Application of Data Representation Methods Using Residue Images for Transmitting and Processing Information in Modern Telecommunication Systems
DOI:
https://doi.org/10.52575/2687-0932-2025-52-3-726-734Keywords:
expansion of the classical theory of finite fields, data and measurement errors, information distortion during transmission, data processing, residual class system, and regularization of ill-posed problemsAbstract
The article is devoted to the development of methods for non-traditional data representation using residue images and the construction of a unified technology that combines the processes of data representation, transmission, and processing in modern telecommunication systems into a consistent system. Previously, these processes were developed independently of each other, but the growing number of contradictions, which is associated with both the complexity of technology and the expansion of the range of tasks that can be solved using it, necessitates the search for new resources that can be used to resolve these issues. This is where the developed constructive theory of measurement and information transmission comes in. It is based on the mathematical theory of finite fields, which is adapted to solving applied problems of data representation, transmission, and processing in the presence of interference. The methodological basis of this approach is the constructive remainder theorem, which has the following key advantages: a significant expansion of the practical application area.
Downloads
References
Список литературы
Булычев Ю.Г., Васильев В.В., Кукушкин С.С. и др. 2016. Информационно-измерительное обеспечение натурных испытаний сложных технических комплексов. М.: Машиностроение, Полёт: 440.
Волков Е.А. 1982. Численные методы. М, Наука: 256–258.
Кнут Д. 1977. Искусство программирования для ЭВМ т. 2. Получисленные алгоритмы. М., Мир: 724.
Князев В.В., Кукушкин С.С. 2011. Математические и методические основы использования конструктивной теоремы об остатках при обработке результатов телеизмерений. М.: Научный Интернет-журнал: Технологии техносферной безопасности (http://ipb.mos.ru/ttb/2011-6/2011- 6.html), вып. 6 (40):6.
Князев В.В., Кукушкин С.С. 2011. Применение конструктивной теоремы об остатках при решении некорректных задач обработки результатов телеизмерений. Научно-технический сборник. Известия № 248. М.: ВА РВСН им. Петра Великого: 78.
Кукушкин С.С. 2000. Конечные поля и информатика (монография): в 2-х томах, т. 1. Методы и алгоритмы, классические и нетрадиционные, основанные на использовании конструктивной теоремы об остатках. М.: МО РФ: 260.
Кукушкин С.С. 1997. Использование конструктивной теоремы об остатках для повышения эффективности вычислений в системах передачи и обработки телеметрической информации. Измерительная техника. М.: «Стандарты», № 4: 13.
Лидл Р., Нидеррайтер Г. 1988. Конечные поля. В 2-х томах. Пер с англ. М.: Мир: 884.
Ширяев А.А. 2023. Анализ методов повышения эффективности систем передачи данных в беспроводных информационных коммуникациях. Сборник статей Межвузовского международного конгресса «Высшая школа: научные исследования», Москва: 138.
Ширяев А.А. 2024. Разработка методов обеспечения помехоустойчивости космических инфокоммуникаций на основе кодирования в системе остаточных классов. Материалы диссертации, изд-во НИУ БелГУ: 103.
References
Bulychev Yu.G., Vasilyev V.V., Kukushkin S.S. 2016. Information and Measurement Support for Field Tests of Complex Technical Systems, Moscow: Mashinostroenie-Polet: 440 (in Russian).
Volkov E.A. 1982. Numerical Methods. M: Nauka: 256 (in Russian).
Knuth D. 1977. The Art of Computer Programming, Vol. 2, Semi-Numerical Algorithms, Moscow: Mir: 724 (in Russian).
Knyazev V.V., Kukushkin S.S. 2011. Mathematical and Methodological Foundations of Using the Constructive Remainder Theorem in Processing Telemetry Results, Moscow, Scientific Internet Journal: Technologies of Technosphere Safety (http://ipb.mos.ru/ttb/2011-6/2011-6.html), Issue 6 (40): 6 (in Russian).
Knyazev V.V., Kukushkin S.S. 2011. Application of the constructive remainder theorem in solving ill-posed problems of processing telemetry results, Scientific and Technical Collection. Izvestiya No. 248. Moscow: Peter the Great Strategic Missile Forces Academy: 78 (in Russian).
Kukushkin S.S. 2000. Finite Fields and Computer Science (Monograph): in 2 volumes, vol. 1. Methods and Algorithms, Classical and Non-Traditional, Based on the Use of the Constructive Remainder Theorem. Moscow: Ministry of Defense of the Russian Federation: 260 (in Russian).
Kukushkin S.S. 1997. Using the constructive remainder theorem to improve the efficiency of calculations in telemetry information transmission and processing systems. Measurement Techniques. Moscow: Standards, No. 4: 13 (in Russian).
Lidl R., Niederreiter H. 1988. Finite Fields. In 2 volumes. Translated from English. Moscow, Mir: 884. Shiryaev A.A. 2023. Analysis of Methods for Improving the Efficiency of Data Transmission Systems in Wireless Information Communications. Collection of Articles from the Interuniversity International Congress «Higher Education: Scientific Research», Moscow: 138 (in Russian).
Shiryaev A.A. 2024. Development of methods for ensuring the noise immunity of space information communications based on coding in the residual class system. Dissertation materials, Belgorod State University:103 (in Russian).
Abstract views: 0
Share
Published
How to Cite
Issue
Section
Copyright (c) 2025 Economics. Information Technologies
This work is licensed under a Creative Commons Attribution 4.0 International License.
