Formalization of Ternary Logic for Application to Digital Signal Processing

Сулейменов, И. Э.; Bakirov, Akhat; Moldakhan, Inabat

doi:10.1007/978-3-030-57453-6_3

Cited by 11 publications

(6 citation statements)

References 18 publications

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“…There is also the possibility to implement operations in Galois fields using the usual "binary" element base. There are also some other possibilities, for example, related to the features of slowly changing signals, the "digital" derivatives of which can be found using frequency filtering [23] and using the apparatus of ternary logic [24], [25].…”

Section: Possibilities For Further Improvement Of the Proposed Methodsmentioning

confidence: 99%

New approaches to the development of information security systems for unmanned vehicles

Ermukhambetova

Mun

Kabdushev

et al. 2023

IJEECS

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<span>A new approach to ensuring information security is proposed for using in the zone of direct radio visibility. The approach is based on a direct analogy between radio and optical radiation. In the latter case, information protection can be ensured by identifying the point or direction from which the signal comes; all other light sources are cut off by the observer. It is shown that a similar method of information protection can also be implemented in the radio range, which corresponds to modern trends in the development of radio holography. The simplest scheme for detecting the direction to a transmitter, identified as “friend” is presented. Its operability is demonstrated by means of simulation modeling. Ways for the further development of this approach are determined, based on the fact that modern technologies make it possible to implement distributed reception of a radio signal (to use a relatively large number of receivers), which makes it possible to implement direct analogues of such optical elements as a lens, holograms.</span>

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Section: Possibilities For Further Improvement Of the Proposed Methodsmentioning

confidence: 99%

New approaches to the development of information security systems for unmanned vehicles

Ermukhambetova

Mun

Kabdushev

et al. 2023

IJEECS

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“…For convenience, we will use a field containing elements (-2, -1,0,1,2). Addition and multiplication (Tables 1 and 2) are defined according to rules similar to those used in [34].…”

Section: Methodsmentioning

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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“…Traditionally, positive integers are used when representing field elements, however, this is not mandatory at all. In particular, as emphasized in [25], it is advisable to use a set of elements {−1,0,1} to represent the field GF (3), where the use of curly brackets emphasizes that the set is being considered.…”

Section: Algorithms Of Calculations Modulo In the Special Case Of The...mentioning

confidence: 99%

Features of digital signal processing algorithms using Galois fields GF(2n+1)

Suleimenov,

Vitulyova,

Matrassulova

2023

PLoS ONE

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An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2n+1. For such numbers, it is possible to implement a multiplication algorithm modulo p, similar to the multiplication algorithm modulo the Mersenne number. It is shown that for such numbers a simple algorithm for digital logarithm calculations may be proposed. This algorithm allows, among other things, to reduce the multiplication operation modulo a prime number p = 2n+1 to an addition operation.

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Formalization of Ternary Logic for Application to Digital Signal Processing

Cited by 11 publications

References 18 publications

New approaches to the development of information security systems for unmanned vehicles

New approaches to the development of information security systems for unmanned vehicles

Algebraic fields and rings as a digital signal processing tool

Features of digital signal processing algorithms using Galois fields GF(2n+1)

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