8700.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.
Includes bibliographical references (p. 303-315).
Error-correcting codes are combinatorial objects designed to cope with the problem of reliable transmission of information on a noisy channel. A fundamental algorithmic challenge in coding theory and practice is to efficiently decode the original transmitted message even when a few symbols of the received word are in error. The naive search algorithm runs in exponential time, and several classical polynomial time decoding algorithms are known for specific code families. Traditionally, however, these algorithms have been constrained to output a unique codeword. Thus they faced a "combinatorial barrier" and could only correct up to d/2 errors, where d is the minimum distance of the code. An alternate notion of decoding called list decoding, proposed independently by Elias and Wozencraft in the late 50s, allows the decoder to output a list of all codewords that differ from the received word in a certain number of positions. Even when constrained to output a relatively small number of answers, list decoding permits recovery from errors well beyond the d/2 barrier, and opens up the possibility of meaningful error-correction from large amounts of noise. However, for nearly four decades after its conception, this potential of list decoding was largely untapped due to the lack of efficient algorithms to list decode beyond d/2 errors for useful families of codes. This thesis presents a detailed investigation of list decoding, and proves its potential, feasibility, and importance as a combinatorial and algorithmic concept.
(cont.) We prove several combinatorial results that sharpen our understanding of the potential and limits of list decoding, and its relation to more classical parameters like the rate and minimum distance. The crux of the thesis is its algorithmic results, which were lacking in the early works on list decoding. Our algorithmic results include: * Efficient list decoding algorithms for classically studied codes such as Reed-Solomon codes and algebraic-geometric codes. In particular, building upon an earlier algorithm due to Sudan, we present the first polynomial time algorithm to decode Reed-Solomon codes beyond d/2 errors for every value of the rate. * A new soft list decoding algorithm for Reed-Solomon and algebraic-geometric codes, and novel decoding algorithms for concatenated codes based on it. * New code constructions using concatenation and/or expander graphs that have good (and sometimes near-optimal) rate and are efficiently list decodable from extremely large amounts of noise. * Expander-based constructions of linear time encodable and decodable codes that can correct up to the maximum possible fraction of errors, using unique (not list) decoding.
by Venkatesan Guruswami.
Ph.D.

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Guo, Alan Xinyu. "New error correcting codes from lifting." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/99776.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 117-121).
Error correcting codes have been widely used for protecting information from noise. The theory of error correcting codes studies the range of parameters achievable by such codes, as well as the efficiency with which one can encode and decode them. In recent years, attention has focused on the study of sublinear-time algorithms for various classical problems, such as decoding and membership verification. This attention was driven in part by theoretical developments in probabilistically checkable proofs (PCPs) and hardness of approximation. Locally testable codes (codes for which membership can be verified using a sublinear number of queries) form the combinatorial core of PCP constructions and thus play a central role in computational complexity theory. Historically, low-degree polynomials (the Reed-Muller code) have been the locally testable code of choice. Recently, "affine-invariant" codes have come under focus as providing potential for new and improved codes. In this thesis, we exploit a natural algebraic operation known as "lifting" to construct new affine-invariant codes from shorter base codes. These lifted codes generically possess desirable combinatorial and algorithmic properties. The lifting operation preserves the distance of the base code. Moreover, lifted codes are naturally locally decodable and testable. We tap deeper into the potential of lifted codes by constructing the "lifted Reed-Solomon code", a supercode of the Reed-Muller code with the same error-correcting capabilities yet vastly greater rate. The lifted Reed-Solomon code is the first high-rate code known to be locally decodable up to half the minimum distance, locally list-decodable up to the Johnson bound, and robustly testable, with robustness that depends only on the distance of the code. In particular, it is the first high-rate code known to be both locally decodable and locally testable. We also apply the lifted Reed-Solomon code to obtain new bounds on the size of Nikodym sets, and also to show that the Reed-Muller code is robustly testable for all field sizes and degrees up to the field size, with robustness that depends only on the distance of the code.
by Alan Xinyu Guo.
Ph. D.

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Vicente, Renato. "Statistical physics of error-correcting codes." Thesis, Aston University, 2000. http://publications.aston.ac.uk/10608/.

