Formation of cascaded Gordon–Mills–Welch sequences for digital information transmission systems

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Abstract

Based on the modification of the algorithm for determining the decimation index vector, which is the main component of the Gordon—Mills—Welch sequence (GMWS) synthesis method, an algorithm for determining the decimation index vector A(l, m, n, r1, r2) for the synthesis of cascaded GMWS (CGMWS) with a period N = 2S — 1 = 2lmn — 1 (l > 2) in the GF[((2l)m)n] field by summing the sequences formed on the basis of decimation according to the obtained indices of the symbols of the basic M-sequence (MS). The modification of the algorithm consists in combining the vectors of the decimation indices for various combinations of the parameters r1 and r2 in the expression for the resulting vector. The results of calculating the maximum values of the equivalent linear complexity (ELC) of cascaded LCGMWS and conventional LGMWS GMWSs for periods 212–1 ≤ N ≤ 236–1 are presented. It is shown that the ELC of cascaded exceeds the ELC of conventional GMWSs, with an increase in the period the gain BS = LCGMWS/LGMWS increases, and for the period N = 236–1 it is equal to BS=36 = 2.25.

About the authors

V. G. Starodubtsev

Mozhaisky Military Space Academy

Author for correspondence.
Email: vgstarod@mail.ru
Russian Federation, Zhdanovskaya Street, 13, Saint Petersburg, 197198

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