Sequences with Low Correlation
Pseudorandom sequences are used extensively in communications and remote sensing. Correlation provides one measure of pseudorandomness, and low correlation is an important factor determining the performance of digital sequences in applications. We consider the problem of constructing pairs (f, g) of sequences such that both f and g have low mean square autocorrelation and f and g have low mean square mutual crosscorrelation. We focus on aperiodic correlation of binary sequences, and review recent contributions along with some historical context.
KeywordsCrosscorrelation Autocorrelation Aperiodic Merit factor Sequence
The author thanks Yakov Sapozhnikov for his careful reading of this paper and his helpful suggestions.
- 14.Golomb, S.W.: Shift register sequences. With portions co-authored by Lloyd R. Welch, Richard M. Goldstein, and Alfred W. Hales, Holden-Day Inc., San Francisco, California-Cambridge-Amsterdam (1967)Google Scholar
- 25.Kärkkäinen, K.H.A.: Mean-square cross-correlation as a performance measure for department of spreading code families. In: IEEE Second International Symposium on Spread Spectrum Techniques and Applications, pp. 147–150 (1992)Google Scholar
- 28.Katz, D.J., Lee, S., Trunov, S.A.: Crosscorrelation of Rudin-Shapiro-like polynomials. Preprint, arXiv:1702.07697 (2017)
- 29.Katz, D.J., Moore, E.: Sequence pairs with lowest combined autocorrelation and crosscorrelation. Preprint, arXiv:1711.02229 (2017)
- 30.Katz, D.J., Lee, S., Trunov, S.A.: Rudin-Shapiro-like polynomials with maximum asymptotic merit factor. Preprint, arXiv:1711.02233 (2017)
- 31.Kirilusha, A., Narayanaswamy, G.: Construction of new asymptotic classes of binary sequences based on existing asymptotic classes. Summer Science Technical report, Department of Mathematics & Computer Science, University of Richmond, VA (1999)Google Scholar
- 33.Littlewood, J.E.: Some Problems in Real and Complex Analysis. D. C. Heath and Co., Raytheon Education Co., Lexington, Massachusetts (1968)Google Scholar
- 41.Schroeder, M.R.: Number Theory in Science and Communication. With Applications in Cryptography, Physics, Digital Information, Computing, and Self-similarity. Springer Series in Information Sciences, vol. 7, 4th edn. Springer, Heidelberg (2006). https://doi.org/10.1007/b137861CrossRefzbMATHGoogle Scholar
- 42.Shapiro, H.S.: Extrenal problems for polynomials and power series. Master’s thesis. Institute of Technology, Cambridge, Massachusetts (1951)Google Scholar