Multi-instance learning (MIL) has become a powerful paradigm for weakly supervised learning tasks, where each sample is a bag of unlabeled instances with only the bag-level label. While graph-based MIL methods enhance bag topological structure modeling, they often suffer from high computation costs and limited representation due to rigid graph construction and insufficient integration of intra-bag semantics. To address these challenges, we propose GDF-MIL, a novel graph-driven MIL framework, which introduces a dual-path feature fusion mechanism to adaptively balance topological structure modeling and semantic feature preservation. First, the adaptive bag mapping module (ABMM) performs soft clustering to extract compact and informative representations. Subsequently, a dynamic graph structure learning (DGSL) component efficiently learns sparse topological structures via weighted connectivity, aggregating them into a comprehensive graph-level representation. Finally, to balance fast graph construction and bag-level knowledge, dual-path feature fusion (DPFF) employs a dual-path gating mechanism to integrate both types of features, which are then passed to the classifier for bag label prediction. Extensive experiments on twenty-four datasets across four domains show that GDF-MIL significantly outperforms eighteen state-of-the-art methods on the majority of datasets.

Within the zero-correlation-zone (ZCZ), ZCZ sequence sets exhibit ideal correlation properties, which is highly advantageous for both wireless communications and radar sensing applications. Recently, to achieve optimal training for spatial modulation (SM), Paiet al. introduced the concept of sparse ZCZ (SZCZ) sequence sets, where each column contains only one non-zero element. In this paper, we first extend the SZCZ sequence set concept by permitting multiple non-zero elements per column, thereby accommodating training design requirements for generalized SM (GSM) systems. Then, we propose a direct construction of SZCZ sequence sets with parameter (qn+k,qm+n+k, (q−1)qπ(2)−1+(q−2)qπ(3)−1, (qn,qm+n)) based on restricted extended Boolean functions. Compared to existing works, the proposed SZCZ sequence sets exhibit a greater ZCZ width and can be applied to both SM and GSM training designs simultaneously. Simulation results show that compared with other training sequences, the channel estimation performance is significantly improved when the proposed SZCZ sequence set is used as the training sequences.

Arrays with good correlation properties have emerged with promising applications in wireless communication, including ultra-wideband (UWB), two-dimensional (2- D) synchronization, and massive multiple-input multiple-output (MIMO). In this paper, we propose two efficient algorithms for designing arrays with low autocorrelation by minimizing the weighted integrated sidelobe level (WISL) and complementary ISL (CISL), respectively. We formulate these metrics as non-convex quartic problems under unimodular constraints in the frequency domain. Using the majorization-minimization (MM) framework, these problems are simplified into quadratic forms, ensuring monotonic convergence to a stationary point. Furthermore, a projection algorithm is introduced to relax unimodular constraints to peak-to-average power ratio (PAPR) constraints, enhancing the correlation performance of the optimized arrays. All proposed algorithms can be efficiently implemented using two-dimensional FFT/IFFT operations. Furthermore, a quasi-complementary array set (QCAS), generated via the proposed MM-ACISL algorithm, is applied as an omnidirectional precoding matrix in massive MIMO systems. Numerical experiments demonstrate that the proposed algorithms outperform existing methods in terms of both correlation performance and computational efficiency. Moreover, the resulting QCAS scheme effectively enables omnidirectional transmission in MIMO systems.

Multimodal biometric systems face critical deployment challenges due to frequent partial modality missing and unreliable modality quality (e.g., blurred fingerprints). Existing methods, relying on unidirectional feature interaction or static fusion, suffer catastrophic performance degradation under such conditions. This paper proposes an adaptive hybrid fusion network (AHFNet) for multimodal hand recognition, which dynamically selects and reweights modalities to correct errors induced by missing or low-quality inputs. The proposed framework comprises three core modules. Initially, a wavelet feature extraction module is implemented to capturing high-frequency biometric feature representations across modalities. Subsequently, a dual-path dynamic fusion module is designed using symmetric cross-attention for bidirectional feature reconstruction, preserving modality specificity via residual projections. Furthermore, this module employs the attention mechanism to perform reweighting, enabling the construction of a dynamic inter-modal compensation pathway at the feature level. Finally, a category-aware dynamic decision fusion module dynamically generates category-level weight coefficients based on input samples, enabling sample-adaptive optimization of multimodal contributions. Experiments on five public hand biometric databases demonstrate AHFNet’s superiority over existing methods across diverse multimodal scenarios, validating its broad applicability. Crucially, AHFNet emphasizes modal reliability differences. Even when certain modalities are missing, it exhibits less than 5% accuracy degradation—a relative improvement of over 75% compared to existing approaches, which typically suffer from more than 20% degradation. This enhanced robustness is consistently observed across all five databases.

A linear code with parameters [n, k, n–k+ 1] is called maximum distance separable (MDS), and one with parameters [n; k; n–k] is called almost MDS (AMDS). A code is near-MDS (NMDS) if both it and its dual are AMDS. NMDS codes supporting combinatorialt-designs have attracted growing interest, yet constructing such codes remains highly challenging. In 2020, Ding and Tang initiated the study of NMDS codes supporting 2-designs by constructing the first infinite family, followed by several other constructions fort> 2, all with length at mostq+ 1. Although NMDS codes can, in principle, exceed this length, known examples supporting 2-designs and having length greater thanq+ 1 are extremely rare and limited to a few sporadic binary and ternary cases. In this paper, we present the firstgeneric constructionofq-ary NMDS codes supporting 2-designs with lengthsexceedingq+1. Our method leverages new connections between elliptic curve codes, finite abelian groups, subset sums, and combinatorial designs, resulting in an infinite family of such codes along with their weight distributions.

The favorable algebraic properties and error-correcting performance of BCH codes have motivated extensive research and diverse applications, whereas the study of extended BCH codes remains relatively less explored. In this paper, we focus on the extended BCH codeC(q,q+1,δ,h)over the finite field Fq. Specifically, we investigate the parameters of three families of extended BCH codes and the weight distributions of their duals by solving certain quadratic and quartic equations:C(q,q+1,3,1)is shown to be NMDS when gcd(q+1,3) = 1;C(q,q+1,δ,q)with 3 ≤ δ ≤ ⌈(q+ 5)/2⌉ is proved to be AMDS; andC(q,q+1,3,q/2)is MDS for evenq.

Low ambiguity zone (LAZ) sequences play a crucial role in modern integrated sensing and communication (ISAC) systems. In this paper, we introduce a novel class of functions known as locally perfect nonlinear functions (LPNFs). By utilizing LPNFs and interleaving techniques, we propose three new classes of both periodic and aperiodic LAZ sequence sets with flexible parameters. The proposed periodic and aperiodic LAZ sequence sets are asymptotically optimal with respect to the periodic and aperiodic lower AF bounds, respectively, which were proposed recently in [IEEE J. Sel. Areas Commun. 40 (6): 1809-1822]. Notably, the aperiodic LAZ sequence sets are the first such sequence sets in the literature that satisfy the bound. Finally, we demonstrate that the proposed sequence sets are cyclically distinct.

This paper proposes a novel multi-carrier modulation framework for high-mobility communication scenarios. Our key idea lies in spreading data symbols across the delay-Doppler (DD) domain through orthogonal chirp-Zak transform (CZT). To enable efficient signal multiplexing, the proposed modulation scheme employs a transmitter signal that maintains orthogonality with the inherent resolution characteristics of the DD plane. Termed as Orthogonal Chirp Delay-Doppler Division Multiplexing (CDDM), we demonstrate a synergistic integration of chirp waveform properties with the channel structure of the DD domain, thereby achieving advantages with both lower computational efficiency and improved detection performance. We introduce a novel CZT-based superimposed sparse pilot structure to enable simultaneous estimation of delay-Doppler shifts and channel coefficients. For enhanced performance, we further develop an embedded pilot scheme that demonstrates channel estimation performance comparable to that of Orthogonal Delay-Doppler Division Multiplexing (ODDM) systems. Simulation results demonstrate that CDDM achieves significant bit error rate (BER) improvements over existing modulation schemes , under perfect channel state information (CSI), as well as superior out-of-band emissions (OOBE). Further, for the imperfect CSI case, the proposed CZT-based superimposed pilot scheme leads to significantly reduced normalized mean square error (NMSE), whilst attaining equivalent estimation accuracy to that of ODDM with lower computational complexity.

