Intelligent OFDM telecommunication system. Part 1. Model of complex and quaternion systems

In this paper, we aim to investigate the superiority and practicability of many-parameter transforms (MPTs) from the physical layer security (PHY-LS) perspective. We propose novel Intelligent OFDM-telecommunication systems based on complex and quaternion MPTs. The new systems use inverse MPT (IMPT) for modulation at the transmitter and MPT for demodulation at the receiver. The purpose of employing the MPT is to improve: 1) the PHY-LS of wireless transmissions against to the wide-band anti-jamming and anti-eavesdropping communication; 2) the bit error rate (BER) performance with respect to the conventional OFDM-TCS; 3) the peak to average power ratio (PAPR). Each MPT depends on finite set of independent parameters (angles). When parameters are changed, many-parametric transform is also changed taking form of a set known (and unknown) orthogonal (or unitary) transforms. For this reason, the concrete values of parameters are specific "key" for entry into OFDM-TCS. Vector of parameters belong to multi-dimension torus space. Scanning of this space for find out the "key" (the concrete values of parameters) is hard problem. MPT has the form of the product of the Jacobi rotation matrixes and it describes a fast algorithm for MPT. The main advantage of using MPT in OFDM TCS is that it is a very flexible anti-eavesdropping and anti-jamming Intelligent OFDM TCS. To the best of our knowledge, this is the first work that utilizes the MPT theory to facilitate the PHY-LS through parameterization of unitary transforms. © 2019 IOP Publishing Ltd. All rights reserved

Intelligent OFDM telecommunication system. Part 2. Examples of complex and quaternion many-parameter transforms

In this paper, we propose unified mathematical forms of many-parametric complex and quaternion Fourier transforms for novel Intelligent OFDM-telecommunication systems (OFDM-TCS). Each many-parametric transform (MPT) depends on many free angle parameters. When parameters are changed in some way, the type and form of transform are changed as well. For example, MPT may be the Fourier transform for one set of parameters, wavelet transform for other parameters and other transforms for other values of parameters. The new Intelligent-OFDM-TCS uses inverse MPT for modulation at the transmitter and direct MPT for demodulation at the receiver. © 2019 IOP Publishing Ltd. All rights reserved

Агрегационный подход к нелинейной фильтрации. Часть 1. SISO-фильтры

In this work, we introduce and analyze a new class of nonlinear SISO-filters that have their roots in aggregation operator theory. We show that a large body of non-linear filters proposed to date constitute a proper subset of aggregation filters

Intelligent OFDM telecommunication system. Part 3. Anti-eavesdropping and anti-jamming properties of system, based on many-parameter wavelet and Golay transforms

In this paper, we aim to investigate the superiority and practicability of many-parameter Fourier transforms (MPFT) from the physical layer security (PHY-LS) perspective. We propose novel Intelligent OFDM-telecommunication system (Intelligent-OFDM-TCS), based on MPFT. New system uses inverse MPFT for modulation at the transmitter and direct MPFT for demodulation at the receiver. The purpose of employing the MPFTs is to improve the PHY-LS of wireless transmissions against to the wide-band anti-jamming communication. Each MPFT depends on finite set of independent parameters (angles), which could be changed independently one from another. When parameters are changed, multi-parametric transform is also changed taking form of a set known (and unknown) orthogonal (or unitary) transforms. We implement the following performances as bit error rate (BER), symbol error rate (SER), the Shannon-Wyner secrecy capacity (SWSC) for novel Intelligent-MPWT-OFDM-TCS. Previous research has shown that the conventional OFDM TCS based on discrete Fourier transform (DFT) has unsatisfactory characteristics in BER, SWSC and in anti-eavesdropping communications. We study Intelligent-MPWT-OFDM-TCS to find out optimal values of angle parameters of MPFT optimized BER, SWSC, anti-eavesdropping effects. Simulation results show that the proposed Intelligent OFDM-TCS have better performances than the conventional OFDM system based on DFT against eavesdropping. © 2019 IOP Publishing Ltd. All rights reserved

Агрегационный подход к нелинейной фильтрации. Часть 2. MIMO-фильтры

В этой статье мы расширяем понятие медианы Фреше до обобщенной медианы, которая минимизирует стоимостную функцию Фреше в форме агрегационной функции (вместо тривиальной суммы) от расстояний. Мы используем обобщенную медиану для конструирования новых нелинейных Фреше MIMO-фильтров для обработки многоканальных изображений.In this paper, we extend the notion of the Fréchet median to the general Fréchet median, which minimizes the Fréchet cost function (FCF) in the form of aggregation of metric distances, instead of the ordinary sum. Moreover, we propose use an aggregation distance instead of classical metric distance. We use generalized Fréchet median for constructing new nonlinear Fréchet MIMO-filters for multispectral image processing

