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...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/147219 |
| _version_ | 1826129505195917312 |
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| author | Luo, Gaojun Cao, Xiwang Shi, Minjia Helleseth, Tor |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Luo, Gaojun Cao, Xiwang Shi, Minjia Helleseth, Tor |
| author_sort | Luo, Gaojun |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T07:41:41Z |
| format | Journal Article |
| id | ntu-10356/147219 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:41:41Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-10356/1472192023-02-28T19:56:05Z Three new constructions of asymptotically optimal periodic quasi-complementary sequence sets with small alphabet sizes Luo, Gaojun Cao, Xiwang Shi, Minjia Helleseth, Tor School of Physical and Mathematical Sciences Science::Physics Quasi-complementary Sequence Set Asymptotically Optimal 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. Nanyang Technological University Accepted version The work of Gaojun Luo was supported by NTU Research under Grant 04INS000047C230GRT01. The work of Xiwang Cao was supported by the National Natural Science Foundation of China under Grant 11771007 and Grant 61572027. The work of Minjia Shi was supported in part by the National Natural Science Foundation of China under Grant 12071001and Grant 61672036, in part by the Excellent Youth Foundation of Natural Science Foundation of Anhui Province under Grant 1808085J20, and in part by the Academic Fund for Outstanding Talents in Universities under Grant gxbjZD03. The work of Tor Helleseth was supported by the Research Council of Norway under Grant 247742//O70 and Grant 311646/O70. 2021-08-11T08:51:01Z 2021-08-11T08:51:01Z 2021 Journal Article Luo, G., Cao, X., Shi, M. & Helleseth, T. (2021). Three new constructions of asymptotically optimal periodic quasi-complementary sequence sets with small alphabet sizes. IEEE Transactions On Information Theory, 67(8), 5168-5177. https://dx.doi.org/10.1109/TIT.2021.3068474 0018-9448 https://hdl.handle.net/10356/147219 10.1109/TIT.2021.3068474 8 67 5168 5177 en 04INS000047C230GRT01 IEEE Transactions on Information Theory © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: https://doi.org/10.1109/TIT.2021.3068474. application/pdf |
| spellingShingle | Science::Physics Quasi-complementary Sequence Set Asymptotically Optimal Luo, Gaojun Cao, Xiwang Shi, Minjia Helleseth, Tor Three new constructions of asymptotically optimal periodic quasi-complementary sequence sets with small alphabet sizes |
| title | Three new constructions of asymptotically optimal periodic quasi-complementary sequence sets with small alphabet sizes |
| title_full | Three new constructions of asymptotically optimal periodic quasi-complementary sequence sets with small alphabet sizes |
| title_fullStr | Three new constructions of asymptotically optimal periodic quasi-complementary sequence sets with small alphabet sizes |
| title_full_unstemmed | Three new constructions of asymptotically optimal periodic quasi-complementary sequence sets with small alphabet sizes |
| title_short | Three new constructions of asymptotically optimal periodic quasi-complementary sequence sets with small alphabet sizes |
| title_sort | three new constructions of asymptotically optimal periodic quasi complementary sequence sets with small alphabet sizes |
| topic | Science::Physics Quasi-complementary Sequence Set Asymptotically Optimal |
| url | https://hdl.handle.net/10356/147219 |
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