Three new constructions of asymptotically optimal periodic quasi-complementary sequence sets with small alphabet sizes

Three new constructions of asymptotically optimal periodic quasi-complementary sequence sets with small alphabet sizes

Quasi-complementary sequence sets (QCSSs) play an important role in multi-carrier code-division multiple-access (MC-CDMA) systems. They can support more users than perfect complementary sequence sets in MC-CDMA systems. It is desirable to design QCSSs with good parameters that are a trade-off o...

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Bibliographic Details
Main Authors: Luo, Gaojun, Cao, Xiwang, Shi, Minjia, Helleseth, Tor
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2021
Subjects:
Science::Physics
Quasi-complementary Sequence Set
Asymptotically Optimal
Online Access:https://hdl.handle.net/10356/147219
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Institution: Nanyang Technological University
Language: English
Description
Summary:Quasi-complementary sequence sets (QCSSs) play an important role in multi-carrier code-division multiple-access (MC-CDMA) systems. They can support more users than perfect complementary sequence sets in MC-CDMA systems. It is desirable to design QCSSs with good parameters that are a trade-off of large set size, small periodic maximum magnitude correlation and small alphabet size. The main results are to construct new infinite families of QCSSs that all have small alphabet size and asymptotically optimal periodic maximum magnitude correlation. In this paper, we propose three new constructions of QCSSs using additive characters over finite fields. Notably, these QCSSs have new parameters and small alphabet sizes. Using the properties of characters and character sums, we determine their maximum periodic correlation magnitudes and prove that these QCSSs are asymptotically optimal with respect to the lower bound.

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