Cryptosystems based on RS and BCH codes over finite noncommutative algebras

The purpose of this paper is to introduce new cryptosystems based on linear Reed-Solomon (RC) and Bose-Chaudhuri-Hocquenghem (BCH) codes over finite Cayley-Dickson and finite Clifford algebras with fast code and encode procedures based on fast Fourier- Clifford-Galois transforms. © 2018 Institute of Physics Publishing. All rights reserved.Springer) p 88 [21] Pall G 1940 On the arithmetic of quaternions Tran. Amer. Math. Soc. 47 487-500 [22] Chernov V M 2015 Quasiparallel algorithm for error-free convolution computation using reduced Mersenne–Lucas codes Computer Optics 39 241-248 [23] Conway J H and Sloane N J A 1993 Sphere Packings, Lattices and Groups (Berlin: Verlag-Springer) p 573 [24] Hurwitz A 1896 Uber die Zahlentheorie der Quaternione Math.-Phys. Klasse (Gottingen: Nachr. Ges. Wiss.) 303-330, 313-340 Acknowledgments This work was supported by grants the RFBR № 17-07-00886 and by Ural State Forest Engineering’s Center of Excellence in ”Quantum and Classical Information Technologies for Remote Sensing Systems”

Intelligent OFDM telecommunication system. Part 4. Anti-eavesdropping and anti-jamming properties of the system, based on many-parameter and fractional Fourier transforms

In this paper, we aim to investigate the superiority and practicability of many-parameter wavelet and Golay transforms (MPWT and MPGT) from the physical layer security (PHY-LS) perspective. We propose novel Intelligent OFDM-telecommunication system (Intelligent-OFDM-TCS), based on many-parameter transforms (MPTs). New system uses inverse MPT for modulation at the transmitter and direct MPT for demodulation at the receiver. The purpose of employing the MPTs is to improve the PHY-LS of wireless transmissions against to the wide-band anti-jamming communication. Each MPT depends on finite set of independent Jacobi parameters (angles), which could be changed independently one of another. When parameters are changed, multi-parametric transform is changed too taking form of a set known (and unknown) orthogonal (or unitary) wavelet transforms. We implement the following performances as bit error rate (BER), symbol error rate (SER), peak to average power ratio (PAPR), the Shannon-Wyner secrecy capacity (SWSC) for novel Intelligent-MPWT-OFDM-TCS. Previous research has shown that the conventional OFDM TCS based on discrete Fourier transform (DFT) has unsatisfactory characteristics in BER, PARP, SWSC and in anti-eavesdropping communications. We study Intelligent-MPT-OFDM-TCS to find out optimal values of angle parameters of MPT optimized BER, PAPR, SWSC, anti-eavesdropping effects. Simulation results show that the proposed Intelligent OFDM-TCS have better performances than the conventional OFDM system based on DFT against eavesdropping. © 2019 IOP Publishing Ltd. All rights reserved

Generalized classical and quantum signal theories on hypergroups. Part 1. Clasical signal theory

In this paper we develop generalized nonharmonic analysis of signals and images on commu­tative hypergroups, associated with arbitrary unitary (orthogonal) transforms. We introduce general­ized convolutions, correlations, Wigner-Ville distributions, and ambiguity functions. All theorems and properties of ordinary classical Fourier harmonic analysis are transferred on nonharmonic analysis Fourier on arbitrary Abelian hypergroups

Клиффордовские модели многоканальных изображений, возникающих в Visual cortex

Одна из главных целей работы состоит в том, чтобы доказать, что аппарат гиперкомплексных алгебр и алгебр Клиффорда более адекватно описывает процессы обработки и распознавания цветных и многоспектральных 2D-, 3D- и nD- изображений, чем векторно-матричный математический аппарат. Можно утверждать, что визуальные системы животных с различной эволюционной историей используют различные коммутативные гиперкомплексные алгебры и алгебры Клиффорда для обработки и распознавания цветных и мультиканальных изображений. Поэтому отдел VC головного мозга вероятно имеет способность оперировать как устройство, работающее в алгебре Клиффорда.The main goal of the paper is to show that commutative hypercomplex algebras and noncommutative Clifford algebras can be used to solve problems of color, multicolor and hypercomplex 2D-, 3D- and nD- images in a natural and effective manner. One can argue that nature has, through evolution, also learned to utilize properties of hypercomplex numbers. Thus, the visual cortex of abrain might have the ability to operate as a Clifford algebra computing device

Клиффордовские модели многоканальных изображений, возникающих в Visual cortex

Одна из главных целей работы состоит в том, чтобы доказать, что аппарат гиперкомплексных алгебр и алгебр Клиффорда более адекватно описывает процессы обработки и распознавания цветных и многоспектральных 2D-, 3D- и nD- изображений, чем векторно-матричный математический аппарат. Можно утверждать, что визуальные системы животных с различной эволюционной историей используют различные коммутативные гиперкомплексные алгебры и алгебры Клиффорда для обработки и распознавания цветных и мультиканальных изображений. Поэтому отдел VC головного мозга вероятно имеет способность оперировать как устройство, работающее в алгебре Клиффорда.The main goal of the paper is to show that commutative hypercomplex algebras and noncommutative Clifford algebras can be used to solve problems of color, multicolor and hypercomplex 2D-, 3D- and nD- images in a natural and effective manner. One can argue that nature has, through evolution, also learned to utilize properties of hypercomplex numbers. Thus, the visual cortex of abrain might have the ability to operate as a Clifford algebra computing device