Error Correcting Network Codes

Belhamra, Mohamed Amine; Souidi, El Mamoun

doi:10.1016/j.comnet.2021.108277

Cited by 2 publications

(1 citation statement)

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“…From this point of view, the operator (matrix) representation of the form (40) is also of interest. Indeed, the classical methods of error-correcting coding [37] use the factor of redundant information. Instead of a sequence containing a certain number of characters, a sequence containing more characters is used, which allows you to identify or eliminate the error.…”

Section: Resultsmentioning

confidence: 99%

Algebraic fields and rings as a digital signal processing tool

Matrassulova

Vitulyova

Konshin

et al. 2022

IJEECS

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It is shown that algebraic fields and rings can become a very promising tool for digital signal processing. This is mainly due to the fact that any digital signals change in a finite range of amplitudes and, therefore, there are only a finite set of levels that can correspond to the amplitudes of a signal reduced to a discrete form. This allows you to establish a one-to-one correspondence between the set of levels and such algebraic structures as fields, rings, etc. This means that a function that takes values in any of the algebraic structures containing a finite set of elements can serve as a model of a signal reduced to a discrete form. A special case of such a signal model are functions that take values in Galois fields. It is shown that, along with Galois fields, in certain cases, algebraic rings contain zero divisors can be used to construct signal models. This representation is convenient because in this case it becomes possible to independently operate with the digits of the number that enumerates the signal levels. A simple and intuitive method for constructing rings is proposed, based on an analogy with the method of algebraic extensions.

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Section: Resultsmentioning

confidence: 99%