A New Generalized Paraunitary Generator for Complementary Sets and Complete Complementary Codes of Size ${2^m}$

Ma, Dongxu; Budisin, S.Z.; Wang, Zilong; Gong, Guang

doi:10.1109/lsp.2018.2876613

Cited by 17 publications

(11 citation statements)

References 28 publications

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“…And the explicit GBF forms are derived in Theorem 7 (in Section 6). This result extends the univariate PU matrices in [26] to the array version and determines all the sequences in PU-matrix-based construction [26]. 5.…”

Section: Introductionmentioning

confidence: 70%

New Construction of Complementary Sequence (or Array) Sets and Complete Complementary Codes

Wang¹,

Ma²,

Gong³

et al. 2020

Preprint

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A new method to construct q-ary complementary sequence sets (CSSs) and complete complementary codes (CCCs) of size N is proposed by using desired para-unitary (PU) matrices. The concept of seed PU matrices is introduced and a systematic approach on how to compute the explicit forms of the functions in constructed CSSs and CCCs from the seed PU matrices is given. A general form of these functions only depends on a basis of the functions from ZN to Zq and representatives in the equivalent class of Butson-type Hadamard (BH) matrices. Especially, the realization of Golay pairs from the our general form exactly coincides with the standard Golay pairs. The realization of ternary complementary sequences of size 3 is first reported here. For the realization of the quaternary complementary sequences of size 4, almost all the sequences derived here are never reported before. Generalized seed PU matrices and the recursive constructions of the desired PU matrices are also studied, and a large number of new constructions of CSSs and CCCs are given accordingly. From the perspective of this paper, all the known results of CSSs and CCCs with explicit GBF form in the literature (except non-standard Golay pairs) are constructed from the Walsh matrices of order 2. This suggests that the proposed method with the BH matrices of higher orders will yield a large number of new CSSs and CCCs with the exponentially increasing number of the sequences of low peak-to-mean envelope power ratio.

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Section: Introductionmentioning

confidence: 70%

New Construction of Complementary Sequence (or Array) Sets and Complete Complementary Codes

Wang¹,

Ma²,

Gong³

et al. 2020

Preprint

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“…In 2007, Schmidt used higher order Reed-Muller codes and extended Paterson's results by constructing GCSs with size 2 k+1 having sequences of length 2 m [16]. In 2019, Ma et al presented a construction of GCSs with size M = 2 m and of length M K by using generalized paraunitary generators [17]. It is noteworthy that the lengths of the GCSs constructed by [12], [15]- [17] is power-of-two.…”

Section: B Prior Work and Main Contributionsmentioning

confidence: 99%

“…In 2019, Ma et al presented a construction of GCSs with size M = 2 m and of length M K by using generalized paraunitary generators [17]. It is noteworthy that the lengths of the GCSs constructed by [12], [15]- [17] is power-of-two. In practice, non-power-of-two sequence lengths are preferred in some scenarios.…”

Section: B Prior Work and Main Contributionsmentioning

confidence: 99%

A Construction of Binary Golay Complementary Sets Based on Even-Shift Complementary Pairs

2020

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Orthogonal frequency division multiplexing (OFDM) has been widely used in multi-carrier communication systems. However, high the peak-to-average power ratio (PAPR) is a very troublesome problem in OFDM system. In the paper, we propose a construction of Golay complementary sets (GCSs) with size 4 of flexible lengths using even-shift complementary pairs (ESCPs). Based on computer search, we find that there exist a large number of even-shift complementary pairs of various lengths, and we also propose some constructions of ESCPs, which are very useful for the construction of GCSs. INDEX TERMS Orthogonal frequency division multiplexing (OFDM), peak-to-average power ratio (PAPR), even-shift complementary pairs, Golay complementary sets.

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“…They have reported BH(M, 6) matrices for M = 2, 3, 4, 6, 7, 8, 9, 10, 12, 13, 14, 16, 18. Later, Szöllősi proved that a BH (19,6) matrix exists in [55]. According to the above discussion, we give the values of M and q for BH(M, q) matrices up to M = 19 in Table II [53]- [55].…”

Section: B Butson-type Hadamard (Bh) Matricesmentioning

confidence: 99%

New Optimal $Z$-Complementary Code Sets from Matrices of Polynomials

Das,

Parampalli,

Majhi

et al. 2019

Preprint

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The concept of paraunitary (PU) matrices arose in the early 1990s in the study of multi-rate filter banks. So far, these matrices have found wide applications in cryptography, digital signal processing, and wireless communications. Existing PU matrices are subject to certain constraints on their existence and hence their availability is not guaranteed in practice. Motivated by this, for the first time, we introduce a novel concept, called Z-paraunitary (ZPU) matrix, whose orthogonality is defined over a matrix of polynomials with identical degree not necessarily taking the maximum value. We show that there exists an equivalence between a ZPU matrix and a Z-complementary code set when the latter is expressed as a matrix with polynomial entries. Furthermore, we investigate some important properties of ZPU matrices, which are useful for the extension of matrix sizes and sequence lengths. Finally, we propose a unifying construction framework for optimal ZPU matrices which includes existing PU matrices as a special case.

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A New Generalized Paraunitary Generator for Complementary Sets and Complete Complementary Codes of Size ${2^m}$

Cited by 17 publications

References 28 publications

New Construction of Complementary Sequence (or Array) Sets and Complete Complementary Codes

New Construction of Complementary Sequence (or Array) Sets and Complete Complementary Codes

A Construction of Binary Golay Complementary Sets Based on Even-Shift Complementary Pairs

New Optimal $Z$-Complementary Code Sets from Matrices of Polynomials

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