Correlation properties of sequences from the 2-D array structure of Sidelnikov sequences of different lengths and their union

Min Kyu Song; Hong Yeop Song; Dae San Kim; Jang Yong Lee

doi:10.1109/ISIT.2016.7541270

Correlation properties of sequences from the 2-D array structure of Sidelnikov sequences of different lengths and their union

Min Kyu Song, Hong Yeop Song, Dae San Kim, Jang Yong Lee

Department of Electrical and Electronic Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Citations (Scopus)

Abstract

In this paper, we show that the cross-correlation of two properly chosen column sequences from the array structure of two different Sidelnikov sequences of periods q^e-1 and q^F - 1, where e ≠ F, is bounded by (e+F-1)√q+1. From this result, we construct new sequence families by combining sequence families from the array structure of Sidelnikov sequences of period q² - 1, q³ - 1., q^d - 1 for some d with 2 ≤ d ≤ 1/2(√q - 2/√q + 1). The maximum non-trivial complex correlation of any two pair of sequences in the constructed sequence family is upper-bounded by (2d - 1)√q + 1: thus, the combining process does not affect the maximum non-trivial complex correlation.

Original language	English
Title of host publication	Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	105-109
Number of pages	5
ISBN (Electronic)	9781509018062
DOIs	https://doi.org/10.1109/ISIT.2016.7541270
Publication status	Published - 2016 Aug 10
Event	2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain Duration: 2016 Jul 10 → 2016 Jul 15

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2016-August
ISSN (Print)	2157-8095

Other

Other	2016 IEEE International Symposium on Information Theory, ISIT 2016
Country	Spain
City	Barcelona
Period	16/7/10 → 16/7/15

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

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10.1109/ISIT.2016.7541270

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Song, M. K., Song, H. Y., Kim, D. S., & Lee, J. Y. (2016). Correlation properties of sequences from the 2-D array structure of Sidelnikov sequences of different lengths and their union. In Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory (pp. 105-109). [7541270] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2016.7541270

Song, Min Kyu ; Song, Hong Yeop ; Kim, Dae San ; Lee, Jang Yong. / Correlation properties of sequences from the 2-D array structure of Sidelnikov sequences of different lengths and their union. Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 105-109 (IEEE International Symposium on Information Theory - Proceedings).

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title = "Correlation properties of sequences from the 2-D array structure of Sidelnikov sequences of different lengths and their union",

abstract = "In this paper, we show that the cross-correlation of two properly chosen column sequences from the array structure of two different Sidelnikov sequences of periods qe-1 and qF - 1, where e ≠ F, is bounded by (e+F-1)√q+1. From this result, we construct new sequence families by combining sequence families from the array structure of Sidelnikov sequences of period q2 - 1, q3 - 1., qd - 1 for some d with 2 ≤ d ≤ 1/2(√q - 2/√q + 1). The maximum non-trivial complex correlation of any two pair of sequences in the constructed sequence family is upper-bounded by (2d - 1)√q + 1: thus, the combining process does not affect the maximum non-trivial complex correlation.",

author = "Song, {Min Kyu} and Song, {Hong Yeop} and Kim, {Dae San} and Lee, {Jang Yong}",

year = "2016",

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note = "2016 IEEE International Symposium on Information Theory, ISIT 2016 ; Conference date: 10-07-2016 Through 15-07-2016",

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Song, MK, Song, HY, Kim, DS & Lee, JY 2016, Correlation properties of sequences from the 2-D array structure of Sidelnikov sequences of different lengths and their union. in Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory., 7541270, IEEE International Symposium on Information Theory - Proceedings, vol. 2016-August, Institute of Electrical and Electronics Engineers Inc., pp. 105-109, 2016 IEEE International Symposium on Information Theory, ISIT 2016, Barcelona, Spain, 16/7/10. https://doi.org/10.1109/ISIT.2016.7541270

Correlation properties of sequences from the 2-D array structure of Sidelnikov sequences of different lengths and their union. / Song, Min Kyu; Song, Hong Yeop; Kim, Dae San; Lee, Jang Yong.

Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc., 2016. p. 105-109 7541270 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - In this paper, we show that the cross-correlation of two properly chosen column sequences from the array structure of two different Sidelnikov sequences of periods qe-1 and qF - 1, where e ≠ F, is bounded by (e+F-1)√q+1. From this result, we construct new sequence families by combining sequence families from the array structure of Sidelnikov sequences of period q2 - 1, q3 - 1., qd - 1 for some d with 2 ≤ d ≤ 1/2(√q - 2/√q + 1). The maximum non-trivial complex correlation of any two pair of sequences in the constructed sequence family is upper-bounded by (2d - 1)√q + 1: thus, the combining process does not affect the maximum non-trivial complex correlation.

AB - In this paper, we show that the cross-correlation of two properly chosen column sequences from the array structure of two different Sidelnikov sequences of periods qe-1 and qF - 1, where e ≠ F, is bounded by (e+F-1)√q+1. From this result, we construct new sequence families by combining sequence families from the array structure of Sidelnikov sequences of period q2 - 1, q3 - 1., qd - 1 for some d with 2 ≤ d ≤ 1/2(√q - 2/√q + 1). The maximum non-trivial complex correlation of any two pair of sequences in the constructed sequence family is upper-bounded by (2d - 1)√q + 1: thus, the combining process does not affect the maximum non-trivial complex correlation.

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Song MK, Song HY, Kim DS, Lee JY. Correlation properties of sequences from the 2-D array structure of Sidelnikov sequences of different lengths and their union. In Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. Institute of Electrical and Electronics Engineers Inc. 2016. p. 105-109. 7541270. (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2016.7541270