How to Construct Mutually Orthogonal Complementary Sets With Non-Power-of-Two Lengths?

Wu, Shou‐Mei; Chen, Chao‐Yu; Liu, Zilong

doi:10.1109/tit.2020.2980818

Cited by 25 publications

(19 citation statements)

References 32 publications

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“…be the binary representations of g, h, i, and j, respectively. Then, four cases are considered as follows to prove (29).…”

Section: A Gcaps Based On Generalized Boolean Functionsmentioning

confidence: 99%

“…The construction from generalized Boolean functions has algebraic structure and hence can be friendly for efficient hardware generations. Since then, there have been a number of literature investigating constructions of 1-D sequences from Boolean functions, including GCSs [9], [21]- [25], complete complementary codes (CCCs) [26]- [29]. Zcomplementary pairs (ZCPs) [30]- [35], and Z-complementary sets (ZCSs) [36], [37].…”

Section: Introductionmentioning

confidence: 99%

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Constructions of Two-Dimensional Golay Complementary Array Pairs Based on Generalized Boolean Functions

Pai

Chen

2020

2020 IEEE International Symposium on Information Theory (ISIT)

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The one-dimensional (1-D) Golay complementary set (GCS) has many well-known properties and has been widely employed in engineering. The concept of 1-D GCS can be extended to the twodimensional (2-D) Golay complementary array set (GCAS) where the 2-D aperiodic autocorrelations of constituent arrays sum to zero except for the 2-D zero shift. The 2-D GCAS includes the 2-D Golay complementary array pair (GCAP) as a special case when the set size is 2. In this paper, 2-D generalized Boolean functions are introduced and novel constructions of 2-D GCAPs, 2-D GCASs, and 2-D Golay complementary array mates based on generalized Boolean functions are proposed. Explicit expressions of 2-D Boolean functions for 2-D GCAPs and 2-D GCASs are given. Therefore, they are all direct constructions without the aid of other existing 1-D or 2-D sequences. Moreover, for the column sequences and row sequences of the constructed 2-D GCAPs, their peak-to-average power ratio (PAPR) properties are also investigated. Index Terms Golay complementary pair (GCP), Golay complementary array pair (GCAP), Golay complementary array mate, Golay complementary array set (GCAS), peak-to-average power ratio (PAPR). * In our previous conference paper [40], we provided constructions of 2-D GCAPs and 2-D Golay complementary array mates from Boolean functions which can be found in [40, Th.6] and [40, Th.7], respectively. The result from [40, Th.6] will be described in Theorem 9 in this paper. Then, we provide more general constructions of 2-D GCAPs and Golay complementary array mates in Theorem 12 and Theorem 16, respectively.

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“…be the binary representations of g, h, i, and j, respectively. Then, four cases are considered as follows to prove (29).…”

Section: A Gcaps Based On Generalized Boolean Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Constructions of Two-Dimensional Golay Complementary Array Pairs Based on Generalized Boolean Functions

Pai

Chen

2020

2020 IEEE International Symposium on Information Theory (ISIT)

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“…Considering C = {C 0 , C 1 , C 2 , C 3 } as a (4, 4, N )-CCC, the search results can be found in Table III, where each element represents a power of (−1). The search results are important in itself, because in recent results [23]- [25], we observe that for a (K, M, N ) mutually orthogonal sequence set, through systematic construction, the maximum achievable K/M ratio is 1/2, when N is not in the form of 2 m . However, for our case, although N is not in the form of power-of-two, since the sequence sets are CCC (i.e., K = M ), the K/M ratio is 1.…”

Section: Let Us Definementioning

confidence: 99%

Asymptotically Optimal Golay-ZCZ Sequence Sets with Flexible Length

Zhi¹,

Zhou²,

Adhikary³

et al. 2021

Preprint

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Zero correlation zone (ZCZ) sequences and Golay complementary sequences are two kinds of sequences with different preferable correlation properties. Golay-ZCZ sequences are special kinds of complementary sequences which also possess a large ZCZ and are good candidates for pilots in OFDM systems. Known Golay-ZCZ sequences reported in the literature have a limitation in the length which is the form of a power of 2. In this paper, we propose two constructions of Golay-ZCZ sequence sets with new parameters which generalize the constructions of Gong et al. (IEEE Transaction on Communications 61(9), 2013) and Chen et al (IEEE Transaction on Communications 61(9), 2018). Notably, one of the constructions results in optimal binary Golay-ZCZ sequences, while the other results in asymptotically optimal polyphase Golay-ZCZ sequences as the number of sequences increases.

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“…, CCCs [19], [20], mutually orthogonal complementary sets (MOCSs) [21], ZCZ sequence sets [22]- [25], nearcomplementary sequences [26], [27], multiple-shift complementary sequences [12], and ZCCSs [28]- [31]. The constructed sequence sets from Boolean functions often lead to sequences of power-of-two length.…”

mentioning

confidence: 99%

“…The constructed sequence sets from Boolean functions often lead to sequences of power-of-two length. In [14]- [17], [21], it was shown that Boolean functions can also be useful to construct GCSs and MOCSs of non-power-of-two length. Recently, a construction of ZCCSs with non-power-of-two length based on Boolean functions was proposed in [31].…”

mentioning

confidence: 99%

Z-Complementary Code Sets With Flexible Lengths From Generalized Boolean Functions

Şahin

Huang

et al. 2021

IEEE Access

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How to Construct Mutually Orthogonal Complementary Sets With Non-Power-of-Two Lengths?

Cited by 25 publications

References 32 publications

Constructions of Two-Dimensional Golay Complementary Array Pairs Based on Generalized Boolean Functions

Constructions of Two-Dimensional Golay Complementary Array Pairs Based on Generalized Boolean Functions

Asymptotically Optimal Golay-ZCZ Sequence Sets with Flexible Length

Z-Complementary Code Sets With Flexible Lengths From Generalized Boolean Functions

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