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Keywords = Peng–Fan bound

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17 pages, 2288 KiB  
Article
Optimal Constructions of Low-Hit Zone Frequency-Hopping Sequence Set Based on m-Sequence
by Changyuan Wang, Yi Zhang, Wanan Yang and Chunhua Ren
Mathematics 2025, 13(14), 2228; https://doi.org/10.3390/math13142228 - 9 Jul 2025
Viewed by 162
Abstract
Quasi-Synchronous Frequency hopping (FH) Multiple Access (QS-FHMA) systems feature high communication efficiency, strong flexibility, and low operational costs, and they have been widely used in various FH communication scenarios such as satellite communication, military communication, and radio measurement. The low-hit zone (LHZ) FH [...] Read more.
Quasi-Synchronous Frequency hopping (FH) Multiple Access (QS-FHMA) systems feature high communication efficiency, strong flexibility, and low operational costs, and they have been widely used in various FH communication scenarios such as satellite communication, military communication, and radio measurement. The low-hit zone (LHZ) FH sequences set (LHZ FHS set) plays a critical role in QS-FHMA systems, enabling user access with permissible time-delay offsets while maintaining superior performance. In this paper, three new methods to construct LHZ FHS sets based on m-sequences are proposed. The newly constructed sequence sets achieve optimality with respect to the Peng–Fan bound. Compared with existing LHZ FHS sets constructed from m-sequences, these new sequence sets offer more flexible parameters. Furthermore, due to the simple structure of m-sequences and their extensive adoption in engineering applications, the proposed new sequence sets possess significant practical value for engineering implementation. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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13 pages, 326 KiB  
Article
New Families of Frequency-Hopping Sequence Sets with a Low-Hit-Zone
by Limengnan Zhou and Hanzhou Wu
Entropy 2024, 26(11), 948; https://doi.org/10.3390/e26110948 - 5 Nov 2024
Cited by 1 | Viewed by 823
Abstract
As a means of spread spectrum communication, frequency-hopping technology has good performance in anti-jamming, multiple-access, security, covert communications, and so on. In order to meet the needs of different frequency-hopping multiple-access (FHMA) communication scenarios, the research on frequency-hopping sequence (FHS) sets with a [...] Read more.
As a means of spread spectrum communication, frequency-hopping technology has good performance in anti-jamming, multiple-access, security, covert communications, and so on. In order to meet the needs of different frequency-hopping multiple-access (FHMA) communication scenarios, the research on frequency-hopping sequence (FHS) sets with a low-hit-zone (LHZ) is now becoming more and more crucial. In this paper, a general construction to obtain new families of LHZ-FHS sets is achieved via interleaving technique. Subsequently, based on two different shift sequences, two classes of LHZ-FHS sets with new flexible parameters not covered in the related literature are presented. The requirements for our new LHZ-FHS sets to obtain optimality or near-optimality with respect to the Peng–Fan–Lee bound are also introduced. Furthermore, as long as the base FHS set is fixed, the performances of new LHZ-FHS sets can be analyzed, such that the parameters of all appropriate shift sequences to obtain desired LHZ-FHS sets are also fixed. Full article
(This article belongs to the Special Issue Advances in Information and Coding Theory, the Third Edition)
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8 pages, 252 KiB  
Article
A Construction of Optimal One-Coincidence Frequency-Hopping Sequences via Generalized Cyclotomy
by Minfeng Shao and Ying Miao
Entropy 2024, 26(11), 935; https://doi.org/10.3390/e26110935 - 31 Oct 2024
Viewed by 806
Abstract
Frequency-hopping sequences (FHSs) with low Hamming correlation are essential for synchronization and multiple-access communication systems. In this paper, we propose a novel construction of FHSs using generalized cyclotomy. Our results reveal that the constructed FHSs exhibit a one-coincidence property, meaning that the smallest [...] Read more.
Frequency-hopping sequences (FHSs) with low Hamming correlation are essential for synchronization and multiple-access communication systems. In this paper, we propose a novel construction of FHSs using generalized cyclotomy. Our results reveal that the constructed FHSs exhibit a one-coincidence property, meaning that the smallest correlation between different FHSs, aside from the trivial case, is minimized. Additionally, the new sets of FHSs achieve an optimal size in relation to a known theoretical bound. Full article
(This article belongs to the Special Issue Advances in Information and Coding Theory, the Third Edition)
14 pages, 336 KiB  
Article
Construction of Optimal Frequency Hopping Sequence Set with Low-Hit-Zone
by Xinyu Tian, Hongyu Han, Xianhua Niu and Xing Liu
Entropy 2023, 25(7), 1044; https://doi.org/10.3390/e25071044 - 11 Jul 2023
Cited by 4 | Viewed by 1943
Abstract
In quasi-synchronous frequency-hopping multiple access (QS-FHMA) systems, low-hit-zone (LHZ) frequency-hopping sequence (FHS) sets have been well-applied to reduce mutual interference (MI). In this paper, we propose three constructions of LHZ FHS sets with new parameters via interleaving techniques. The obtained sequences can be [...] Read more.
In quasi-synchronous frequency-hopping multiple access (QS-FHMA) systems, low-hit-zone (LHZ) frequency-hopping sequence (FHS) sets have been well-applied to reduce mutual interference (MI). In this paper, we propose three constructions of LHZ FHS sets with new parameters via interleaving techniques. The obtained sequences can be verified that they are optimal with respect to the Peng–Fan–Lee bound. Full article
(This article belongs to the Special Issue Coding and Entropy)
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