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

• Published in: 2016 IEEE International Symposium on Information Theory (ISIT) pp. 105 - 109
• Main Authors: Song, Min Kyu, Song, Hong-Yeop, Kim, Dae San, Lee, Jang Yong
• Format: Conference Proceeding Journal Article
• Language: English
• Published: IEEE 01.07.2016
• Subjects: Arrays; Channel estimation; Columnar structure; Columns (structural); Construction; Correlation; Cryptography; Electronic mail; Information theory; Periodic structures; Two dimensional displays; Unions
• ISSN: 2157-8117
• DOI: 10.1109/ISIT.2016.7541270

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 q 2 - 1, q 3 - 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.