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Construction of spectrally-null-constrained zero-correlation zone sequences with flexible support

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Abstract

In recent years, zero-correlation zone (ZCZ) sequences have been studied due to their significant applications in quasi-synchronous code division multiple access (QS-CDMA) systems and other wireless communication domains. However, in a cognitive radio (CR) network, it is desirable to design ZCZ sequences having spectrally-null-constrained (SNC) property to achieve a low spectral density profile. This paper focuses on the construction of SNC-ZCZ sequences having flexible support, where support refers to a collection of indices corresponding to non-zero entries in the sequence. The proposed SNC-ZCZ sequences are reduced to traditional ZCZ sequences when the support size is equal to the length of the sequence. To obtain ZCZ sequences, we first propose a construction of traditional/SNC-complete complementary codes (SNC-CCCs) using a class of extended Boolean functions (EBFs). With the help of this class, we propose another class of EBFs that generates asymptotically optimal traditional/SNC-ZCZ sequences of prime-power lengths with respect to Tang-Fan-Matsufuzi bound. Furthermore, a relation between the second-order cosets of first-order generalized Reed-Muller (GRM) code and the proposed traditional ZCZ sequences is also established. The enumeration of traditional ZCZ sequences within a GRM code is also established. This enumeration is achieved by tallying the distinct second-order cosets of the first-order GRM code and quantifying the number of ZCZ sequences residing within a particular coset. Moreover, the Hamming distance of the proposed traditional ZCZ sequences is also computed.

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Acknowledgements

The authors are very grateful to the reviewers and the Editor for their valuable comments and suggestions that improved the presentation and quality of this paper. The work of Nishant Kumar was supported by the CSIR, Govt. of India (under grant no. 09/1023(0031)/2019-EMR-I). The work of Palash Sarkar was supported by the Research Council of Norway under Grant 311646/O70. The work of Sudhan Majhi was supported by the SERB, Govt. of India (under grant no. CRG/2022/000529 and EEQ/2022/001018).

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Authors and Affiliations

  1. Department of Mathematics, IIT Patna, Patna, 801106, Bihar, India

    Nishant Kumar

  2. Department of Informatics, Selmar Center, University of Bergen, N-5020, Bergen, Norway

    Palash Sarkar

  3. Department of Electrical Communication Engineering, IISC, Bangalore, 560012, Karnataka, India

    Sudhan Majhi

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  1. Nishant Kumar
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  2. Palash Sarkar
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Contributions

Palash Sarkar gave the problem statement. Nishant Kumar generated the idea, solved the problem, and wrote the manuscript. Sudhan Majhi polished the manuscript. All the authors did the proofreading.

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Correspondence to Sudhan Majhi.

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Kumar, N., Sarkar, P. & Majhi, S. Construction of spectrally-null-constrained zero-correlation zone sequences with flexible support. Cryptogr. Commun. 16, 1059–1075 (2024). https://doi.org/10.1007/s12095-024-00715-0

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