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Complete mutually orthogonal golay complementary sets from Reed-Muller codes

IEEE TRANSACTIONS ON INFORMATION THEORY 2008年第3期54卷 1339-1346页

作者： Rathinakumar, Appuswamy Chaturvedi, Ajit Kumar Indian Inst Technol Dept Elect Engn Kanpur 208016 Uttar Pradesh India

Recently Golay complementary sets were shown to exist in the subsets of second-order cosets of a q-ary generalization of the first-order Reed-Muller (RM) code. We show that mutually orthogonal Golay complementary sets can also be directly constructed from second-order cosets of a q-ary generalization of the first-order RM code. This identification can be used to construct zero correlation zone (ZCZ) sequences directly and it also enables the construction of ZCZ sequences with special subsets.

关键词： complementary sets generalized boolean function mutually orthogonal Golay complementary sets Reed-Muller (RM) codes zero correlation zone (ZCZ) sequences

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New Constructions of Quadratic Bent functions in Polynomial Form

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IEEE TRANSACTIONS ON INFORMATION THEORY 2014年第9期60卷 5760-5767页

作者： Li, Nian Tang, Xiaohu Helleseth, Tor Southwest Jiaotong Univ Informat Secur & Natl Comp Grid Lab Chengdu 610031 Peoples R China Univ Bergen Dept Informat N-5020 Bergen Norway

New quadratic bent functions in polynomial form are constructed in this paper. The constructions give new boolean bent, generalized boolean bent and p-ary bent functions. Based on Z(4)-valued quadratic forms, a simple method provides several new constructions of generalized boolean bent functions. From these generalized boolean bent functions a method is presented to transform them into boolean bent and semi-bent functions. Moreover, many new p-ary bent functions can also be obtained by applying similar methods.

关键词： boolean bent function Galois ring generalized boolean function p-ary bent function quadratic form

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A Brief Proof of General QAM Golay Complementary Sequences in Cases I-III Constructions

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2015年第10期E98A卷 2203-2206页

作者： Zeng, Fanxin Zhang, Zhenyu Chongqing Commun Inst Chongqing Key Lab Emergency Commun Chongqing 400035 Peoples R China Chongqing Univ Coll Commun Engn Chongqing 400044 Peoples R China

By investigating the properties that the offsets should satisfy, this letter presents a brief proof of general QAM Golay complementary sequences (GCSs) in Cases I-III constructions. Our aim is to provide a brief, clear, and intelligible derivation so that it is easy for the reader to understand the known Cases I-III constructions of general QAM GCSs.

关键词： Golay complementary sequences (GCSs) QAM constellation offset generalized boolean function standard QPSK GDJ CSs

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A Novel Construction of Two-Dimensional Z-Complementary Array Pairs With Large Zero Correlation Zone

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IEEE SIGNAL PROCESSING LETTERS 2021年 28卷 1245-1249页

作者： Pai, Cheng-Yu Chen, Chao-Yu Natl Cheng Kung Univ Dept Engn Sci Tainan 701 Taiwan

The two-dimensional (2-D) Z-complementary array pair (ZCAP) can be viewed as an extension of the well-known one-dimensional (1-D) Z-complementary pair (ZCP). To date, most constructions of 2-D ZCAPs are indirect and based on existing 1-D sequences or 2-D arrays. In this letter, a new direct construction of 2-D ZCAPs with flexible array sizes based on 2-D generalized boolean functions is proposed. Compared with the state-of-the-art method, the proposed 2-D ZCAPs have larger 2-D zero correlation zone (ZCZ) sizes and more flexible array sizes. Furthermore, the peak-to-average power ratio of column sequences of the proposed 2-D ZCAPs is analyzed and upper bounded by 2.

