INTRODUCTION
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Large-scale digitalization of our planet, artificial intelligence, and much more are coming. The level of people's comfort will be enhanced due to intelligent digi- tal technologies based on modern digital systems. Each such system has many im- portant characteristics, of which we single out noise immunity. It determines the number of errors in the document depending on the signal level and interference. Currently, digital systems provide one error per ten million bits of information. In relation to the document, we can talk about one error in the text with font 12 on one hundred sheets of A4 paper. Is it a lot or a little? If we consider a hundred pages of an e-book, then this is not enough. If we take a document in the form of one hundred receipts for the transfer of funds to recipients, then this is a lot, since an error can alter the amount of payment to any one of the hundred clients. There should not be a similar and any other mistake in the digital economy. Therefore, for the introduction of the digital economy, it will be necessary to increase the noise immunity of digital systems by several orders of magnitude at once. Historically, it has become a rule for the transmission of messages to modulate the parameters of a deterministic oscillation, believing that its presence in practice is possible by inertia. This confidence existed until the results of measurements of amplitude, phase, and frequency fluctuations of physical sources of harmonic os- cillations appeared in 1950. After that, it turned out that the deterministic vibration is nothing more than some kind of mathematical abstraction, which is unrealizable in practice. Then the experimentally established fluctuations of the oscillation pa- rameters were hidden by the term "parasitic amplitude, phase, frequency fluctua- tions". This has survived to the present, they are being fought. And as a result of this, the theoretically established indicators of noise immunity of communication systems are still unattainable. To overcome the current situation and increase the noise immunity of digital systems by a big leap forward, we propose an alternative option, namely, to abandon the unpromising deterministic oscillation and switch to a random or, at the first stage, to a quasi-deterministic signal. Both signals, in our understanding, are synonymous with dynamic chaos, which opens up great opportunities in the development of new methods for transmitting, storing and processing information. When applying dynamic chaos, it would be appropriate to talk about digital systems with high noise immunity, in which the error probabil- ity will be 1∙10-41, i.e. one error when receiving one hundred duodecillion binary characters. In addition, to achieve high noise immunity of digital systems, a new approach to signal modulation is proposed, which includes what was said above about chaos and the transition to modulation of the characteristic function of the signal, which, will serve as a “space suit” for the modulated signal by analogy with astronautics. The new method of random signal modulation will be conditionally called statistical modulation, which forms the basis of the theory of statistical communication. The results of the analysis show that with the help of the new method it is possible to achieve the limiting values of noise immunity, spectral and energy efficiency of digital systems. Thus, the monography is devoted to increasing the noise immunity of digital data transmission systems by several orders of magnitude using new methods, techniques and devices. Its material complements the content of the avant-garde direction of statistical radio engineering, aimed at involving random processes in solving problems in the theory of statistical communication, which remain rele- vant to this day. Using random signals with probabilistic characteristics, the author in his research proves the promise of using dynamic chaos in a new generation of radio engineering devices, for example, in modems. The monography considers various modem structures, algorithms for modu- lation and demodulation of a quasi-deterministic signal, and characteristic func- tions of signals that are proposed to be used in digital data transmission. Along the way, new knowledge was obtained regarding the characteristic function and the distribution law of signals, which were not known in probability theory. It is shown that the signal, characteristic function, signal modulation and demodulation algorithms in aggregate are the product of digital technology. The noise immunity of modems of the new generation when operating in a noisy channel was assessed qualitatively and quantitatively. At the same time, it was found that with a signal- to-noise ratio of 3 dB, the noise immunity of the modem is at least ten orders of magnitude higher than the same characteristic of known analogues, for example, with phase modulation.
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