Two-Valued Periodic Complementary Sequences

Xudong Li; Zilong Liu; Yong Liang Guan; Pingzhi Fan

doi:10.1109/LSP.2017.2722423

Two-Valued Periodic Complementary Sequences

Xudong Li, Zilong Liu^*, Yong Liang Guan, Pingzhi Fan

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

We present a novel transform for periodic complementary sets (PCSs) over two-valued alphabets from a large set of difference families. This is achieved by generalizing Golomb's idea in 1992, which was for transformed perfect sequences with zero autocorrelations only. Based on the properties of difference family, a sufficient condition for such two-valued PCSs is derived. Systematic constructions of two-valued periodic complementary pairs are presented. It is shown that many lengths for which binary PCSs do not exist become admissible for our proposed two-valued PCSs.

Original language	English
Article number	7964719
Pages (from-to)	1270-1274
Number of pages	5
Journal	IEEE Signal Processing Letters
Volume	24
Issue number	9
DOIs	https://doi.org/10.1109/LSP.2017.2722423
Publication status	Published - Sept 2017
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 1994-2012 IEEE.

ASJC Scopus Subject Areas

Signal Processing
Applied Mathematics
Electrical and Electronic Engineering

Keywords

Difference family (DF)
difference set
periodic autocorrelation function (ACF)
periodic complementary pairs (PCPs)
periodic complementary sets (PCSs)

Access to Document

10.1109/LSP.2017.2722423

Cite this

@article{4af4e56224524300b7b40adcdb51a375,

title = "Two-Valued Periodic Complementary Sequences",

abstract = "We present a novel transform for periodic complementary sets (PCSs) over two-valued alphabets from a large set of difference families. This is achieved by generalizing Golomb's idea in 1992, which was for transformed perfect sequences with zero autocorrelations only. Based on the properties of difference family, a sufficient condition for such two-valued PCSs is derived. Systematic constructions of two-valued periodic complementary pairs are presented. It is shown that many lengths for which binary PCSs do not exist become admissible for our proposed two-valued PCSs.",

keywords = "Difference family (DF), difference set, periodic autocorrelation function (ACF), periodic complementary pairs (PCPs), periodic complementary sets (PCSs)",

author = "Xudong Li and Zilong Liu and Guan, {Yong Liang} and Pingzhi Fan",

note = "Publisher Copyright: {\textcopyright} 1994-2012 IEEE.",

year = "2017",

month = sep,

doi = "10.1109/LSP.2017.2722423",

language = "English",

volume = "24",

pages = "1270--1274",

journal = "IEEE Signal Processing Letters",

issn = "1070-9908",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "9",

}

TY - JOUR

T1 - Two-Valued Periodic Complementary Sequences

AU - Li, Xudong

AU - Liu, Zilong

AU - Guan, Yong Liang

AU - Fan, Pingzhi

PY - 2017/9

Y1 - 2017/9

N2 - We present a novel transform for periodic complementary sets (PCSs) over two-valued alphabets from a large set of difference families. This is achieved by generalizing Golomb's idea in 1992, which was for transformed perfect sequences with zero autocorrelations only. Based on the properties of difference family, a sufficient condition for such two-valued PCSs is derived. Systematic constructions of two-valued periodic complementary pairs are presented. It is shown that many lengths for which binary PCSs do not exist become admissible for our proposed two-valued PCSs.

AB - We present a novel transform for periodic complementary sets (PCSs) over two-valued alphabets from a large set of difference families. This is achieved by generalizing Golomb's idea in 1992, which was for transformed perfect sequences with zero autocorrelations only. Based on the properties of difference family, a sufficient condition for such two-valued PCSs is derived. Systematic constructions of two-valued periodic complementary pairs are presented. It is shown that many lengths for which binary PCSs do not exist become admissible for our proposed two-valued PCSs.

KW - Difference family (DF)

KW - difference set

KW - periodic autocorrelation function (ACF)

KW - periodic complementary pairs (PCPs)

KW - periodic complementary sets (PCSs)

UR - http://www.scopus.com/inward/record.url?scp=85021977443&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021977443&partnerID=8YFLogxK

U2 - 10.1109/LSP.2017.2722423

DO - 10.1109/LSP.2017.2722423

M3 - Article

AN - SCOPUS:85021977443

SN - 1070-9908

VL - 24

SP - 1270

EP - 1274

JO - IEEE Signal Processing Letters

JF - IEEE Signal Processing Letters

IS - 9

M1 - 7964719

ER -

Two-Valued Periodic Complementary Sequences

Abstract

Bibliographical note

ASJC Scopus Subject Areas

Keywords

Access to Document

Other files and links

Fingerprint

Cite this