We are interested in the mobile target state detection (TSD) based on multi-input-multi-output (MIMO) orthogonal-frequency-division-multiplexing (OFDM) communication signals. Yet, communication-based TSD is of challenge, due to complex problem structures and communication symbol randomness. To address this challenge, we exploit structured features of low-speed and narrow-band systems to decouple the target state parameters and random communication symbols, and then use coherent detection to equalize random symbols. As such, a simplified sensing model holding an explicit space-time-frequency-domain correlation structure with respect to target direction angle, radial speed and relative distance, respectively, is obtained. Then, an efficient MIMO OFDM waveform-based TSD method extracting space-time-frequency correlation features is devised. It is verified by simulations that the proposed TSD method outperforms state-of-the-art baselines, due to the above problem-specific algorithm design. In addition, we establish the closed-form boundaries of the maximum detectable speed and maximum detectable range for MIMO OFDM-based TSD, which are essentially subject to the limited coherent time and bandwidth, respectively. The impact of system parameters (e.g., signal bandwidth, subcarrier spacing and carrier frequency) on the detection capability boundaries is analysed to gain insights into the fundamental limits of MIMO OFDM communication-based TSD. This work does not only build a technical foundation for sensing-assisted communication design, but also provide a unified framework for understanding the potentials of MIMO OFDM communication-based sensing.

Affine frequency division multiplexing (AFDM) has recently emerged as an excellent backward-compatible 6G waveform. In this paper, we study matched filtering (MF) assisted channel estimation (CE) for AFDM systems in complex doubly selective channels. By deriving the complete input-output relationship of the continuous-time signal, the inter-chirp-carrier interference, signal-to-interference-plus-noise ratio (SINR), and the effective SINR loss of AFDM, are investigated in discrete affine Fourier transform (DAFT) domain. Further, we propose two low-complexity methods for constructing the channel matrix by taking advantage of its inherent discrete Fourier transform structure and the staircase structure of the piecewise functions in the channel matrix, respectively. It is shown that complexity reduction by at least two orders of magnitude can be achieved for a large number of chirp subcarriers. For the CE problem in doubly selective channels, we introduce an MF assisted CE scheme. This allows us to sequentially estimate the parameters of each path by exploiting the separability and approximate orthogonality of different paths in the DAFT domain, thus leading to significantly reduced complexity. Furthermore, based on generalized Fibonacci search (GFS), an MF-GFS scheme is proposed to avoid significantly redundant computation, which can be extended to typical wide-band systems. Extensive simulation results indicate that the proposed schemes offer superior advantages in terms of their improved communication performance and lower complexity.

Traditional logic-based belief revision research focuses on designing rules to constrain the behavior of revision operators. Frameworks have been proposed to characterize iterated revision rules, but they are often too loose, leading to multiple revision operators that all satisfy the rules under the same belief condition. In many practical applications, such as safety critical ones, it is important to specify a definite revision operator to enable agents to iteratively revise their beliefs in a deterministic way. In this paper, we propose a novel framework for iterated belief revision by characterizing belief information through preference relations. Semantically, both beliefs and new evidence are represented as belief algebras, which provide a rich and expressive foundation for belief revision. Building on traditional revision rules, we introduce additional postulates for revision with belief algebra, including an upper-bound constraint on the outcomes of revision. We prove that the revision result is uniquely determined given the current belief state and new evidence. Furthermore, to make the framework more useful in practice, we develop a particular algorithm for performing the proposed revision process. We argue that this approach may offer a more predictable and principled method for belief revision, making it suitable for real-world applications.

This paper proposes a novel multi-carrier modulation scheme, orthogonal chirp delay-Doppler division Multiplexing (CDDM), tailored for future high mobility communications. The core innovation lies in spreading data symbols over chirps in the Delay-Doppler (DD) domain using a novel chirp-Zak transform (CZT), and enabling orthogonal pulse transmission within the DD plane. This approach fully leverages the advantages of both chirp signals and DD channels. Key contributions of CDDM include: efficient implementation through pre-computation techniques, synergistic exploitation of chirp signal characteristics and DD channel properties, and novel data detection via DD chirp correlation. Simulation results demonstrate that CDDM achieves significant bit error rate (BER) improvements compared to benchmarking schemes, validating its potential for high mobility communication systems.

Abstract. In this work, we study the subspace clustering and recovery of multidimensional images. Existing matrix-based/tensor-based subspace clustering methods successfully consider unilateral information (i.e., the similarity between image samples) to cluster samples into subspaces by using low-rank representation. The key issue of the unilateral representation-based methods is that the number of samples in each subspace should be sufficient for subspace representation. In practice, the clustering performance can be degraded when there is only a small number of observed samples in each subspace. To address the problem of insufficient observed samples, we propose to introduce hidden tensor data to supplement an insufficient number of observed samples. We employ both observed samples and hidden tensor data under low-rank constraints so that a new bilateral tensor low-rank representation (BTLRR) in subspace clustering is formulated. We show that a closed-form solution of block-diagonal tensor structure is obtained in subspace clustering of observed samples and hidden tensor data. Also the proposed BTLRR optimization problem can be solved by using the convex relaxation technique and augmented Lagrangian multiplier algorithm. The proposed BTLRR can fully explore the bilateral information of observations, including not only the similarity between samples but also the relationship among features. Extensive numerical results on multidimensional image data clustering and recovery illustrate that the effectiveness and robustness of the proposed bilateral representation are better than those of state-of-the-art methods (e.g., the popular LRR and TLRR methods).

Abstract. The orthogonal matching pursuit (OMP) algorithm, known for its exceptional ability to reconstruct sparse signals, is a widely employed algorithm in compressed sensing. Numerous studies have provided theoretical analyses supporting its capability for achieving exact recovery. However, when applied to large-scale sparse signal recovery, the OMP algorithm incurs substantial computational overhead, leading to prolonged running time. To address this challenge, we design a Randomized OMP with Adaptive Partial Selection (AROMP) algorithm to mitigate computational overhead and reduce runtime. The novelty of the AROMP algorithm lies in its utilization of a randomized index selection method rather than a greedy approach to select the index in each iteration. Subsequently, we theoretically characterize the gap between AROMP and OMP for exactly recovering an [Formula: see text]-sparse signal and show that the gap decreases as the number of comparisons [Formula: see text] increases, sparsity [Formula: see text] decreases, or signal dimension [Formula: see text] decreases. As [Formula: see text] approaches [Formula: see text], the gap between AROMP and OMP tends to 0. The experimental results substantiate that our proposed method significantly reduces running time while maintaining satisfactory accuracy in sparse signal recovery, face recognition tasks, and image reconstruction tasks.

Sequences with low ambiguity zone (LAZ) properties are employed in integrated sensing and communication (ISAC) systems. In this letter, we introduce a new class of LAZ sequence sets based on cubic sequences. The proposed LAZ sequence set is asymptotically optimal with respect to the Ye-Zhou-Fan-Liu-Lei-Tang (YZFLLT) bound when the sequence length is odd. Otherwise, it achieves$\sqrt{2}$times of the YZFLLT bound. Furthermore, the sequence sets provide flexible choices for the sequence lengths, set size, and the LAZ region.