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In this thesis we use statistical physics techniques to study the typical performance of four families of error-correcting codes based on very sparse linear transformations: Sourlas codes, Gallager codes, MacKay-Neal codes and Kanter-Saad codes. We map the decoding problem onto an Ising spin system with many-spins interactions. We then employ the replica method to calculate averages over the quenched disorder represented by the code constructions, the arbitrary messages and the random noise vectors. We find, as the noise level increases, a phase transition between successful decoding and failure phases. This phase transition coincides with upper bounds derived in the information theory literature in most of the cases. We connect the practical decoding algorithm known as probability propagation with the task of finding local minima of the related Bethe free-energy. We show that the practical decoding thresholds correspond to noise levels where suboptimal minima of the free-energy emerge. Simulations of practical decoding scenarios using probability propagation agree with theoretical predictions of the replica symmetric theory. The typical performance predicted by the thermodynamic phase transitions is shown to be attainable in computation times that grow exponentially with the system size. We use the insights obtained to design a method to calculate the performance and optimise parameters of the high performance codes proposed by Kanter and Saad.

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Erxleben, Wayne Henry 1963. "Error-correcting two-dimensional modulation codes." Thesis, The University of Arizona, 1993. http://hdl.handle.net/10150/291577.

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Modulation coding, to limit the number of consecutive zeroes in a data stream, is essential in digital magnetic recording/playback systems. Additionally, such systems require error correction coding to ensure that the decoded output matches the recorder input, even if noise is present. Typically these two coding steps have been performed independently, although various methods of combining them into one step have recently appeared. Another recent development is two-dimensional modulation codes, which meet runlength constraints using several parallel recording tracks, significantly increasing channel capacity. This thesis combines these two ideas. Previous techniques (both block and trellis structures) for combining error correction and modulation coding are surveyed, with discussion of their applicability in the two-dimensional case. One approach, based on trellis-coded modulation, is explored in detail, and a class of codes developed which exploit the increased capacity to achieve good error-correcting ability at the same rate as common non-error-correcting one-dimensional codes.

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Joseph, Binoy. "Clustering For Designing Error Correcting Codes." Thesis, Indian Institute of Science, 1994. https://etd.iisc.ac.in/handle/2005/3915.

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In this thesis we address the problem of designing codes for specific applications. To do so we make use of the relationship between clusters and codes. Designing a block code over any finite dimensional space may be thought of as forming the corresponding number of clusters over the particular dimensional space. In literature we have a number of algorithms available for clustering. We have examined the performance of a number of such algorithms, such as Linde-Buzo-Gray, Simulated Annealing, Simulated Annealing with Linde-Buzo-Gray, Deterministic Annealing, etc, for design of codes. But all these algorithms make use of the Eucledian squared error distance measure for clustering. This distance measure does not match with the distance measure of interest in the error correcting scenario, namely, Hamming distance. Consequently we have developed an algorithm that can be used for clustering with Hamming distance as the distance measure. Also, it has been observed that stochastic algorithms, such as Simulated Annealing fail to produce optimum codes due to very slow convergence near the end. As a remedy, we have proposed a modification based on the code structure, for such algorithms for code design which makes it possible to converge to the optimum codes.

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Books on the topic "Error correcting index codes"

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Baylis, John. Error-correcting Codes. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4899-3276-1.

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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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Xambó-Descamps, Sebastià. Block Error-Correcting Codes. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-18997-5.

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

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Buttigieg, Victor. Variable-length error-correcting codes.. Manchester: University of Manchester, 1995.

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

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Calmet, Jacques, ed. Algebraic Algorithms and Error-Correcting Codes. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/3-540-16776-5.

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Guruswami, Venkatesan. List Decoding of Error-Correcting Codes. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/b104335.

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Cancellieri, Giovanni. Polynomial Theory of Error Correcting Codes. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-01727-3.

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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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Book chapters on the topic "Error correcting index codes"

1

Basu, Riddhipratim, Subhamoy Maitra, Goutam Paul, and Tanmoy Talukdar. "On Some Sequences of the Secret Pseudo-random Index j in RC4 Key Scheduling." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 137–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02181-7_15.

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Lally, Kristine. "Quasicyclic Codes of Index ℓ over F q Viewed as F q[x]-Submodules of F q ℓ[x]/〈x m−1〉." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 244–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-44828-4_26.

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Slinko, Arkadii. "Error-Correcting Codes." In Springer Undergraduate Mathematics Series, 191–234. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44074-9_7.

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Jones, Gareth A., and J. Mary Jones. "Error-correcting Codes." In Springer Undergraduate Mathematics Series, 97–119. London: Springer London, 2000. http://dx.doi.org/10.1007/978-1-4471-0361-5_6.