关键词： boolean functions Peak to average power ratio Correlation Zero correlation zone Two dimensional displays Array signal processing Multicarrier code division multiple access generalized boolean function peak-to-average power ratio (PAPR) Z-complementary array pair (ZCAP) Z-complementary pair (ZCP) zero correlation zone (ZCZ)

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Novel 16-QAM Golay Complementary Sequences

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2014年第7期E97A卷 1631-1634页

作者： Zeng, Fanxin Zeng, Xiaoping Zhang, Zhenyu Xuan, Guixin Chongqing Univ Coll Commun Engn Chongqing 400044 Peoples R China Chongqing Commun Inst Chongqing Key Lab Emergency Commun Chongqing 400035 Peoples R China

Based on the non-standard generalized boolean functions (GBFs) over Z(4), we propose a new method to convert those functions into the 16-QAM Go lay complementary sequences (CSs). The resultant 16-QAM Go lay CSs have the upper bound of peak-to-mean envelope power ratio (PMEPR) as low as 2. In addition, we obtain multiple 16-QAM Go lay CSs for a given quadrature phase shift keying (QPSK) Go lay CS.

关键词： non-standard QPSK GDJ complementary sequences 16-QAM Golay complementary sequences PMEPR generalized boolean function

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

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IEEE TRANSACTIONS ON INFORMATION THEORY 2021年第6期67卷 3464-3472页

作者： Wu, Shing-Wei Chen, Chao-Yu Liu, Zilong Natl Cheng Kung Univ Dept Engn Sci Tainan 70101 Taiwan Univ Essex Sch Comp Sci & Elect Engn Colchester CO4 3SQ Essex England

Mutually orthogonal complementary sets (MOCSs) have received significant research attention in recent years due to their wide applications in communications and radar. Existing MOCSs which are constructed based on generalized boolean functions (GBFs) mostly have lengths of power-of-two. How to construct MOCSs with non-power-of-two lengths whilst having large set sizes is a largely open problem. With the aid of GBFs, in this paper, we present new constructions of such MOCSs and show that the maximal achievable set size is 1/2 of the flock size of an MOCS.

关键词： Correlation boolean functions OFDM Upper bound Multicarrier code division multiple access Chaotic communication Radar applications Golay complementary set (GCS) mutually orthogonal complementary set (MOCS) complete complementary code (CCC) generalized boolean function

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A Sufficient Condition Producing 16-QAM Golay Complementary Sequences

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IEEE COMMUNICATIONS LETTERS 2014年第11期18卷 1875-1878页

作者： Zeng, Fanxin Chongqing Commun Inst Chongqing Key Lab Emergency Commun Chongqing 400035 Peoples R China

This letter discusses the construction of 16-quadratic-amplitude modulation (QAM) Golay complementary sequences of length N = 2(m). Based on the standard binary Golay-Davis-Jedwab (GDJ) complementary sequences (CSs), we present a method to convert the aforementioned GDJ CSs into the required sequences. The resultant sequences have the upper bounds 3.6N, 2.8N, 2N, 1.2N, and 0.4N of peak envelope powers, respectively, depending on the choices of their offsets. The numbers of the proposed sequences, corresponding to five upper bounds referred to above, are (24m - 16)(m!/2)(2m+1), 128(m - 1)(m!/2)(2m+1), (176m - 160)(m!/2)(2m+1), 128(m - 1)(m!/2)(2m+1), and (24m - 16)(m!/2)(2m+1). Our sequences can be potentially applied to the QAM systems whose input signals are binary signals.

关键词： Complementary sequences 16-QAM constellation standard binary GDJ CSs generalized boolean function peak envelope power

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Improvement of Code Rate in OFDM Communication Systems Encoded by QAM Complementary Sequences 9

Improvement of Code Rate in OFDM Communication Systems Encod...

