EXCEEDING THE BANDWIDTH OF THE CHANNEL WITHOUT MEMORY IN THE DISCRETE-CONTINUOUS DETERMINISTIC CHANNEL WITH THE MEMORY AND SET RESTRICTIONS
DOI: 10.36724/2072-8735-2020-14-5-15-26
Alexander S. Sukhorukov, Moscow Technical University of Communications and Informatics, Moscow, Russia, suhas@yandex.ru
Abstract
The article summarizes the results of the author’s research, presented in the works [7-14]. The main conclusion is that the bandwidth of the communication channel with memory under certain restrictions can exceed the bandwidth of the channel without memory. Reducing the duration of information pulses and their period increases the speed of receipt of information at the input of the communication channel. However, a communication channel (CC) without memory turns into a CC with memory, and the resulting intersymbol interference (ISI) reduces the speed of information transmission through the CC. The corresponding formulas show the need to find the optimal ratio between the baud rate and the probability of error for a given level of additive noise. The article considers a discrete-continuous deterministic channel with memory (DCDCM), for which the transmitted signals are discrete in time and continuous in levels combinations. CC parameters are known at the transmission and reception sides. Representing the processes at the input and output of the DCDCM in the form of L-dimensional vectors, the coding theorem is proved in this article when restrictions on the energy and the energy of the difference of combinations are imposed on the transmitted combinations. The exponential dependence of the average error probability on the duration of the combination is shown in case of reception as a whole of the L-dimensional vector. The restrictions imposed on the allowable combinations do not change the exponential dependence of the error probability on the duration of the combination. The coding theorem is proved if only good codes are used for transmission with a given energy and the difference energy of combinations. This enables to specify constructive ways to increase the bandwidth of the CC. For CC with memory, the duration of the combination should be increased in proportion to the number of symbols in the code combination, but the factor should be less than 1. For different signal-to-noise ratios, a range of values of this factor is defined, which allow to obtain a transmission rate greater than the capacity of the channel without memory, and the error probability tends to zero with the length of the combination tending to infinity. The same result can be obtained by using the optimal indicator. The optimal indicator eliminates intersymbol interference, enabling a separation of the information pulses at a pulse repetition interval greater than an arbitrarily small value. The error probability can be made arbitrarily small for a particular form of CC frequency response. At the same time, the requirements for CC parameters increase and the decoder becomes significantly more complicated.
Keywords: coding theorem, bandwidth, discrete memory channel, intersymbol interference, probability of error, immunity, code combination, permitted combination, protective time interval, additive noise, entropy, mutual information, optimal indicator.
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Information about author:
Alexander S. Sukhorukov, Cand.tech.Sci., Associate Professor of Faculty of the general theory of the Moscow Technical University of Communications and Informatics, Moscow, Russia