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Network coding and error correction
Proceedings of the IEEE Information Theory Workshop, 2003We introduce network error-correcting codes for error correction when a source message is transmitted to a set of receiving nodes on a network. The usual approach in existing networks, namely link-by-link error correction, is a special case of network error correction. The network generalizations of the Hamming bound and the Gilbert-Varshamov bound are
Ning Cai 0001, Raymond W. Yeung
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On the Trustworthiness of Error-Correcting Codes
IEEE Transactions on Information Theory, 2007The use of error-correcting codes protects data against accidental or intentional errors, but to what extent can a decoded message be trusted? To answer this question, one has to take the role of the receiver. First, the maximum number of errors Lambda acceptable for decoding is fixed. With the weight distribution, the probability of false decoding can
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On error-correcting balanced codes
IEEE Transactions on Information Theory, 1989Results are presented on families of balanced binary error-correcting codes that extend those in the literature. The idea is to consider balanced blocks as symbols over an alphabet and to construct error-correcting codes over that alphabet. Encoding and decoding procedures are presented. Several improvements to the general construction are discussed.
Tilborg, van, H.C.A., Blaum, M.
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IEEE Transactions on Information Theory, 1973
The purpose of this paper is to develop more general techniques for the synthesis of error-correcting codes that dispense with the requirement that coding elements and operations must be associated with finite fields. This approach permits an extension of the class of coded messages and coding operations and leads in certain cases to a reduction of ...
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The purpose of this paper is to develop more general techniques for the synthesis of error-correcting codes that dispense with the requirement that coding elements and operations must be associated with finite fields. This approach permits an extension of the class of coded messages and coding operations and leads in certain cases to a reduction of ...
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Error-correcting codes and cryptography
Applicable Algebra in Engineering, Communication and Computing, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hideki Imai, Manabu Hagiwara
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Metacyclic error-correcting codes
Applicable Algebra in Engineering, Communication and Computing, 1995The group codes are ideals of group algebras. Let \(G\) and \(H\) be groups of the same order, \(F\) be a finite field, let \(FG\) and \(FH\) be the corresponding group rings. The combinatorial equivalence is an \(F\) vector space isomorphism \(\gamma: FG\to FH\) induced by a bijection \(\gamma: G\to H\). Codes \(C1 \subseteq FG\) and \(C2 \subseteq FH\
Roberta Evans Sabin, Samuel J. Lomonaco
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1979
In Chapter I-13, we looked at ways of coding messages so that if in the transmission an error occurred in one of the digits of a coded word, the receiver would be able to correct the error. Those codes, called Hamming codes, were based on defining coded words as vectors of solutions in ℤ2 to sets of linear equations.
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In Chapter I-13, we looked at ways of coding messages so that if in the transmission an error occurred in one of the digits of a coded word, the receiver would be able to correct the error. Those codes, called Hamming codes, were based on defining coded words as vectors of solutions in ℤ2 to sets of linear equations.
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Multiple error-correcting WOM-codes
2010 IEEE International Symposium on Information Theory, 2010A Write Once Memory (WOM) is a storage medium with binary memory elements, called cells, that can change from the zero state to the one state only once. Examples of WOMs are punch cards, optical disks, and more recently flash memories. WOM-codes were first presented by Rivest and Shamir and are designed for efficiently storing and updating data in the ...
Eitan Yaakobi +3 more
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IEEE Transactions on Information Theory, 2019
Coding schemes are presented that provide the ability to locate computational errors above a prescribed threshold while using analog resistive devices for approximate real vector–matrix multiplication. In such devices, the matrix is programmed into the device by setting an array of resistors to have conductances proportional to the respective entries ...
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Coding schemes are presented that provide the ability to locate computational errors above a prescribed threshold while using analog resistive devices for approximate real vector–matrix multiplication. In such devices, the matrix is programmed into the device by setting an array of resistors to have conductances proportional to the respective entries ...
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Codes for the correction of 'clustered' errors
IEEE Transactions on Information Theory, 1960A method is described which permits the systematic construction of codes capable of error-free transmission, provided errors occur in "clusters" of limited duration. The method is valid for error clusters of any prescribed duration. The codes are relatively easy to implement and decoding operations are straightforward.
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