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Finston, David R., and Patrick J. Morandi. "Error Correcting Codes." In Abstract Algebra, 23–40. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-04498-9_2.

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Kumar, P. Vijay. "Error-Correcting Codes." In Space Communication and Nuclear Scintillation, 224–313. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-017-5418-7_2.

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Salomon, David. "Error Correcting Codes." In Data Compression, 337–48. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4757-2939-9_10.

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Liu, Andrew Chiang-Fung. "Error-Correcting Codes." In S.M.A.R.T. Circle Projects, 1–16. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56811-9_1.

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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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Slinko, Arkadii. "Error-Correcting Codes." In Springer Undergraduate Mathematics Series, 171–211. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-21951-6_7.

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Conference papers on the topic "Error correcting index codes"

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Thomas, Anoop, and B. Sundar Rajan. "Error correcting index codes and matroids." In 2015 IEEE International Symposium on Information Theory (ISIT). IEEE, 2015. http://dx.doi.org/10.1109/isit.2015.7282611.

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Chinmayananda, A., and B. Sundar Rajan. "Optimal Error Correcting Index Codes for Extended Index Coding Problems." In 2019 19th International Symposium on Communications and Information Technologies (ISCIT). IEEE, 2019. http://dx.doi.org/10.1109/iscit.2019.8905117.

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Karat, Nujoom Sageer, and B. Sundar Rajan. "Optimal Linear Error Correcting Index Codes for Some Index Coding Problems." In 2017 IEEE Wireless Communications and Networking Conference (WCNC). IEEE, 2017. http://dx.doi.org/10.1109/wcnc.2017.7925744.

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Thomas, Anoop, and B. Sundar Rajan. "Vector linear error correcting index codes and discrete polymatroids." In 2015 IEEE International Symposium on Information Theory (ISIT). IEEE, 2015. http://dx.doi.org/10.1109/isit.2015.7282613.

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Vaddi, Mahesh Babu, and B. Sundar Rajan. "Optimal error correcting index codes for two classes of index coding problems." In 2018 52nd Annual Conference on Information Sciences and Systems (CISS). IEEE, 2018. http://dx.doi.org/10.1109/ciss.2018.8362252.

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Samuel, Simon, Nujoom Sageer Karat, and B. Sundar Rajan. "Optimal linear error-correcting index codes for some generalized index coding problems." In 2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC). IEEE, 2017. http://dx.doi.org/10.1109/pimrc.2017.8292448.

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Gupta, Anindya, and B. Sundar Rajan. "Error-correcting functional index codes, generalized exclusive laws and graph coloring." In ICC 2016 - 2016 IEEE International Conference on Communications. IEEE, 2016. http://dx.doi.org/10.1109/icc.2016.7511555.

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Samuel, Simon, and B. Sundar Rajan. "Optimal Linear Error-Correcting Index Codes for Single-Prior Index-Coding with Side Information." In 2017 IEEE Wireless Communications and Networking Conference (WCNC). IEEE, 2017. http://dx.doi.org/10.1109/wcnc.2017.7925745.

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HAGIWARA, MANABU. "QUANTUM ERROR-CORRECTING CODES." In Summer School on Mathematical Aspects of Quantum Computing. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812814487_0006.

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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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Reports on the topic "Error correcting index codes"

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Auslander, Louis. Weil Transform and Error Correcting Codes. Fort Belvoir, VA: Defense Technical Information Center, July 1996. http://dx.doi.org/10.21236/ada376721.

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Zhang, Xinmiao. Sensor Network Optimization by Using Error-Correcting Codes. Fort Belvoir, VA: Defense Technical Information Center, February 2011. http://dx.doi.org/10.21236/ada565196.

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Mitchell, Gregory. Investigation of Hamming, Reed-Solomon, and Turbo Forward Error Correcting Codes. Fort Belvoir, VA: Defense Technical Information Center, July 2009. http://dx.doi.org/10.21236/ada505116.

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McEliece, Robert, and Padhraic Smyth. Turbo Decoding of High Performance Error-Correcting Codes via Belief Propagation. Fort Belvoir, VA: Defense Technical Information Center, December 1998. http://dx.doi.org/10.21236/ada386835.

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Lala, P. K., and H. L. Martin. Application of Error Correcting Codes in Fault-Tolerant Logic Design for VLSI Circuits. Fort Belvoir, VA: Defense Technical Information Center, May 1990. http://dx.doi.org/10.21236/ada228840.

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