ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)
Menu

10
Issue
vol 62 / November, 2019
Article

DOI 10.17586/0021-3454-2019-62-7-610-620

UDC 519.725

PREFERRED PAIRS OF GMW–SEQUENCES FOR DIGITAL INFORMATION TRANSFER SYSTEMS

V. G. Starodubtsev
Multiservice Nets and Telecommunications, Ltd., St. Petersburg; Head of Department


Y. V. Osadchaya
А. F. Mozhaysky Military Space Academy ;


Abstract. An analysis of periodic cross-correlation functions (PCCF) of M-sequences (MS) and Gordon-Mills-Welch sequences (GMWS), which have a two-level autocorrelation function, is presented. A higher structural secrecy of GMWS as compared with the MS determines the preference for the use of GMWS in digital information transmission systems (DITS) subject to increased confidentiality requirements. An algorithm for formation of preferred pairs of GMWS and their definitions for periods N = 63 and N = 255 are developed. Mathematical apparatus of the theory of finite fields, linear algebra and correlation analysis are used in the research. Values of PCCF of various pairs of MS and GMWS are obtained for periods N = 63 and N = 255. It is shown that GMWS, forming preferred pairs, are formed based on MS, also forming preferred pairs. The obtained results can be used in the formation of spread-spectrum signals in the noise-proof DITS, as well as in the synthesis of signal systems that allow an analytical representation in finite fields.
Keywords: pseudorandom sequences, preferred pairs, correlation function, structural secrecy, indivisible and primitive polynomials, finite fields

References:
  1. Vishnevskiy V.M., Lyakhov A.I., Portnoy S.L., Shakhnovich I.V. Shirokopolosnye besprovodnye seti peredachi informatsii (Broadband Wireless Networks of Information Transfer), Moscow, 592 р. (in Russ.)
  2. Ipatov V.P. Periodicheskie diskretnye signaly s optimal'nymi korrelyatsionnymi svoystvami (Periodic Discrete Signals with Optimum Correlation Properties), Moscow, 1992, 152 p. (in Russ.)
  3. Sklar B. Digital Communications: Fundamentals and Applications, Prentice-Hall, 2001.
  4. Ipatov V.P. Spread Spectrum and CDMA. Principles and Applications, Wiley, 2005, 400 р.
  5. Golomb S.W., Gong G. Signal Design for Good Correlation for Wireless Communication, Criptography and Radar, Cambridge University Press, 2005, 438 p.
  6. Tsankov T., Trifonov T., Staneva L. Journal Scientific & Applied Research, 2013, vol. 4, рp. 80–87.
  7. Chung H.B., No J.S. IEEE Trans. on Information Theory, 1999, no. 6(45), pp. 2060–2065.
  8. No Jong-Seon. IEEE Trans. on Information Theory, 1996, no. 1(42), pp. 260–262.
  9. Coulter R.S., Mesnager S. IEEE Trans. on Information Theory, 2018, no. 4(64), pp. 2979–2986.
  10. Zhengchun Zhou, Tor Helleseth, Udaya Parampalli. IEEE Trans. on Information Theory, 2018, no. 4(64), pp. 2896–2900.
  11. Popović B.M. IEEE Trans. on Information Theory, 2018, no. 4(64), pp. 2876–2882.
  12. Min Kyu Song, Hong-Yeop Song. IEEE Trans. on Information Theory, 2018, no. 4(64), pp. 2901–2909.
  13. Varakin L.E., Shinakov Yu.S., ed., CDMA: proshloe, nastoyashchee, budushchee (CDMA: Last, Real, Future), Moscow, 2003, 608 p. (in Russ.)
  14. Tao Zhang, Shuxing Li, Tao Feng, Gennian Ge. IEEE Trans. on Information Theory, 2014, no. 5(60), pp. 3062–3068.
  15. Liang H., Tang Y. Finite Fields and Their Applications, 2015, vol. 31, рр. 137–161.
  16. Rizomiliotis P., Kalouptsidis N. IEEE Trans. on Information Theory, 2005, vol. IT–51, рp. 1555–1563.
  17. Starodubtsev V.G., Borodko D.N., Myshko V.V. Aerospace Instrument-Making, 2018, no. 5, pp. 3–15. (in Russ.)
  18. Starodubtsev V.G., Myshko V.V., Tkachenko V.V. H&ES Research, 2018, no. 3(10), pp. 13–20. (in Russ.)
  19. Peterson W.W. & Weldon E.J. Error-Correcting Codes, Second Edition, MIT Press, 1972, 560 p.