Correlation of column sequences from the arrays of Sidelnikov sequences of different periods

Min Kyu Song, Hong Yeop Song

Research output: Contribution to journalArticle

Abstract

We show that the non-trivial correlation of two properly chosen column sequences of length q − 1 from the array structure of two Sidelnikov sequences of periods qe − 1 and qd − 1, respectively, is upper-bounded by (2d − 1)q + 1, if 2 ≤ e < d < 2 1 (q − 2 q + 1). Based on this, we propose a construction by combining properly chosen columns from arrays of size (q − 1) × q q e 1 1 with e = 2, 3, ..., d. The combining process enlarge the family size while maintaining the upper-bound of maximum non-trivial correlation. We also propose an algorithm for generating the sequence family based on Chinese remainder theorem. The proposed algorithm is more efficient than brute force approach.

Original languageEnglish
Pages (from-to)1333-1339
Number of pages7
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE102A
Issue number10
DOIs
Publication statusPublished - 2019 Jan 1

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Chinese remainder theorem
3D
Upper bound
Family

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

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abstract = "We show that the non-trivial correlation of two properly chosen column sequences of length q − 1 from the array structure of two Sidelnikov sequences of periods qe − 1 and qd − 1, respectively, is upper-bounded by (2d − 1)q + 1, if 2 ≤ e < d < 2 1 (q − 2 q + 1). Based on this, we propose a construction by combining properly chosen columns from arrays of size (q − 1) × q q e − − 1 1 with e = 2, 3, ..., d. The combining process enlarge the family size while maintaining the upper-bound of maximum non-trivial correlation. We also propose an algorithm for generating the sequence family based on Chinese remainder theorem. The proposed algorithm is more efficient than brute force approach.",
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AU - Song, Min Kyu

AU - Song, Hong Yeop

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N2 - We show that the non-trivial correlation of two properly chosen column sequences of length q − 1 from the array structure of two Sidelnikov sequences of periods qe − 1 and qd − 1, respectively, is upper-bounded by (2d − 1)q + 1, if 2 ≤ e < d < 2 1 (q − 2 q + 1). Based on this, we propose a construction by combining properly chosen columns from arrays of size (q − 1) × q q e − − 1 1 with e = 2, 3, ..., d. The combining process enlarge the family size while maintaining the upper-bound of maximum non-trivial correlation. We also propose an algorithm for generating the sequence family based on Chinese remainder theorem. The proposed algorithm is more efficient than brute force approach.

AB - We show that the non-trivial correlation of two properly chosen column sequences of length q − 1 from the array structure of two Sidelnikov sequences of periods qe − 1 and qd − 1, respectively, is upper-bounded by (2d − 1)q + 1, if 2 ≤ e < d < 2 1 (q − 2 q + 1). Based on this, we propose a construction by combining properly chosen columns from arrays of size (q − 1) × q q e − − 1 1 with e = 2, 3, ..., d. The combining process enlarge the family size while maintaining the upper-bound of maximum non-trivial correlation. We also propose an algorithm for generating the sequence family based on Chinese remainder theorem. The proposed algorithm is more efficient than brute force approach.

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