Direct Construction of Optimal Z-Complementary Code Sets With Even Lengths by Using Generalized Boolean Functions

Ghosh, Gobinda; Majhi, Sudhan; Sarkar, Palash; Upadhyay, Ashish Kumar

doi:10.1109/lsp.2022.3159401

Cited by 16 publications

(11 citation statements)

References 20 publications

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“…From Table 2, we know the constructions of ZCCSs in the literature mainly divided into direct and indirect approaches. The direct methods are mainly based on GBFs [19,26,[28][29][30][31], Pseudo-Boolean functions (PBFs) [37,38], EBFs [40] and MVFs [39]. In fact, all existing ZCCSs constructed based on GBFs and PBFs have multiples of two lengths and the ZCCSs based on MVFs have limited set sizes.…”

Section: Comparisonmentioning

confidence: 99%

“…Adhikary and Majhi in [35] employed Hadamard product to construct ZCCSs with new parameters. Further constructions of ZCCSs have been proposed in [36][37][38][39]. In most previous designs, however, the optimal ZCCSs based on direct methods have limited lengths and the optimal ZCCSs based on indirect methods have limited hardware generations.…”

Section: Introductionmentioning

confidence: 99%

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New Constructions of Mutually Orthogonal Complementary Sets and Z-Complementary Sequence Sets Based on Extended Boolean Functions

Xiao

Cao

2022

Preprint

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Mutually orthogonal complementary sets (MOCSs) have many applications in practical scenarios such as synthetic aperture imaging systems, orthogonal frequency division multiplexing code division multiple access (OFDM-CDMA) systems and multicarrier code division multiple access (MC-CDMA) systems. Z-complementary code sets (ZCCSs) will be useful if the practical situation focuses more on the set size. Most ofthe known constructions of MOCSs and ZCCSs based on generalized Boolean functions (GBFs) have lengths with the form of 2m or 2m+2t. Some constructions of MOCSs and ZCCSs based on other methods mostly have restrictive lengths. In this paper, we not only present constructions of an optimal ZCCS, but also construct MOCSs with flexible lengths. Both these constructions are based on extended Boolean functions. Though our proposed constructions generalize several previously known methods, we show that the parameters of these constructions are new and include previous parameters as special cases. In addition, a wide range of q-ary MOCSs and ZCCSs can be obtained by assigning different values to q.

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Section: Comparisonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Constructions of Mutually Orthogonal Complementary Sets and Z-Complementary Sequence Sets Based on Extended Boolean Functions

Xiao

Cao

2022

Preprint

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“…is more adaptable than the set size of 2D-ZCACS given in [10]. Unlike [10], the proposed 2D-ZCACS can be reduced to 1D-ZCCS [11][12][13][14][15][16][17][18] also. As a result, many existing optimal 1D-ZCCSs have become special cases of the proposed construction [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

“…Unlike [10], the proposed 2D-ZCACS can be reduced to 1D-ZCCS [11][12][13][14][15][16][17][18] also. As a result, many existing optimal 1D-ZCCSs have become special cases of the proposed construction [16][17][18]. The proposed construction also derived a new set of optimal 1D-ZCCS that had not previously been presented by direct method.…”

Section: Introductionmentioning

confidence: 99%

A Direct Construction of Optimal 2D-ZCACS with Flexible Array Size and Large Set Size

Ghosh

Majhi

Paul

2023

Preprint

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In this paper, we propose a direct construction of optimal two-dimensional Z-complementary array code sets (2D-ZCACS) using multivariable functions (MVFs). In contrast to earlier works, the proposed construction allows for a flexible array size and a large set size. Additionally, the proposed design can be transformed into a one-dimensional Z-complementary code set (1D-ZCCS). Many of the 1D-ZCCS described in the literature appeared to be special cases of this proposed construction. At last, we compare our work with the current state of the art and then draw our conclusions.

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“…The idea of ZCPs introduced in [1] was generalized to Z-complementary code set (ZCCS) by Feng et al in [15]. ZCCSs only consider the front-end ZCZ of the AACSs and ACCSs [16]- [19]. Recently, the idea of ZCCS is extended to Praveen Kumar and Subhabrata Paul are with the Department of Mathematics, IIT Patna, Bihta, Patna, 801106, Bihar, India (e-mail: praveen 2021ma03@iitp.ac.in; subhabrata@iitp.ac.in).…”

Section: Introductionmentioning

confidence: 99%

A Direct Construction of Cross Z-Complementary Sequence Sets with Large Set Size

Prabhash¹,

Majhi²,

Shrivastava³

2022

Preprint

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This letter presents a direct construction of cross Z-complementary sequence sets (CZCSSs), whose aperiodic correlation sums exhibit zero correlation zones at both the front-end and tail-end shifts. CZCSS can be regarded as an extension of the symmetrical Z-complementary code set (SZCCS). The available construction of SZCCS has a limitation on the set size, with a maximum set size of 8. The proposed generalized Boolean function based construction can generate CZCSS of length in the form of non-power-of-two with variable set size 2 n+1 , where each code has 2 n+1 constituent sequences. The proposed construction also yields cross Z-complementary pairs and cross Z-complementary sets with a large number of constituent sequences compared to the existing work.

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Direct Construction of Optimal Z-Complementary Code Sets With Even Lengths by Using Generalized Boolean Functions

Cited by 16 publications

References 20 publications

New Constructions of Mutually Orthogonal Complementary Sets and Z-Complementary Sequence Sets Based on Extended Boolean Functions

New Constructions of Mutually Orthogonal Complementary Sets and Z-Complementary Sequence Sets Based on Extended Boolean Functions

A Direct Construction of Optimal 2D-ZCACS with Flexible Array Size and Large Set Size

A Direct Construction of Cross Z-Complementary Sequence Sets with Large Set Size

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