Article 2419

Title of the article

PSEUDO-RANDOM SEQUENCE GENERATORS OF NON-MAXIMUM LENGTH ON SHIFT REGISTERS WITH LINEAR FEEDBACK BASED ON A PRIMITIVE POLYNOMIAL OF SOME POWER 

Authors

Pesoshin Valeriy Andreevich, Doctor of engineering sciences, professor, sub-department of computer systems, Kazan National Research Technical University named after A. N. Tupolev – KAI (10 K. Marksa street, Kazan, Russia), E-mail: pesoshin-kai@mail.ru
Kuznetsov Valeriy Mikhaylovich, Doctor of engineering sciences, professor, sub-department of computer systems, Kazan National Research Technical University named after A. N. Tupolev – KAI (10 K. Marksa street, Kazan, Russia), E-mail: kuznet_evm@mail.ru
Kuznetsova Aleksandra Sergeevna, Student, Kazan National Research Technical University named after A. N. Tupolev – KAI (10 K. Marksa street, Kazan, Russia), E-mail: sasha_kzncv@mail.ru 

Index UDK

681.325: 621.391.3:518.5:519.95 

DOI

10.21685/2072-3059-2019-4-2 

Abstract

Background. Modern methods of organizing machine experiments in the form of simulation models are based on the use of numerical sequences of probabilisticstatistical nature, adequate to real processes and phenomena. The purpose of the article is to demonstrate the new possibilities of binary sequence generators as pseudo-random, not limited to the implementation of the Bernoulli scheme of independent tests.
Materials and methods. Poorly studied methods of hardware formation of binary recurrence sequences by register-type generators with linear feedback are proposed. The mathematical basis of the generators is a composite characteristic polynomial consisting of primitive polynomials, one of which is raised to an integer power.
Results. It is shown that in homogeneous and inhomogeneous operating modes of the generator, a variety of formed sequences is observed. Correlation relationships of sequence elements are presented in statistical and functional forms. The problem of initializing the generator to form cycles of non-maximum length of a given order is solved.
Conclusions. The proposed analytical conditions and circuit design of sequence generators of non-maximum length with various probabilistic and correlation properties that expand the functionality of a simulation experiment. 

Key words

pseudo-random sequence generator, shift register, sequence variety, homogeneous and heterogeneous sequences, indicator sequences, correlation functions 

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References

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Дата создания: 12.03.2020 09:52
Дата обновления: 12.03.2020 10:20