Pilot sequence design over doubly selective channels (DSC) is challenging due to the variations in both the time- and frequency-domains. Against this background, the contribution of this paper is twofold: Firstly, we investigate the optimal sequence design criteria for efficient channel estimation in orthogonal frequency division multiplexing systems under DSC. Secondly, to design pilot sequences that can satisfy the derived criteria, we propose a new metric called oversampled ambiguity function (O-AF), which considers both fractional and integer Doppler frequency shifts. Optimizing the sidelobes of O-AF through a modified iterative twisted approximation (ITROX) algorithm, we develop a new class of pilot sequences called “oversampled low ambiguity zone (O-LAZ) sequences”. Through numerical experiments, we evaluate the efficiency of the proposed O-LAZ sequences over the traditional low ambiguity zone (LAZ) sequences, Zadoff-Chu (ZC) sequences and m-sequences, by comparing their channel estimation performances over DSC.

In this paper, we consider the physical layer security (PLS) problem for integrated sensing and communication (ISAC) systems in the presence of hybrid-colluding eavesdroppers, where an active eavesdropper (AE) and a passive eavesdropper (PE) collude to intercept the confidential information. To ensure the accuracy of sensing while preventing the eavesdropping, a base station transmits a signal consisting of information symbols and sensing waveform, in which the sensing waveform can be also used as artificial noise to interfere with eavesdroppers. Under this setup, we propose an alternating optimization-based two stage scheme (AO-TSS) for improving the sensing and communication performance. In the first stage, based on the assumptions that the perfect channel state information (CSI) of the AE and statistical CSI of the PE are known, the communication and sensing beamforming problem is formulated with the objective of minimizing the weighted sum of the beampattern matching mean squared error (MSE) and cross-correlation, subject to the secure transmission constraint. To tackle the non-convexity, we propose a semi-definite relaxation (SDR) algorithm and a reduced-complexity zero-forcing (ZF) algorithm. Then, the scenarios are further extended to more general cases with imperfect AE CSI and unknown PE CSI. To further improve the communication performance, the second-stage problem is developed to optimize the secrecy rate threshold under the radar performance constraint. Finally, numerical results demonstrate the superiority of the proposed scheme in terms of sensing and secure communication.

In this paper, aimed to protect the transmitted waveform from being intercepted by advanced electronic support measure systems, a low probability of intercept (LPI) signal design, taking into account the transmitted waveform and precoder of communication users, is developed for multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) systems. The considered system simultaneously senses multiple targets and communicates with multiple users in the presence of various interferences. Specifically, based on the analysis of cyclic spectrum, the desired LPI performance is achieved by minimizing the cyclic frequency sidelobe level. Moreover, sensing and communication requirements are satisfied by respectively maximizing the minimum signal-to-interference-plus-noise ratio (SINR) of targets and constraining the received SINR lower bound of each user. Energy budget and peak-to-average power ratio constraints are introduced to meet the practical resources limits, while similarity constraint is constructed to further ensure the target sensing. Next, in order to solve the formulated nonconvex problem, an efficient iterative algorithm is proposed based on the idea of successive convex approximation (SCA). Finally, simulation results demonstrate the effectiveness of our proposed scheme and display the trade-off among LPI, sensing and communication performance.

Quasi complementary sequence sets (QCSSs) are important in modern communication systems as they are capable of supporting more users, which is desired in applications like MC-CDMA nowadays. In this paper, we first derive a tighter bound on the maximum aperiodic correlation among all constituent complementary sequence sets in QCSSs. By proposing a new combinatorial structure called quasi-Florentine rectangles, we obtain a new construction of QCSSs with large set sizes. Using Butson-type Hadamard matrices and quasi-Florentine rectangles, we propose another construction which can construct QCSSs with flexible parameters over any given alphabet size, including small alphabets. All the proposed sequences are optimal with respect to the newly proposed bound. Also, through some of the constructions, the column sequence PMEPR of the proposed QCSSs are upper bounded by 2.

This paper studies Doppler resilient complementary sequences (DRCSs) whereby the ambiguity functions (AFs) of multiple element sequences are summed to attain low/zero AF values. We first derive a set of AF lower bounds for unimodular DRCS sets, which include the existing bounds on AFs as special cases. These bounds may be used as theoretical design guidelines to measure the optimality of DRCS sets against Doppler effect. In addition, we introduce some constructions of DRCS sets based on mathematical tools such as orthogonal matrices, circular Florentine rectangles and difference sets, which can generate the optimal DRCS set. Finally, we evaluate the feasibility of DRCSs for pulse train waveform design.

Frequency hopping sequences (FHSs) play a crucial role in frequency hopping (FH) communication systems due to their strong anti-interference ability, low interception probability, high confidentiality and strong concealment. The objective of this paper is to construct FHSs for quasi-synchronous frequency-hopping multiple access (FHMA) communication systems that simultaneously achieve optimal no-hit zone (NHZ) length and optimal gap. To accomplish this, the paper first derives tighter upper bounds for the gap size in both periodic and aperiodic scenarios under the assumption that all frequencies within the designated frequency slot set are fully utilized. Subsequently, this paper proposes a class of wide-gap frequency hopping sequences (WGFHSs) and a class of multi-timeslot wide-gap frequency hopping sequences (MTWGFHSs), both of which simultaneously exhibit optimal NHZ length and optimal gap.

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.

Neural networks, especially those update parameters by optimizing the difference between fit values and actual labels, often encounter challenges with real-world data containing mislabeled samples (called label noise). This label noise adversely affects the generalization performance of the network by disturbing local fit values. While existing network regularization methods such as data augmentation and label smoothing (LS) have shown usefulness in mitigating the devastation caused by label noise, they primarily focus on global constraints and overlook the local impacts of label noise. Furthermore, the detailed influence of label noise on network function remains underexplored. To fill this gap, our article presents an in-depth analysis of the local effects of label noise on neural networks from a topological perspective. A novel regularization method, network boundary topology regularization (NBTR), based on persistent homology, is introduced. This method is specifically designed for local fit values of the network, with the aim of simplifying the topology of each class boundary. By doing so, it effectively reduces the tendency of a network to memorize label noise. Extensive experiments have been conducted across a range of datasets, network structures, and noise types to validate the effectiveness of this method. Our findings demonstrate that this method not only surpasses strong baseline methods in network generalization accuracy, especially in asymmetric noise conditions (improving average generalization accuracy by 7.72%), but also enhances the anti-noise capabilities of traditional methods when integrated as a complementary method.

For the correlated input, the Volterra kernel-based least mean-square (LMS) algorithm in the time-domain exhibits a slow learning rate caused by the large eigenvalue spread of the input covariance matrix. To tackle such an issue, this paper develops a novel frequency-domain Volterra kernel-based filter, resulting in the periodic update constrained frequency-domain second-order Volterra normalized LMS (named as P-CFDSOV-NLMS1) algorithm. Subsequently, by using one- and two-dimensional discrete Fourier transforms (DFTs) simultaneously, another frequency-domain implementation and corresponding P-CFDSOV-NLMS2 algorithm are constructed. In contrast, the P-CFDSOV-NLMS1 scheme only requires one-dimensional DFT operations and takes advantage of the joint information between the block input vectors. Then, the mean and mean-square convergence behaviors of the P-CFDSOV-NLMS1 algorithm are investigated. Furthermore, the designed frequency-domain method is extended to three different widely complex-valued Volterra kernel-based models. Finally, computer simulations reveal that the suggested algorithms outperform the previously reported frequency-domain techniques in terms of convergence speed and tracking ability.

In this paper, a general class of polyphase sequences called Generalized Zadoff-Chu (GZC) sequences is presented, which is based on a quadratic function with real-valued coefficients. The conventional ZC sequences, P3, and P4 codes are included as special cases of GZC sequences. It is shown that, with the help of grid search algorithm, the optimized GZC sequences have significantly lower PMEPR than the well-known sequences such as Golay sequences, m-sequences, P3 and P4 codes, and ZC sequences. Numerical simulations suggest that the minimum PMEPR tends to a small constant of less than 1.43 dB as the sequence length approaches infinity.

