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Z-complementary code sets (ZCCSs) can support interference-free multi-carrier code-division multiple access (MC-CDMA) in quasi-synchronous channels due to their favourable correlation properties. In this letter, based on the existing optimal ZCCSs and CCCs, we propose new class of optimal ZCCSs using Kronecker product. The resultant sequence sets have enlarged set size and sequence lengths which have not been reported before. [ABSTRACT FROM AUTHOR]

Quasi-complementary sequence sets (QCSSs) can be seen as a generalized version of complete complementary codes (CCCs), which enables multicarrier communication systems to support more users. The contribution of this work is two-fold. First, we propose a systematic construction of Florentine rectangles. Secondly, we propose several sets of CCCs and QCSSs, using Florentine rectangles. The CCCs and QCSSs are constructed over $\mathbb {Z}_{N}$ , where $N\geq 2$ is any integer. The cross-correlation magnitude of any two of the constructed CCCs is upper bounded by $N$. By combining the proposed CCCs, we propose asymptotically optimal and near-optimal QCSSs with new parameters. [ABSTRACT FROM AUTHOR]

Spatial modulation (SM) is a special kind of multiple-input multiple-output (MIMO) technique, in which one transmit antenna is activated during each symbol duration. Recently, cross Z-complementary sequence pairs (CZCPs) have been evolved as a new sequence pair to be used for pilot design in SM over frequency-selective channels. CZCPs are sequence pairs having zero autocorrelation sums and zero cross-correlation sums within specific time-shifts. In this letter, we propose systematic constructions of binary CZCPs with new lengths of the form $2^\alpha 10^\beta 26^\gamma ~(\alpha \geq 1)$ , $10^\beta $ , $26^\gamma $ and $10^\beta 26^\gamma $. We have also proved that for a specific kind of binary CZCP, the magnitude of non-zero aperiodic cross-correlation sums at each time shift outside the zero cross-correlation zone is lower bounded by 4. Finally, we have compared our proposed constructions with the previous constructions. [ABSTRACT FROM AUTHOR]

In recent years, complete complementary codes (CCCs) and quasi-complementary sequence sets (QCSSs) have found many important applications in multi-carrier code-division multiple-access (MC-CDMA) systems for their good correlation properties. In this paper, we propose a generic construction of multiple sets of CCCs over $\mathbb {Z}_{N}$ , consisting of sequences of length $N$ , where $N\geq 3$ is an arbitrary odd integer. Interestingly, the maximum inter-set aperiodic cross-correlation magnitude of the proposed CCCs is upper bounded by $N$. It turns out that the combination of the generated CCCs results in a new set of sequences to obtain asymptotically optimal and near-optimal aperiodic QCSSs. The proposed construction includes a recent optimal construction of QCSSs with prime length as a special case and leads to asymptotically optimal QCSSs with new flexible parameters. [ABSTRACT FROM AUTHOR]

A pair of sequences is called a Z-complementary pair (ZCP) if it has zero aperiodic autocorrelation sums (AACSs) for time-shifts within a certain region, called zero correlation zone (ZCZ). Optimal odd-length binary ZCPs (OB-ZCPs) display closest correlation properties to Golay complementary pairs (GCPs) in that each OB-ZCP achieves maximum ZCZ of width $({N}+1)/2$ (where N is the sequence length) and every out-of-zone AACSs reaches the minimum magnitude value, i.e. 2. Till date, systematic constructions of optimal OB-ZCPs exist only for lengths $2^{\alpha } \pm 1$ , where $\alpha $ is a positive integer. In this paper, we construct optimal OB-ZCPs of generic lengths $2^\alpha 10^\beta 26^\gamma +1$ (where $\alpha,~\beta,~\gamma $ are non-negative integers and $\alpha \geq 1$) from inserted versions of binary GCPs. The key leading to the proposed constructions is several newly identified structure properties of binary GCPs obtained from Turyn’s method. This key also allows us to construct OB-ZCPs with possible ZCZ widths of $4 \times 10^{\beta -1} +1$ , $12 \times 26^{\gamma -1}+1$ and $12 \times 10^\beta 26^{\gamma -1}+1$ through proper insertions of GCPs of lengths $10^\beta,~26^\gamma, \text {and } 10^\beta 26^\gamma $ , respectively. Our proposed OB-ZCPs have applications in communications and radar (as an alternative to GCPs). [ABSTRACT FROM AUTHOR]

The zero correlation zone (ZCZ) ratio, i.e., the ratio of the width of the ZCZ and the length of the sequence plays a major role in reducing interference in an asynchronous environment of communication systems. However, to the best of the authors knowledge, for $q=\text{2}$ , the highest ZCZ ratio for even-length Z-complementary pairs which are directly constructed using generalized Boolean functions (GBFs), is $\text{2}/\text{3}$. In this letter, we present a direct construction of $q$ -ary even-length Z-complementary pairs through GBFs, which can achieve a ZCZ ratio of $\text{3}/\text{4}$. In general, the constructed $q$ -ary even-length Z-complementary pairs are of length $\text{2}^{m-\text{1}}+\text{2}$ ($m \in \mathbb {Z}^+$), having a ZCZ width of $\text{2}^{m-\text{2}}+\text{2}^{\pi (m-\text{3})}+\text{1}$ where $\pi$ is a permutation over $m-\text{2}$ variables. [ABSTRACT FROM AUTHOR]