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9th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI)

作者： Zeng, Fanxin Zhang, Zhenyu Qian, Linjie Chongqing Commun Inst Chongqing Key Lab Emergency Commun Chongqing 400035 Peoples R China Chongqing Univ Coll Commun Engn Chongqing 400044 Peoples R China

ISBN: (纸本)9781509037100

Based on the description Q-type-2 of quadrature amplitude modulation (QAM) constellation and standard Golay-Davis-Jedwab (GDJ) quaternary complementary sequences (CSs), this paper presents a new family of QAM Golay complementary sequences (GCSs), and determines their family size. The proposed QAM GCSs includes the known QAM GCSs from Cases I-III constructions as a special case. It is worthy of mentioning that the family size of new sequences is fairly larger than the one of the known sequences so that the code rate of the code consisting of new sequences is improved, which therefrom results in the increase of number of sub-carriers in OFDM communication systems employing the resultant QAM GCSs. More clearly, in a 64-QAM OFDM communication system whose signals are encoded by QAM GCSs, the number of subcarriers in this system is at most 16 when the known QAM GCSs from Cases I-III constructions are employed. However, such number can be increased up to 32 when the proposed QAM GCSs are used. Finally, it should be pointed out that the peak envelope power (PEP) upper bounds, educed from the usage of both new and known QAM GCSs in an OFDM communication system, are the same.

关键词： complementary sequences QAM constellation standard Golay-Davis-Jedwab complementary sequences generalized boolean function peak envelope power

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New Family of Cross Z-Complementary Sequences With Large ZCZ Width

New Family of Cross Z-Complementary Sequences With Large ZCZ...

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IEEE International Symposium on Information Theory (ISIT)

作者： Das, Shibsankar Banerjee, Adrish Liu, Zilong Indian Inst Technol Kanpur Dept Elect Engn Kanpur Uttar Pradesh India Univ Essex Sch Comp Sci & Elect Engn Colchester Campus Colchester 1NW 412 Essex England

ISBN: (纸本)9781665421607;9781665421591

In this paper, we present a new family of cross Z-complementary pairs (CZCPs) based on generalized boolean functions and two roots of unity. Our key idea is to consider an arbitrary partition of the set {1, 2, center dot center dot center dot, n} with two subsets corresponding to two given roots of unity for which two truncated sequences of new alphabet size determined by the two roots of unity are obtained. We show that these two truncated sequences form a new q-ary CZCP with flexible sequence length and large zero-correlation zone width. Furthermore, we derive an enumeration formula by considering the Stirling number of the second kind for the partitions and show that the number of constructed CZCPs increases significantly compared to the existing works.

关键词： Stirling number of the second kind generalized boolean function Cross Z-complementary pair

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New 16-QAM Golay Complementary Sequences 11

New 16-QAM Golay Complementary Sequences

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IEEE 11th International Conference on Communication Software and Networks (ICCSN)

作者： Zeng, Yue Zhang, Lisheng Zeng, Fanxin He, Xiping Xuan, Guixin Zhang, Zhenyu Chongqing Univ Posts & Telecom Coll Software Engn Chongqing 400065 Peoples R China Chongqing Inst Engn Sch Elect & Informat Chongqing 400056 Peoples R China Chongqing Technol & Business Univ Chongqing Engn Lab DCIS Chongqing 400067 Peoples R China Acad Army Engn Univ PLA Commun NCO Chongqing 400035 Peoples R China

ISBN: (纸本)9781728121840

Quadrature amplitude modulation (QAM) Golay complementary sequences (GCSs) are widely applied to communications, in particular, QAM GCSs can efficiently control peak envelope power (PEP) of transmitted signals in an orthogonal frequency division multiplexing (OFDM) communication system. In this paper, a new family of 16-QAM GCSs is presented, and the resultant sequences have the same PEP upper bounds as the known 16-QAM GCSs. It should be noted that new sequences have the larger family size than the known sequences, which results in the increase of the relevant code rate. Hence, the proposed sequences are good candidates for the applications of OFDM communication systems.

关键词： complementary sequences 16-QAM constellation peak envelope power generalized boolean function code rate

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