Federated learning enables clients to train models locally and provide local updates to the server instead of raw dataset, thereby preserving data privacy to some extent. However, adversaries can still pry users’ privacy by inferring updates, and compromise the integrity of the global model through poisoning attack. Therefore, many related works have integrated poisoning attack detection method with secure computation to address both issues. Nevertheless, they still encounter two major challenges: (i) the efficiency is too low to be applied in practice, and (ii) the privacy is still at risk of being leaked, e.g., the distance of two local updates for detecting poisoning attack could be exposed to the server. Aiming at the challenges, in this paper, we propose an Efficient Privacy-preserving and Poisoning attack Resistant scheme for Federated Learning, named EPPRFL, which preserves the privacy for local updates and some intermediate information used to detect poisoning attack. In particular, we design an efficient poisoning attack detection method based on Euclidean distance filtering & clipping technique, named F&C. Then, considering the privacy preservation of the F&C method, we efficiently customize secure comparison, secure median, secure distance computation and secure clipping protocols based on additive secret sharing. Experimental results and theoretical analysis show that compared with existing schemes, EPPRFL can better resist poisoning attack and has lower computational and communication overheads on the client side.

Image watermarking techniques have continuously evolved to address new challenges and incorporate advanced features. The advent of data-driven approaches has enabled the processing and analysis of large volumes of data, extracting valuable insights and patterns. In this paper, we propose two content-aware quantization index modulation (QIM) algorithms: Content-Aware QIM (CA-QIM) and Content-Aware Minimum Distortion QIM (CAMD-QIM). These algorithms aim to improve the embedding distortion of QIM-based watermarking schemes by considering the statistics of the cover signal vectors and messages. CA-QIM introduces a canonical labeling approach, where the closest coset to each cover vector is determined during the embedding process. An adjacency matrix is constructed to capture the relationships between the cover vectors and messages. CAMD-QIM extends the concept of minimum distortion (MD) principle to content-aware QIM. Instead of quantizing the carriers to lattice points, CAMD-QIM quantizes them to close points in the correct decoding region. Canonical labeling is also employed in CAMD-QIM to enhance its performance. Both schemes can be categorized as (key-aided) semi-blind watermarking. Simulation results demonstrate the effectiveness of CA-QIM and CAMD-QIM in reducing embedding distortion compared to traditional QIM. The combination of canonical labeling and the minimum distortion principle proves to be powerful, minimizing the need for changes to most cover vectors/carriers. These content-aware QIM algorithms provide improved performance and robustness for watermarking applications.

Gold functions are well-known for designing sequences with good correlation properties. This paper reveals a fascinating relationship between Gold functions and Golay-Davis-Jedwab (GDJ) Boolean functions to design sequences with low correlation and low PAPR, which is the first of its kind. The bent and semi-bent properties of the Gold functions are utilized to derive the correlation of the resultant binary spreading sequence sets, while the complementary properties of the GDJ Boolean functions are used to derive the low PAPR. Based on this idea we propose three new sets of binary spreading sequences with low PAPR and low correlation. The proposed sequence sets have the potential to be used as spreading sequences in non-orthogonal multiple access (NOMA). They have a very large set size, which in turn results in a high overloading factor as compared to the existing sequence sets with the same length and the same correlation, which are generated through systematic constructions.

In this work, a distributed server system composed of multiple servers that holds some coded files and multiple users that are interested in retrieving the linear functions of the files is investigated, where the servers are robust, blind and adversarial in the sense that any J servers can together recover all files, while any I colluding servers cannot obtain any information about the files, and at most A servers maliciously provides erroneous information. In addition, the file library must be secure from a wiretapper who obtains all the signals, and the demands of any subset of users must kept private from the other users and servers, even if they collude. A coding scheme is proposed by incorporating the ideas of Shamir’s secret sharing and key superposition into the framework of Placement Delivery Array (PDA), originally proposed to characterize the single-server coded caching system without any security or privacy constraints. It is shown that PDAs associated to Maddah-Ali and Niesen’s coded caching scheme results in an achievable memory-storage-communication region, such that the storage size and communication load were optimal to within a multiplicative gap, except for the small memory regime when the number of files was smaller than the number of users.

With the explosive growth of spectrum demand for various wireless devices and applications, it is more and more difficult to allocate contiguous spectral bands for radar and communication nowadays. In this paper, the problem of dual-functional radar-communication (DFRC) multiple-input multiple-output (MIMO)-orthogonal frequency division multiplexing (OFDM) waveform design under non-contiguous spectrum bands is studied. We consider a flexible spectrum structure where a large number of non-contiguous bands are used for communication and some idle bands which are complementary to the communication bands are exploited for radar detection. The symbols transmitted on the communication bands are first designed by minimizing the multi-user interference (MUI) to enhance the performance of communication. Meanwhile, the radar performance is improved by designing the waveform of idle bands. We formulate the radar beampattern design as a rank-1 approximation problem, which can be solved with a closed-form solution. Numerical results show that we can achieve omnidirectional strict beampattern design and data transmission with zero MUI.

Iterative Twisted Approximation (ITROX), proposed in 2012 by Soltanalian et al., is an interesting algorithm for designing sequences with desired correlation properties. However, when aperiodic correlation of unimodular complementary and Zcomplementary sets (ZCSs) are considered, the correlation magnitudes of the resultant sequence sets of the ITROX algorithm, are not as good as desired. In this work, we have proposed a new modified ITROX algorithm, which can design unimodular ZCSs. Also the correlation levels of the resultant unimodular complementary sequence sets are better as compared to the previous ITROX.

Complete complementary codes (CCCs) have important applications in communication, radar, and information security. In modern communication and radar systems, certain spectrum is reserved or prohibited from transmission, which leads to the so-called spectrally null constrained (SNC) problem. Compared with vast works on conventional CCCs, relatively little is known about SNC-CCCs. One objective of this paper is to derive several constructions of CCCs with more flexible settings from the graph of extended Boolean functions. This generalizes earlier achievements on CCCs from recent literature. Another objective of this paper is to employ the graphs of extended Boolean functions and polynomial representation of sequences to construct SNC-CCCs.

Spectrally constrained sequences (SCSs) play an important role in modern communication and radar systems operating over non-contiguous spectrum. Despite numerous research attempts over the past years, very few works are known on the constructions of optimal SCSs with low cross-correlations. In this paper, we address such a major problem by introducing a unifying framework to construct unimodular SCS families using circular Florentine rectangles (CFRs) and interleaving techniques. By leveraging the uniform power allocation in the frequency domain for all the admissible carriers (a necessary condition for beating the existing periodic correlation lower bound of SCSs), we present a tighter correlation lower bound and show that it is achievable by our proposed SCS families including multiple SCS sets with zero correlation zone properties.

Massive machine type communication (mMTC) is one of the core components of 6G communication systems to fulfil the demand of massive connectivity of billions of Internet-of-Things (IoT) devices. Due to its various advantages, grant-free random access schemes are considered as a promising technique to implement mMTC. The key to grant-free random access is active device detection at the base station. In this paper, firstly we introduce the odd total squared correlation (OTSC) of binary signature sets, then derive a corresponding lower bound. Systematic constructions of optimal signature sets based on the known odd periodic complementary sets (OPCS), almost binary sequences, large Kasami subsets and ideal sequences are presented, which are all optimal with respect to the derived OTSC lower bound. Next, it is demonstrated that the optimal OTSC signature sets can be effectively used in massive device activity detection. Using efficient approximate message passing with minimum mean squared error (AMP-MMSE) algorithm, it is shown that the sensing matrices arising from OTSC-optimal signature sets and periodic total squared correlation (PTSC)-optimal signature sets performs better than the popular Gaussian random matrix.

Sequences play an important role in many engineering applications. Searching sequences with desired properties has long been an intriguing but also challenging research topic. This article proposes a novel method, called HpGAN, to search desired sequences algorithmically using generative adversarial networks (GANs). HpGAN is based on the idea of zero-sum game to train a generative model, which can generate sequences with characteristics similar to the training sequences. In HpGAN, we design the Hopfield network as an encoder to avoid the limitations of GAN in generating discrete data. Compared with traditional sequence construction by algebraic tools, HpGAN is particularly suitable for complex problems which are intractable by mathematical analysis. We demonstrate the search capabilities of HpGAN in two applications: 1) HpGAN successfully found many different mutually orthogonal complementary sequence sets (MOCSSs) and optimal odd-length binary Z-complementary pairs (OB-ZCPs) which are not part of the training set. In the literature, both MOCSSs and OB-ZCPs have found wide applications in wireless communications and 2) HpGAN found new sequences which achieve a four-times increase of signal-to-interference ratio-benchmarked against the well-known Legendre sequences-of a mismatched filter (MMF) estimator in pulse compression radar systems. These sequences outperform those found by AlphaSeq.

Sequences with low correlation sidelobes have found a wide range of applications in communication systems and RADAR. In this work, we have proposed a computational framework of aperiodic mismatched filtering sequence pairs using iterative twisted approximation (ITROX). A mismatched-filter is a filter where the transmitting sequence and receiving sequence are different (not matched). We have used singular value decomposition (SVD) instead of eigenvalue decomposition (EVD), which is more general, to obtain the resultant sequences. Numerical simulation shows that the resultant aperiodic mismatched filtering sequences have lower sidelobes without reducing too much loss-in-processing gain.

In radar sensing and communications, designing Doppler resilient sequences (DRSs) with low ambiguity function for delay over the entire signal duration and Doppler shift over the entire signal bandwidth is an extremely difficult task. However, in practice, the Doppler frequency range is normally much smaller than the bandwidth of the transmitted signal, and it is relatively easy to attain quasi-synchronization for delays far less than the entire signal duration. Motivated by this observation, we propose a new concept called low ambiguity zone (LAZ) which is a small area of the corresponding ambiguity function of interest defined by the certain Doppler frequency and delay. Such an LAZ will reduce to a zero ambiguity zone (ZAZ) if the maximum ambiguity values of interest are zero. In this paper, we derive a set of theoretical bounds on periodic LAZ/ZAZ of unimodular DRSs with and without spectral constraints, which include the existing bounds on periodic global ambiguity function as special cases. These bounds may be used as theoretical design guidelines to measure the optimality of sequences against Doppler effect. We then introduce four optimal constructions of DRSs with respect to the derived ambiguity lower bounds based on some algebraic tools such as characters over finite field and cyclic difference sets.

The affine combination of two complex-valued least-mean-squares filters (aff-CLMS) addresses the trade-off between fast convergence rate and small steady-state misadjustment error. However, a rigorous analysis of the aff-CLMS algorithm for second-order non-circular inputs is still under investigation. To this end, the focus in this letter is on the full mean-square analysis of the aff-CLMS algorithm, in which the transient analyses of the mixing parameter, as well as the standard and complementary weight-error covariance matrices, are completed. In addition, we derive the closed-form solutions of the steady-state weight-error power and its complementary version of the aff-CLMS. Finally, the effectiveness of the theoretical analysis is supported by computer simulations.

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.

In frequency hopping (FH) communication systems, frequency hopping sequences (FHSs) are crucial in determining the system’s anti-jamming performance. If FHSs can ensure a wide-gap between two adjacent frequency points to avoid the frequency points with high interference probability, it will significantly improve the FH communication system’s anti-interference ability. Moreover, if each frequency point appears at the same number of times in a sequence period, the system’s anti-electromagnetic interference will be enhanced. Therefore, it is desirable to employ FHSs with low Hamming autocorrelation, wide frequency-hopping gap, and good uniformity in practical applications. However, to the best of our knowledge, no such infinite classes of FHSs have been reported in the literature to date. This paper aims to present two constructions of uniform wide-gap frequency-hopping sequences (WGFHSs) by concatenating two or three adequately designed sequences. For the first time, we obtain two infinite classes of WGFHSs, which are optimal with respect to the well-known Lempel-Greenberger bound.

Due to their beautiful aperiodic correlation properties and low peak-to-average power ratio (PAPR), Golay complementary pairs (GCPs) and complementary sequence sets (CSSs) have been well studied. However, conventional GCPs and CSSs can only adapt to contiguous spectral resource allocation in wireless communication systems, and it is difficult for them to be compatible with non-contiguous resource allocation. Inspired by recent constructions of non-contiguous GCPs given by Şahin and Yang, we propose a new construction of non-contiguous GCPs, which can be regarded as an extension of Turyn’s construction. Besides, we then propose some constructions of non-contiguous CSSs, which can adapt to flexible resource allocation, having more flexible lengths, and lower time domain cross correlation than non-contiguous GCPs. Finally, we propose a CSS-based physical uplink control channels (PUCCH) scheme for up to 2 uplink control information (UCI) bits. Simulations show that its performance is similar to the GCP-based PUCCH scheme.

Since its inception in 2013, Golay complementary sequences with periodic zero autocorrelation zones (ZACZs) and cross-correlation zones (ZCCZs), or Golay-ZCZ (zero correlation zone) sequences have special importance in modern communication systems. Till date, all the proposed complementary sequences with periodic ZACZs and ZCCZs have lengths in the form$2^{m}$, where$m$is a natural number. In this paper, we extend such complementary sequences with large periodic ZACZs and ZCCZs to more flexible lengths in the form of non-power-of-two.

Recently, mutually orthogonal complementary sequence sets (MOCSSs) have been found many important applications in communication systems, radar, etc. Most of the known constructions of MOCSSs are based on generalized Boolean functions (GBFs) and hence mostly have lengths of power-of-two. A few constructions of MOCSSs are also based on paraunitary (PU) matrices and hence mostly have power-of-an-integer lengths. The objective of this paper is to develop a general framework to construct more MOCSSs consisting of sequences with non-power-of-two lengths. The proposed framework is based on complete complementary codes and even-shift complementary sequence sets.

Z-complementary code sets (ZCCSs), extended from complete complementary codes (CCCs), have ideal correlations within a zone around the in-phase position named zero correlation zone (ZCZ). In this article, two classes of aperiodic ZCCSs with good cross-correlation subsets are investigated. They are multiple CCCs with inter-set zero cross-correlation zone (ZCCZ) property and multiple aperiodic ZCCSs with ideal inter-set aperiodic cross-correlation property respectively, the latter is referred to as an aperiodic inter-group complementary (IGC) code set and each ZCCS is called a group. First of all, based on polyphase paraunitary (PU) matrices and special permutation matrices, a construction of multiple polyphase CCCs with an inter-set ZCCZ is proposed. The obtained multiple CCCs have potential applications in interference-free multi-cell environments to support a large number of users. In addition, a construction of aperiodic polyphase IGC code sets is presented from polyphase PU matrices. We remark that different groups of the derived IGC code sets yield different constituent sequence lengths, thus they could provide a variety of quality of service (QoS) in quasi-synchronous multi-cell multi-rate communication systems. To the best of our knowledge, the aforementioned constructions of ZCCSs with good cross-correlation subsets based on PU matrices have not been reported in the literature.

A pair of sequences is called a Z-complementary pair (ZCP) if it has zero aperiodic autocorrelation sums at each of the non-zero time-shifts within a certain region, called the zero correlation zone (ZCZ). ZCPs are categorised into two types: Type-I ZCPs and Type-II ZCPs. Type-I ZCPs have the ZCZ around the in-phase position and Type-II ZCPs have the ZCZ around the end-shift position. Till now only a few constructions of Type-II ZCPs are reported in the literature, and all have lengths of the form 2m±1 or N+1 where N=2a10b26cand a, b, c are non-negative integers. In this paper, we propose a recursive construction of ZCPs based on concatenation of sequences. Inspired by Turyn's construction of Golay complementary pairs, we also propose a construction of Type-II ZCPs from known ones. The proposed constructions can generate optimal Type-II ZCPs with new flexible parameters and Z-optimal Type-II ZCPs with any odd length. In addition, we give upper bounds for the PMEPR of the proposed ZCPs. It turns out that our constructions lead to ZCPs with low PMEPR.

In a prior paper (Ellingsenet al., 2020), two of us, along with P. Ellingsen, P. Felke, and A. Tkachenko, defined a new (output) multiplicative differential and the corresponding$c$-differential uniformity, which has the potential of extending differential cryptanalysis. Here, we continue the work by looking at some APN functions through the mentioned concept and showing that their$c$-differential uniformity increases significantly in some cases.

In this paper, we first study in detail the relationship between minimal linear codes and cutting blocking sets, recently introduced by Bonini and Borello, and then completely characterize minimal linear codes as cutting blocking sets. As a direct result, minimal projective codes of dimension 3 and t-fold blocking sets with t ≥ 2 in projective planes are identical objects. Some bounds on the parameters of minimal codes are derived from this characterization. Using this new link between minimal codes and blocking sets, we also present new general primary and secondary constructions of minimal linear codes. As a result, infinite families of minimal linear codes not satisfying the Aschikhmin-Barg's condition are obtained. In addition to this, open problems on the parameters and the weight distributions of some generated linear codes are presented.

One objective of this paper is to propose a novel class of sequence pairs, called “quasi-orthogonal Z-complementary pairs (QOZCPs)”, each depicting Z-complementary property for their aperiodic auto-correlation sums and also having a low correlation zone when their aperiodic cross-correlation is considered. Construction of QOZCPs based on Successively Distributed Algorithms under Majorization Minimization (SDAMM) is presented. Another objective of this paper is to apply the proposed QOZCPs in fully polarimetric radar systems and analyse the corresponding ambiguity functions. It turns out that QOZCP waveforms are much more Doppler resilient than the known Golay complementary waveforms.

Generalized spatial modulation (GSM), which is a novel multiple-input multiple-output (MIMO) transmission technique, has attracted massive research attention in recent years. In this paper, we first utilize the orthogonal least squares (OLS) based detector for GSM detection. Then, we develop a sufficient condition of successful detection for the OLS based detector based on the restricted isometry property (RIP) of the channel matrix. Moreover, we prove that our sufficient condition is optimal. Finally, numerical simulations are conducted to illustrate that the proposed OLS based detector has better detection performance than the orthogonal matching pursuit (OMP) based detector with more or less the same time complexity.

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 2α(α 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 2m-1+ 2v(m is natural number, 0 ≤ 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.

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 ZN, consisting of sequences of length N, where N ≥ 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.

Orthogonal Frequency Division Multiple Access (OFDMA) with Dynamic spectrum allocation (DSA) is able to provide a wide range of data rate requirements. This paper is focused on the design of preamble sequences in OFDMA systems with low peak-to-mean envelope power ratio (PMEPR) property in the context of DSA. We propose a systematic preamble sequence design which gives rise to low PMEPR for possibly non-contiguous spectrum allocations. With the aid of Golay-Davis-Jedwab (GDJ) sequences, two classes of preamble sequences are presented. We prove that their PMEPRs are upper bounded by 4 for any DSA over a chunk of four contiguous resource blocks.

Complementary set sequences (CSSs) are useful for dealing with the high peak-to-average power ratio (PAPR) problem in orthogonal frequency division multiplexing (OFDM) systems. In practical OFDM transmission, however, certain sub-carriers maybe reserved and/or prohibited to transmit signals, leading to the so-called spectral null constraint (SNC) design problem. For example, the DC sub-carrier is reserved to avoid the offsets in D/A and A/D converter in the LTE systems. While most of the current research focus on the design of low PAPR CSSs to improve the code-rate, few works address the aforementioned SNC in their designs. This motivates us to investigate CSSs with SNC as well as low PAPR property. In this article, we present systematic constructions of CSSs under SNCs and low PAPR. First, we show that mutually orthogonal complementary sets (MOCSs) can be used as seed sequences to generate new CSSs with SNC and low PAPR, and then provide an iterative technique for the construction of MOCSs which can be further used to generate complementary sets (CSs) with low PAPRs and spectral nulls at varying positions in the designed sequences. Next, inspired by a recent idea of Chen, we propose a novel construction of these seed MOCSs with non-power-of-two lengths from generalized Boolean functions.

In this paper, we consider pilot-aided channel estimation and equalization for single-carrier and single-carrier frequency division multiple-access (SC-FDMA) transmission over doubly-selective channels (DSC). To reduce the channel estimation (CE) parameters, the DSC is modelled using a complex-exponential basis expansion model (CX-BEM) with non-uniform BEM frequencies. We optimize the CX-BEM basis functions using CE error minimization as the objective. As a result, the channel modelling error is greatly reduced. Next, we propose a BEM-based per-survivor processing (PSP) technique and combine it with a decision-directed channel estimator to obtain a channel-tracking equalizer at the receiver. The resultant BEM-PSP receiver significantly improves the channel estimation mean square error (MSE) and the bit error rates (BER) performance in fast fading multi-path channel, thanks to the channel tracking capability embedded within its Viterbi equalizer. Finally, we employ cross-frame channel interpolation, and power distribution between the data and pilot symbols to further improve the system performance at high fading rates. Extensive simulation results show that our BEM-PSP receiver outperforms many existing methods and approaches close to an ideal receiver with perfectly known CSI under various fading scenarios.

This paper focuses on designing a set of dedicated sequences for Multi-Static Primary Surveillance Radar (MSPSR) systems. An efficient algorithm to generate a set of unimodular sequences with good local auto-ambiguity functions (AFs) and cross-AFs over specific Doppler bins and delay bins of interest is proposed. The performance of the proposed algorithm is evaluated in comparison with a prior art called the energy gradient method via numerical simulation. The numerical results show that the newly generated sequences possess lower maximum sidelobe in the area of interest.

A pair of sequences is called odd-length binary Z-complementary pair (OB-ZCP) if it is of odd-length and has zero aperiodic autocorrelation sums (AACSs) for all time-shifts within a certain region around the in-phase position, commonly known as zero correlation zone (ZCZ). There are two types of OB-ZCPs, namely Type-I OB-ZCPs and Type-II OB-ZCPs. Type-I OB-ZCPs have ZCZ around the in-phase position. Type-II OB-ZCPs have the ZCZ around the end-shift position. An OB-ZCP (Type-I or Type-II) of odd-length N is called Z-optimal if it achieves a maximum ZCZ width of (N + 1)/2. To date, a systematic construction of Type-II Z-optimal OB-ZCPs exist only for very limited lengths of the form 2m± 1, where m is a positive integer. It employs insertion method and delete method on binary Golay complementary pairs (GCPs) of length 2mderived from second order Reed-Muller codes. In this article, based on iterative insertion method, we construct Type-II Z-optimal OB-ZCPs of lengths 2m+ 3.

This paper is focused on the optimal design and performance analysis of a novel class of no-hit-zone frequencyhopping sequences (NHZ-FHSs) in quasi-synchronous FH multiple-access (QS-FHMA) systems. Although traditional NHZ-FHSs can offer interference-free FHMA performance when the signal arrival delay (τ) does not exceed the width of NHZ (Znh), i.e., |τ| ≤ Znh, the same performance cannot be guaranteed for |τ| > Znhin which traditional NHZ-FHZs may have large Hamming correlation (which denotes the total number of frequency hits of sequences) and consequently poor error probability performance. Since the strict quasi-synchronization (i.e., |τ| ≤ Znh) may be hard to maintain at all times in practical FHMA networks (e.g., infrastructureless ad hoc networks), it is also important to minimize the Hamming correlation for time-shifts outside of the NHZ. Such FHSs are called strong NHZ-FHSs (SNHZ-FHSs) in this paper. We derive a lower bound on the maximum Hamming correlation outside of the NHZ and then present a design algorithm for the optimal SNHZ-FHS set meeting our proposed lower bound with equality. We analyze the bit-error-rate (BER) performance of the FHMA system employing the proposed SNHZ-FHS sets using the average Hamming correlation function. The theoretical analysis and simulation results show that the proposed optimal SNHZ-FHS sets are feasible for practical FHMA networks with relaxed timing requirement and enhanced BER performance.

Functions with low differential uniformity have important applications in cryptography, coding theory, and sequence design. The differential spectrum of a cryptographic function is of great interest for estimating its resistance to some variants of differential cryptanalysis. Finding power permutations (i.e., monomial bijective mappings) over finite fields with low differential uniformity and determining their differential spectra have received a lot of attention over the past two decades. The objective of this paper is to study the differential properties of the well-known Kasami power permutations x p2k-pk+1 over GF(pn), where p is an odd prime and k is an integer with gcd(n, k) = 1. It turns out that this family of monomials is differentially (p + 1)-uniform. Our result in the case of p = 3 gives an affirmative solution to a recent conjecture by Xu, Cao, and Xu. Most notably, the differential spectrum of this family of power permutations is completely determined.

Linear codes with certain special properties have received renewed attention in recent years due to their practical applications. Among them, binary linear complementary dual (LCD) codes play an important role in implementations against side-channel attacks and fault injection attacks. Self-orthogonal codes can be used to construct quantum codes. In this paper, four classes of binary linear codes are constructed via a generic construction which has been intensively investigated in the past decade. Simple characterizations of these linear codes to be LCD or self-orthogonal are presented. Resultantly, infinite families of binary LCD codes and self-orthogonal codes are obtained. Infinite families of binary LCD codes from the duals of these four classes of linear codes are produced. Many LCD codes and self-orthogonal codes obtained in this paper are optimal or almost optimal in the sense that they meet certain bounds on general linear codes. In addition, the weight distributions of two sub-families of the proposed linear codes are established in terms of Krawtchouk polynomials.

In addition to their applications in data communication and storage, linear codes also have nice applications in combinatorics and cryptography. Minimal linear codes, a special type of linear codes, are preferred in secret sharing. In this paper, a necessary and sufficient condition for a binary linear code to be minimal is derived. This condition enables us to obtain three infinite families of minimal binary linear codes with Wmin/Wmax≤ 1/2 from a generic construction, where Wminand Wmax, respectively, denote the minimum and maximum nonzero weights in a code. The weight distributions of all these minimal binary linear codes are also determined.

Sequences with low correlation have important applications in communications, radar, and cryptography. In this paper, a simple construction of polyphase sequences using additive and multiplicative characters over the finite field Fqis proposed. The construction works for any finite field Fqwith q > 2 and generates a family of q - 1 sequences with period q - 1 and maximum correlation √q. This family is asymptotically optimal with respect to the well-known Welch bound. Most notably, the maximum autocorrelation magnitude of each sequence in this family is equal to 1, and every two distinct sequences are orthogonal to each other. The distribution of the correlation magnitudes of this family is also established.

Zero correlation zone (ZCZ) sequences are a class of spreading sequences having ideal auto-correlation and cross correlation in a zone around the origin. They have been extensively studied in recent years due to their important applications in quasi-synchronous code division multiple access systems. In this paper, a construction of ZCZ sequence sets is proposed based on perfect nonlinear functions. It generates multiple ZCZ sequence sets with the properties: 1) each sequence is perfect in the sense that its out-of-phase auto-correlation is always zero; 2) each ZCZ sequence set is optimal with respect to the Tang-Fan-Matsufuji bound in which all the sequences are pairwise cyclically distinct; and 3) the maximum inter-set cross correlation of multiple sequence sets achieves the well-known Sarwate bound.

As an optimal combinatorial object, zero-difference balanced (ZDB) functions introduced by Ding in 2008, are a generalization of the well-known perfect nonlinear functions. ZDB functions have received much attention in recent years due to its important applications in coding theory and sequence design. One objective of this paper is to present a construction of ZDB functions based on a kind of generalized cyclotomy. It generates ZDB functions over cyclic group with new parameters which can not be produced by earlier constructions. Another objective of this paper is to employ these ZDB functions to obtain at the same time: 1) optimal constant-composition codes; 2) perfect difference systems of sets; and 3) optimal frequency-hopping sequences, all with new parameters.

In 2013, Tang, Carlet, and Tang [IEEE TIT 59(1): 653-664, 2013] presented two classes of Boolean functions. The functions in the first class are unbalanced and the functions in the second one are balanced. Both of those two classes of functions have high nonlinearity, high algebraic degree, optimal algebraic immunity, and high fast algebraic immunity. However, they are not 1-resilient which represents a drawback for their use as filter functions in stream ciphers. In this paper, we first propose a large family of 1-resilient Boolean functions having high lower bound on nonlinearity, optimal algebraic immunity, and optimal algebraic degree, that is, meeting the Siegenthaler bound. Most notably, we can mathematically prove that every function in n variables belonging to this family has fast algebraic immunity no less than n - 6, which is the first time that an infinite family of 1-resilient functions with provably high fast algebraic immunity has been invented. Furthermore, we exhibit a subclass of the family which has higher lower bound on nonlinearity than all the known 1-resilient functions with (potentially) optimal algebraic immunity and potentially high fast algebraic immunity.

As a class of optimal combinatorial objects, bent functions have important applications in cryptography, sequence design, and coding theory. Bent idempotents are a subclass of bent functions and of great interest, since they can be stored in less space and allow faster computation of the Walsh-Hadamard transform. The objective of this paper is to present a generic construction of bent functions from known ones. It includes the previous constructions of bent functions by Mesnager and Xu et al. as special cases, and produces new bent functions, which cannot be produced by earlier ones. In particular, it also generates infinite families of bent idempotents over F22mof any algebraic degree between 2 and m. This together with a recent construction by Su and Tang gives a positive answer to an open problem on bent idempotents proposed by Carlet. In addition, an infinite family of anti-self-dual bent functions is obtained in which the sum of any three distinct functions is again an anti-self-dual bent function in this family. This solves an open problem recently proposed by Mesnager.

Constant composition codes (CCCs) are a special class of constant-weight codes. They include permutation codes as a subclass. The construction of CCCs with parameters achieving certain bounds has been an interesting research topic in coding theory. Recently, Ding established a bridge from zero difference balanced (ZDB) functions to CCCs with parameters meeting the Luo-Fu-Vinck-Chen bound. This provides a new approach for obtaining optimal CCCs. One objective of this paper is to present two new classes of ZDB functions whose parameters have been not covered in the literature. Another objective of this paper is to introduce two classes of CCCs meeting the Luo-Fu-Vinck-Chen bound from these new ZDB functions.

Support recovery of sparse signals from noisy measurements with orthogonal matching pursuit (OMP) has been extensively studied in the literature. In this paper, we show that for any K-sparse signal x, if the sensing matrix A satisfies the restricted isometry property (RIP) of order K+1 with restricted isometry constant (RIC) δK+1K+1since for any given positive integer K ≥ 2 and any 1/√K+1 ≤ tK+1= t for which OMP may fail to recover the signal x in K iterations. Moreover, the constraint on the minimum magnitude of the nonzero elements of x is weaker than existing results.

Codebooks with small inner-product correlation are preferred in many practical applications such as direct spread code division multiple access communications, coding theory, and compressed sensing. The well-known Welch bound and Levenstein bound are useful benchmarks for the correlation of codebooks. In general, it is very hard to obtain codebooks achieving the Welch bound or the Levenstein bound. The objective of this letter is to present a construction of codebooks based on additive and multiplicative characters of finite fields. It generates codebooks nearly achieving the Levenstein bound.

Frequency-hopping sequences (FHSs) with favorable partial Hamming correlation properties are desirable in many synchronization and multiple-access systems. An FHS set is said to be strictly optimal if it has optimal partial Hamming correlation for any correlation window. In this paper, we derive upper bounds on the family sizes of FHS sets with respect to partial Hamming correlation from some classical bounds on error-correcting codes. We then present strictly optimal FHS sets having optimal family sizes with respect to one of the new bounds. In particular, our construction gives new parameters not covered in the literature.

Linear codes with a few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of constructing two-weight and three-weight linear codes of Ding et al. and Zhou et al. to general weakly regular bent functions and determines the weight distributions of these linear codes. It solves an open problem proposed by Ding et al. Furthermore, this paper constructs new linear codes with two or three weights and presents their weight distributions. They contain some optimal codes meeting certain bound on linear codes.

Sequences with good odd periodic autocorrelation property are of importance in applications. In this paper, we presented a lower bound of the magnitude of the odd periodic autocorrelation of binary sequences, and by using Parker's transformation, constructed new binary sequences with odd periodic autocorrelation magnitude achieving the lower bound.

In this paper, we give a lower bound on odd periodic total squared correlation (OPTSC for short) of binary signature sets, which indicates that odd periodic complementary sets and PTSC-optimal signature sets of odd period can be used to design optimal OPTSC signature sets which achieve the new lower bound. Besides, we give three kinds of PTSC-optimal signature sets from ideal sequences and large Kasami subsets.

Without limitation on the number of mates, Z-periodic complementary sequence (ZPCS) sets, which have potential applications in multi-carriers CDMA communication systems and MIMO channel estimation, can support more users than conventional complementary sequence sets. In this paper, a generic construction of ZPCS sets is proposed based on perfect sequences and orthogonal matrices. It generalizes the earlier constructions by Li et al., and produces new ZPCS sets which cannot generated by earlier ones. The parameters of our ZPCS sets are flexible and are thus suitable for different application scenarios.

Cyclic codes are an interesting class of linear codes due to their efficient encoding and decoding algorithms. Bose-Ray-Chaudhuri-Hocquenghem (BCH) codes form a subclass of cyclic codes and are very important in both theory and practice as they have good error-correcting capability and are widely used in communication systems, storage devices, and consumer electronics. However, the dimension and minimum distance of BCH codes are not known in general. The objective of this paper is to determine the Bose and minimum distances of a class of narrow-sense primitive BCH codes.

Frequency-hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. In this paper, lower bounds on the partial Hamming correlation of FHSs and FHS sets are proposed. They slightly improve the known bounds by Eun et al. and Zhou et al. A construction of FHSs and FHS sets having optimal partial Hamming correlation with respect to the improved bounds is also presented based on the theory of generalized cyclotomy. Our construction yields optimal FHSs and FHS sets with new and flexible parameters not covered in this paper.

In this paper, a construction of codebooks based on a set of bent functions satisfying certain conditions is introduced. It includes some earlier constructions of codebooks meeting the Levenstein bound as special cases. With this construction, two new families of codebooks achieving the Levenstein bound are obtained. The codebooks constructed in this paper could have a very small alphabet size.

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms, compared with linear block codes. In this paper, seven classes of three-weight cyclic codes over \gf(p) whose duals have two zeros are presented, where p is an odd prime. The weight distributions of the seven classes of cyclic codes are settled. Some of the cyclic codes are optimal in the sense that they meet certain bounds on linear codes. The application of these cyclic codes in secret sharing is also considered.

As a subclass of linear codes, cyclic codes have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, five families of three-weight ternary cyclic codes whose duals have two zeros are presented. The weight distributions of the five families of cyclic codes are settled. The duals of two families of the cyclic codes are optimal.

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, a family of p-ary cyclic codes whose duals have three pairwise nonconjugate zeros is proposed. The weight distribution of this family of cyclic codes is determined. It turns out that the proposed cyclic codes have five nonzero weights.

Cyclic codes are a subclass of linear codes and have wide applications in consumer electronics, data storage systems, and communication systems due to their efficient encoding and decoding algorithms. Cyclic codes with many zeros and their dual codes have been a subject of study for many years. However, their weight distributions are known only for a very small number of cases. In general, the calculation of the weight distribution of cyclic codes is heavily based on the evaluation of some exponential sums over finite fields. Very recently, Li studied a class of p-ary cyclic codes of length p2m-1, where p is a prime and m is odd. They determined the weight distribution of this class of cyclic codes by establishing a connection between the involved exponential sums with the spectrum of Hermitian forms graphs. In this paper, this class of p-ary cyclic codes is generalized and the weight distribution of the generalized cyclic codes is settled for both even m and odd m along with the idea of Li The weight distributions of two related families of cyclic codes are also determined.

A Gaussian integer is a complex number whose real and imaginary parts are both integers. A Gaussian integer sequence is called perfect (odd perfect) if the out-of-phase values of the periodic (odd periodic) autocorrelation function are equal to zero. In this letter, for any odd prime p, using the cyclotomic classes of order 2 and 4 with respect to GF(p), we propose perfect and odd perfect Gaussian integer sequences of length p. Several examples are also given.

In this paper, the partial Hamming correlation properties of frequency-hopping sequences (FHSs) are discussed. The Peng-Fan bounds on sets of FHSs are generalized to the case of partial correlation. Both individual FHSs with optimal partial autocorrelation and sets of FHSs with optimal partial correlation are presented. The former has more new parameters compared with the known individual FHSs with optimal partial autocorrelation, while the later is obtained in the literature for the first time.

Zero-difference balanced (ZDB) functions were introduced recently by Ding for the construction of optimal constant-composition codes, and optimal and perfect difference systems of sets. They are closely related to partitioned difference families. In this paper, we present generic constructions of ZDB functions from functions with difference-balanced property. In particular, two classes of ZDB functions with new and flexible parameters are reported. Employing these new ZDB functions, we obtain at the same time optimal (1) constant-composition codes, (2) constant-weight codes, and (3) perfect difference systems of sets, all with new and flexible parameters.

In this paper, an upper bound for a hybrid incomplete exponential sum over finite fields is derived. This bound is then used to obtain lower and upper bounds for aperiodic Hamming correlation of frequency-hopping sequences based on power functions.

In this paper, two generic constructions of optimal frequency-hopping sequence (FHS) sets employingd-form functions with difference-balanced property are presented. They generalize the previous constructions of optimal FHS sets usingm-sequences and produce new optimal FHS sets that cannot be produced by the earlier constructions. By choosing appropriated-form functions with difference-balanced property, both constructions lead to FHSs with large linear complexity. In addition, one of the proposed constructions gives new optimal parameters of FHS sets.

In this letter, based on a pair of mismatched binary sequences with perfect cross-correlation function (PCCF), a new method for constructing zero correlation zone (ZCZ) sequences sets with mismatched filtering is presented. The resultant optimal sets of quadriphase ZCZ sequence have flexible parameters and high efficiency. Compared with the one proposed by Trinh, our method gives cyclically distinct transmitted sequences and corresponding mismatched sequences at the receiver.

By interleaving one length-N perfect sequence or ideal sequence according to elaborate phases, a new method of construction of zero correlation zone (ZCZ) and low correlation zone (LCZ) sequence sets is presented. The resultant sequence sets are optimal or almost optimal with respect to Tang, Fan, and Matsufuji bound. Furthermore, the new method provides flexible choice for the ZCZ and LCZ lengths.

The algorithm of shadowmap and its basic principle are studied in this paper. The cause of self-shadow and aliasing are also explained in a mathematical way. The paper presents a multi-sampling algorithm to smooth shadow, and reduce aliasing by increasing precision of depth information and making use of z-bias. The algorithm is implemented by DirectX3D. Experimental results show the feasibility of the algorithm.

The paper proposes a real-time terrain tiling method for extra-large scale terrain rendering. The core idea is based on a loading-on-demand technique which dynamically loads visible parts of the terrain model, then tiling and rendering. The method solves the boundary match problem for adjacent terrain blocks in dynamic loading which avoids "cracks" and rebuilds the whole terrain identically and seamlessly. Using this method, real-time walkthrough of 144 km2terrain data is implemented on platform of PIV 2.4 GHz, 512 MB, ATI 9550. Experimental results show that the efficiency of algorithm is high on both time and memory and the method supports real-time visualization of extra-large scale terrain. It is also a functional module in our newly-designed game engine.