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

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”

Algebra and geometry of multichannel images. Part 1. Hypercomplex models of retinal images

We present a new theoretical framework for multichannel image processing using hypercomplex commutative algebras. Hypercomplex algebras generalize the algebras of complex numbers. The main goal of the work is to show that hypercomplex algebras can be used to solve problems of multichannel (color, multicolor, and hyperspectral) image processing in a natural and effective manner. In this work we suppose that animal brain operates with hypercomplex numbers when processing and recognizing multichannel retinal images. In our approach, each multichannel pixel is considered not as an K–D vector, but as an K–D hypercomplex number, where K is the number of different optical channels. The aim of this part is to present algebraic models of subjective perceptual color, multicolor and multichannel spaces. Note, that the perceived color is the result of the human mind, not a physical property of an object. We also proposed a model of the MacAdam ellipses based on the triplet (color) geometry

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