DOI 10.17586/0021-3454-2024-67-2-107-115
UDC 519.725
FORMATION OF SETS OF FIVE-FOLD GOLD-TYPE SEQUENCES FOR DIGITAL INFORMATION TRANSMISSION SYSTEMS
Multiservice Nets and Telecommunications, Ltd., St. Petersburg; Head of Department
V. V. Tkachenko
A. F. Mozhaisky Military Space Academy;
Reference for citation: Starodubtsev V. G., Tkachenko V. V. Formation of sets of five-fold Gold-type sequences for digital information transmission systems. Journal of Instrument Engineering. 2024. Vol. 67, N 2. P. 107—115 (in Russian). DOI: 10.17586/0021-3454-2024-67-2-107-115.
Abstract. Sets of vectors of decimation indices IS = (id1, id2, …, idn) for the formation of sets of five-fold Gold-type sequences in finite fields GF(5S) (S = 3, 4, 5, 6) based on М- sequences with verification polynomials hМП(x) for periods N = 5S – 1 < 20 000, are presented. The sets include both the well–known decimation indices obtained by Trachtenberg, Helleset, Kumar and satisfying the condition LCD(idi, 5S – 1) = 1 (LCD is the largest common divisor), and the newly found indices that allow the formation of sets of five-fold Gold-type sequences with volumes VS = N + 1 and low levels of periodic auto- and the cross-correlation functions. For the considered values of S, boundary estimates of the maximum value of the correlation function modulus Rmax are given.
Abstract. Sets of vectors of decimation indices IS = (id1, id2, …, idn) for the formation of sets of five-fold Gold-type sequences in finite fields GF(5S) (S = 3, 4, 5, 6) based on М- sequences with verification polynomials hМП(x) for periods N = 5S – 1 < 20 000, are presented. The sets include both the well–known decimation indices obtained by Trachtenberg, Helleset, Kumar and satisfying the condition LCD(idi, 5S – 1) = 1 (LCD is the largest common divisor), and the newly found indices that allow the formation of sets of five-fold Gold-type sequences with volumes VS = N + 1 and low levels of periodic auto- and the cross-correlation functions. For the considered values of S, boundary estimates of the maximum value of the correlation function modulus Rmax are given.
Keywords: finite fields, Gold sequences, correlation function, M-sequences, decimation indices
References:
References:
- Sklar B. Digital Communications: Fundamentals and Applications, Prentice Hall, 2001, 1079 р.
- Ipatov V.P. Spread Spectrum and CDMA. Principles and Applications, NY, John Wiley and Sons Ltd., 2005, 488 р.
- Golomb S.W., Gong G. Signal Design for Good Correlation for Wireless Communication, Cryptography and Radar, Cambridge University Press, 2005, 438 p.
- Yang Y., Tang X. IEEE Trans. Inf. Theory, 2018, no. 1(64), pp. 384.
- Varakin L.E. and Shinakov Yu.S., ed., CDMA: proshloe, nastoyashchee, budushchee (CDMA: Past, Present, Future), Moscow, 2003, 608 p. (in Russ.)
- Gold R. IEEE Trans. Inf. Theory, 1968, no. 1(14), pp. 154.
- Trachtenberg H.M. On the cross-correlation functions of maximal recurring sequences, Candidate’s thesis, Univ. Southern California, Los Angeles, CA, 1970.
- Dobbertin H., Helleseth T., Kumar P.V., Martinsen H. IEEE Trans. Inf. Theory, 2001, no. 4(47), pp. 1473.
- Starodubtsev V.G., Myshko V.V. Journal of Instrument Engineering, 2023, no. 7(66), pp. 568–575. (in Russ.)
- Muller E.N. IEEE Trans. Inf. Theory, 1999, no. 1(45), pp. 289.
- Hu Z., Li X., Mills D., Muller E., Sun W., Williems W., Yang Y., Zhang Z. Applicable Algebra Eng. Commun. Comput., 2001, vol. 12, p. 255.
- Seo E.Y., Kim Y.S., No J.S., Shin D.J. IEEE Trans. Inf. Theory, 2008, no. 7(54), pp. 3140.
- Seo E.Y., Kim Y.S., No J.S., Shin D.J. IEICE Trans. Fund. Electron., Commun. Comput. Sci., 2007, no. 11(E90-A), pp. 2568.
- Jang J.W., Kim Y.S., No J.S., Helleseth T. IEEE Trans. Inf. Theory, 2004, no. 8(50), pp. 1839.