The construction of complementary sets (CSs) of sequences with different set size and sequence length become important due to its practical application for OFDM systems. Most of the constructions of CSs, based on generalized Boolean functions (GBFs), are of length $2^\alpha$ ($\alpha$ is a natural number). Recently some works have been reported on construction of CSs having lengths non-power of two, i.e., in the form of $2^{m-1}+2^v$ ($m$ is natural number, $0\leq v < m$), $N+1$ and $N+2$ , where $N$ is a length for which $q$ -ary complementary pairs exist. In this letter, we propose a construction of CSs of lengths $M+N$ for set size $4n$ , using concatenation of CSs of lengths $M$ and $N$ , and set size $4n$ , where $M$ and $N$ are lengths for which $q$ -ary complementary pairs exists. Also, we construct CSs of length $M+P$ for set size $8n$ by concatenating CSs of lengths $M$ and $P$ , and set size $8n$ , where $M$ and $P$ are lengths for which $q$ -ary complementary pairs and complementary sets of size 4 exists, respectively. The proposed constructions cover all the previous constructions as special cases in terms of lengths and lead to more CSs of new sequence lengths which have not been reported before. [ABSTRACT FROM AUTHOR]

The construction of complementary sets (CSs) of sequences with different set sizes and sequence lengths become important due to the practical application in orthogonal frequency-division multiplexing (OFDM) systems. Most of the constructions of CSs based on generalized Boolean functions (GBFs) are of length $2^\alpha $ ($\alpha $ is the non-negative integer). Recently, some works have reported on the construction of CSs having lengths non-power of two, i.e., in the form of $2^{m-1}+2^{v}$ ($m$ is the non-negative integer, $0\leq v < m $). In this letter, we propose the constructions of CSs of lengths $N+1$ and $N+2$ for set size $4n$ , and CSs of length $2N+3$ for set size $8n$ , by employing the insertion method on Golay complementary pairs of length $N$. This systematic construction can generate more CSs of the new sequence length and set size, which has not been reported before. [ABSTRACT FROM AUTHOR]

This letter is focused on increasing the zero correlation zone (ZCZ) of even-length binary Z-complementary pairs (EB-ZCPs). Till date, the maximum ZCZ ratio (i.e., ZCZ width over the sequence length) for systematically constructed EB-ZCPs is $2/3$. In this letter, we give a construction of EB-ZCPs with lengths $2^{\alpha +2} 10^\beta 26^\gamma +2$ (where $\alpha$ , $\beta$ , and $\gamma$ are nonnegative integers) and ZCZ widths $3 \times 2^\alpha 10^\beta 26^\gamma +1$ , thus achieving asymptotic ZCZ ratio of $3/4$. The proposed EB-ZCPs are constructed via proper insertion of concatenated odd-length binary ZCPs. The ZCZ width is proved by exploiting several newly identified intrinsic structure properties of binary Golay complementary pairs, obtained from Turyn's method. The proposed EB-ZCPs have aperiodic autocorrelation sums (AACS) magnitude of 4 outside the ZCZ region (except for the last time-shift taking AACS value of zero). [ABSTRACT FROM AUTHOR]

A pair of sequences is called a periodic complementary pair (PCP) if the periodic autocorrelations of the constituent sequences sum up to zero for all nonzero time shifts. Owing to the scarcity of PCPs, we investigate optimal binary periodic almost-complementary pairs (BP-ACPs), each displaying correlation property closest to that of PCP. We show that an optimal BP-ACP of even length $N$ has zero out-of-phase periodic autocorrelation sums (PACSs) except at the time shift of N/2$, where the corresponding PACS has minimum magnitude of 4. We also show that for any arbitrary odd N$ , all the out-of-phase PACSs of an optimal BP-ACP should have identical magnitude of . A number of optimal BP-ACPs from analytical constructions as well as computer search are presented. In addition, our proposed optimal BP-ACPs for the even-length case lead to two new families of base-two almost difference families. [ABSTRACT FROM PUBLISHER]

Multi-instance learning (MIL) is a widely applied technique in practical applications that involve complex data structures. MIL can be broadly categorized into two types: traditional methods and those based on deep learning. These approaches have yielded significant results, especially regarding their problem-solving strategies and experiment validation, providing valuable insights for researchers in the MIL field. However, considerable knowledge is often trapped within the algorithm, leading to subsequent MIL algorithms that rely solely on the model's data fitting to predict unlabeled samples. This results in a significant loss of knowledge and impedes the development of more powerful models. In this article, we propose a novel data-driven knowledge fusion for deep MIL (DKMIL) algorithm. DKMIL adopts a completely different idea from existing deep MIL methods by analyzing the decision-making of key samples in the dataset (referred to as the data-driven) and using the knowledge fusion module designed to extract valuable information from these samples to assist the model's learning. In other words, this module serves as a new interface between data and the model, providing strong scalability and enabling prior knowledge from existing algorithms to enhance the model's learning ability. Furthermore, to adapt the downstream modules of the model to more knowledge-enriched features extracted from the data-driven knowledge fusion (DDKF) module, we propose a two-level attention (TLA) module that gradually learns shallow-and deep-level features of the samples to achieve more effective classification. We will prove the scalability of the knowledge fusion module and verify the efficiency of the proposed architecture by conducting experiments on 62 datasets across five categories.