Координатный метод синхронизации и распознавания …
17
Coordinate method of synchronization and recognition
of binary compound code sequences
© A.S. Kosolapov, A.V. Vtorov
Bauman Moscow State Techical University, Moscow, 105005, Russia
Pseudonoise signals are widely used in various communication systems and control sys-
tems. The development of processing devices of input signals of such systems, able to solve
tasks of synchronization and recognition of received code sequences simultaneously, is of
current importance. A possibility of using the coordinate method for synchronization and
recognition of M-sequences, as well as composite code sequences, built on their basis, is
presented in this article, based on the structural features of complex code sequences and
using the basic provisions of the Galois fields theory. The possibility of using the coordinate
method being proposed is considered by the example of code sequences of small Kasami
family. The solution of this problem is possible provided that compound code sequence was
decomposed into component M-sequences. The use of accompanying matrixes of polynomi-
als, generating component M-sequences, made it possible to calculate the coordinates of
current symbols of the components. The problem is solved after defining the vector-column
of coordinates of follow-related consecutive symbols and establishment of their orderliness
in accordance with a certain criteria of correct synchronization and recognition. The dia-
grams present the results of computing of the required probability characteristics.
Keywords:
the coordinate method, pseudonoise signals, Galois fields, field element, an
accompanying matrix, vector of coordinates, majoritarian element, parity-check equations.
REFERENCES
[1] Chebotarev N.G.
Osnovy teorii Galua
[The fundamentals of the Galois’s theory].
Part. 1. Moscow, Yo-Yo Media Publ., 2012, 221 p.
[2] Kosolapov A.S., Timoshenkov V.F., Naumkin S.I.
Tekhnika sredstv svyazi. Seri-
ya Tekhnika svyazi
[The techniques of the communication facilities. Seriya
Communication engineering], 1989, iss. 1, pp. 20–26.
[3] Berlekamp E.
Algebraic coding theory.
McGraw-Hill Book Company, 1968, 474 p.
[4] Kosolapov A.S., Galev A.V.
Inzhenernyi zhurnal: nauka i innovatsii — Engi-
neering Journal: Science and Innovation
, 2014, iss. 1. Available at:
[5] Kosolapov A.S. (USSR).
Sistema dekodirovaniya dvoichnykh posledovatel’no-
stei
[The system of decoding of the binary sequences]. A.c. 1295527 USSR, Pub-
lished 07.03.87, bulletin no. 9, 5 p.
[6] Varakin L.E.
Sistemy svyazi s shumopodobnymi signalami
[Communication sys-
tems with noise-type signals]. Moscow, Radio i svyaz’ Publ., 1985, 384 p.
Kosolapov A.S.
(b. 1939) graduated from Bauman Moscow Higher Technical
School in 1962. Ph. D., assoc. professor of the Radioelectronic Systems and Devices De-
partment of the Radioelectronics and Laser Technology Faculty at Bauman Moscow
State Technical University. Author of more than 100 scientific works, patents and manu-
als. Sphere of scientific interests includes research of structural properties of wideband
signals and their processing. e-mail:
Vtorov A.V.
(b. 1991) graduated from Bauman Moscow State Technical University
in 2014. Sphere of scientific interests includes problems of processing of wideband sig-
nals and their use in communication systems. e-mail:
