In the literature, it has been shown that the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel with noise-free feedback equals the capacity of the same model without secrecy constraint, and the classical Schalkwijk-Kailath (SK) scheme achieves the secrecy capacity. In this paper, we show that in finite blocklength regime, the SK scheme is not optimal, and propose a modified SK scheme which may perform better than the classical one. Besides this, this paper establishes a finite blocklength converse for the AWGN wiretap channel with feedback, which can also be viewed as a converse for the same model without secrecy constraint. To the best of the authors' knowledge, this is the first paper to address such a problem, and the results of this paper are further explained via numerical examples.

Secure aggregation is a vital component for mitigating gradient leakage in federated learning, but its communication cost conventionally scales with the gradient dimension. This becomes prohibitive for large models and even more pronounced in decentralized federated learning with limited bandwidth and unreliable nodes. Top-K gradient sparsification is an effective approach to reduce communication by transmitting only a few entries of the full gradient, while maintaining competitive model accuracy. Nevertheless, the top-K entries selected by each user are unpredictable and vary across users, which poses a challenge for efficient sparse secure aggregation. This paper studies information-theoretic secure aggregation with top-K sparsification in decentralized federated learning under user dropouts and user collusion. We propose a communication-efficient sparse secure aggregation scheme that offloads dimension-dependent overhead to an offline phase and protects private gradients using random masks and permutations. Experimental results demonstrate that our scheme preserves accuracy comparable to full-gradient aggregation even with only 1% gradient sparsification, while substantially reducing the communication cost.

This paper proposes a secure active reconfigurable intelligent surfaces (RIS)-assisted multiple input multiple output integrated sensing, communication, and computation over-theair system. Distributed sensors simultaneously sense targets and transmit private data to an access point (AP) via over-the-air computation, while a passive eavesdropper attempts to intercept. We formulate a joint optimization problem to minimize the AP’s computational mean-squared error (MSE) under constraints on the eavesdropper’s computational MSE, sensing accuracy, and transmit power through the jointly design of transmit beam-forming, aggregation beamforming, and active RIS reflection coefficients. Under perfect wiretap channel state information (CSI), the formulated non-convex problem is decomposed and solved via a penalty-based alternating optimization algorithm, using closed-form aggregation beamformer and successive convex approximation. The framework is extended to imperfect wiretap CSI with norm-bounded uncertainty. By deriving a conservative lower bound on the eavesdropper’s distortion and applying the Generalized S-Procedure, a robust alternating optimization algorithm is developed to solve the reformulated problem. Simulations validate the superiority of the proposed scheme over benchmarks with passive or randomly configured active RIS. Key system parameters, including sensor count, security and sensing accuracy thresholds, are analyzed to provide practical insights.

Privacy-preserving $k$-nearest neighbors (KNN) classification has attracted significant attention in recent years. However, existing schemes often face challenges such as high computational cost and excessive communication rounds, which limit their practical applicability. In this paper, we propose a constant-round privacy-preserving KNN classification scheme based on function secret sharing (FSS) with two non-colluding servers. To enhance data privacy and computation efficiency in secure KNN classification, we design several lightweight secure two-party computation (2PC) protocols, including Euclidean distance computation, integer comparisons, and frequency computation. To further reduce communication rounds, we introduce a batch comparison algorithm that efficiently sorts a set to extract the $k$-minimum values and the maximum value. Compared to the best-known schemes that require $\mathcal{O}(n + k \log n)$ or $\mathcal{O}(kn)$ communication rounds, where $n$ represents the dataset size, our approach achieves only 10 communication rounds. Security analysis confirms that the proposed scheme effectively preserves data privacy. Performance evaluations demonstrate that our scheme is competitive with existing works in terms of accuracy, computation cost, and communication efficiency.

This paper explores the security issues of a rate-splitting multiple access (RSMA)-aided integrated sensing and communication (ISAC) system. A dual-function base station communicates with multiple users via rate-splitting technology and simultaneously senses multiple targets, which also act as colluding malicious eavesdroppers. For the case where coarse target locations are known but subject to estimation errors, we construct an equivalent wiretap channel model incorporating channel uncertainty under the collusion scenario. Based on this model, the transmit covariance matrix is optimized for the sensing-only task, representing an ideal sensing-oriented transmitter design. However, in ISAC systems, the practical transmit covariance also needs to account for communication performance. In order to improve the sensing performance while ensuring communication security, we formulate an optimization problem that jointly optimizes transmit beamforming and rate-splitting to minimize covariance mismatch, subject to secrecy rate and transmit power constraints. This non-convex problem is transformed using convex relaxation techniques and solved via a robust block coordinate descent algorithm. We further consider the case where the locations of malicious sensing targets are unknown, and then formulate an optimization problem to minimize communication power while enhancing sensing capability via an omnidirectional beam, subject to rate constraints. We then develop an efficient block-wise algorithm based on convex reformulation. Simulation results confirm the efficacy of the proposed RSMA scheme in addressing system uncertainties, as well as reveal influences of various key parameters.

Jamming in some cases observed at its transmitting side could be modeled as a constant amplitude but random phase signal:J(t)= AJ · ejϕ(t). Such situation may happen in single-tone or multi-tone jammed frequency hopping systems, in cellular mobile systems under co-channel interference, etc. In order to appropriately handle this kind of jamming through channel coding technologies, a jamming model based log-likelihood ratio (LLR) initialization method is proposed to replace their conventional AWGN model based LLR initialization method. Accordingly, the optimal LLR initialization formula is derived based on the analysis of the probability density function of jammed signals. Then, the approximation of optimal LLR initialization as well as its robust variant are further provided, hence the complexity is significantly reduced and only the signal-to-noise ratio (SNR) and signal-to-jamming ratio (SJR) are required as thea prioriknowledge. The proposed LLR initialization method is tested in a Polar Code (PC) coded Orthogonal Frequency Division Multi-plexing (OFDM) system, where both the AWGN and the Rayleigh fading channel models are considered. The obtained simulation results demonstrate that the proposed method outperforms the conventional Gaussian model based one and other existed robust initialization methods.

Federated Learning (FL) allows collaborative model training across distributed clients without sharing raw data, thus preserving privacy. However, the system remains vulnerable to privacy leakage from gradient updates and Byzantine attacks from malicious clients. Existing solutions face a critical trade-off among privacy preservation, Byzantine robustness, and computational efficiency. We propose a novel scheme that effectively balances these competing objectives by integrating homomorphic encryption with dimension compression based on the Johnson-Lindenstrauss transformation. Our approach employs a dual-server architecture that enables secure Byzantine defense in the ciphertext domain while dramatically reducing computational overhead through gradient compression. The dimension compression technique preserves the geometric relationships necessary for Byzantine defence while reducing computation complexity fromO(dn)toO(kn)cryptographic operations, wherekd. Extensive experiments across diverse datasets demonstrate that our approach maintains model accuracy comparable to non-private FL while effectively defending against Byzantine clients comprising up to 40% of the network. Our approach also demonstrates substantial improvements in computational and communication efficiency. Experimental evaluation shows that the dimension compression technique achieves 25× ~ 35× reduction in computational overhead and 17× reduction in communication overhead compared to our non-compression version. When compared to state-of-the-art methods like ShieldFL [1], our approach demonstrates order-of-magnitude improvements in both computational and communication efficiency while maintaining equivalent privacy guarantees and achieving superior Byzantine robustness comparable to FLTrust [2]. These substantial efficiency enhancements make secure FL practical for deployment in large-scale neural networks with millions of parameters.

In this paper, we consider convertible codes with the locally repairable property. We present an improved lower bound on access cost associated with (r, δ ⩾ 2)-locality, which extends the known lower bound only related tor.We then provide a general construction of convertible codes with optimal access cost which shows that these codes can have super-linear length or maximally recoverable property. Furthermore, we propose explicit constructions of convertible codes with the final code achieving super-linear length or maximally recoverable property when the initial codes have super-linear length or maximally recoverable property respectively. Specifically, compared with known constructions, our construction is applicable to the case δ > 2 for the first time.

Let Z4denote the ring of integers modulo 4. The Galois ring GR(4,m), which consists of 4melements, represents the Galois extension of degreemover Z4. The constructions of codes over Z4have garnered significant interest in recent years. In this paper, building upon previous research, we utilize the defining-set approach to construct several classes of linear codes over Z4by effectively using the properties of the trace function from GR(4,m) to Z4. As a result, we have been able to obtain new infinite families of linear codes over Z4and completely determine their Lee weight distributions.

In this paper, we address the multi-node recovery problem for Reed-Solomon (RS) codes. To overcome the obstacle that most existing cooperative schemes can only deal with scenarios involving fewer than three failures, we consider a new repair model, referred to as the individual repair mode, in which each failed node can be repaired individually. Building upon this model, we propose a repair scheme for$[n, k]$Reed-Solomon codes that is applicable to any$0

Unmanned aerial vehicles (UAVs), with the advantage in on-demand and cost-effective deployment, have emerged as an aerial communication platform for supporting constant high-data rate transmission services for terrestrial stations with different mobility patterns. To this end, developing high-accuracy localization functionality is of crucial importance in tracking the target users. However, the limited payload size of a single UAV restricts precise direction-of-arrival (DOA) estimation, and the UAV-swarm based collaborative estimation architectures have become a promising remedy. In this paper, the UAV swarm is utilized to form a nested array (NA) architecture to improve the DOA estimation accuracy. A two-stage alternating iterative approach is proposed to jointly estimate the UAV position errors and DOAs through iterative feedback. Specifically, position error estimation is performed using the gradient descent method, whereas DOA estimation is achieved through a novel NA-Bessel atomic transformation and norm minimization (NA-BATNM) framework, built upon an off-grid atomic norm minimization algorithm. Simulation results demonstrate that the proposed method achieves high-precision estimation of both DOAs and UAV position errors. Furthermore, the proposed NA-BATNM method exhibits superior performance compared to grid-based DOA estimation algorithms.

By dividing Variable Nodes (VNs) into groups and processing groups sequentially, the Shuffled Min-Sum (SMS) decoding of Low-Density Parity-Check (LDPC) codes achieves a good trade-off between hardware resource and throughput. However, under the grouping strategy where at least one Check Node (CN) has multiple VN neighbors in one group, the CN update of State-Of-The-Art (SOTA) SMS decoding has long latency and high complexity. To address the issue, this paper presents two efficient CN update schemes. The first one uses the first two minimum Variable-to-Check (V2C) message magnitudes in each group and a size-λ Monotone Double-ended Queue (λMDQ), leading to an Improved λMDQ (I-λMDQ) scheme. The second one called the Modified λMDQ (M-λMDQ) scheme uses only the minimum in each group. As a result, our schemes reduce the number of Selection Modules (SMs) required by the CN update to only one. Simulation results show that both of our schemes have comparable error-correction performance to the SOTA schemes. Furthermore, we simplify the SM via a decomposition design and also present the detailed hardware architectures for our schemes. Analysis using the 90nm CMOS technology library shows that, compared to the SOTA schemes, our I-λMDQ scheme reduces the area and latency by up to 75% and 72%, respectively, while improving the throughput by up to 254%. Similarly, our M-λMDQ scheme reduces the area and latency by up to 79% and 70%, respectively, and improves the throughput by up to 229%.

GC-content and homopolymers are two constraints widely considered in DNA storage. Extensive experiments show that DNA strings with too high/low GC-content and/or long homopolymers are more likely to suffer from errors. We say a length-n DNA string satisfies the$(\epsilon ,\ell)$-constraints if no homopolymer exceeds$\ell $and its GC-content falls between$(0.5-\epsilon)n$and$(0.5+\epsilon)n$, where$\epsilon $is a positive real number and$\ell $is a positive integer; say it satisfies the$(\delta ,\ell)$-prefix-constraints if no homopolymer exceeds$\ell $and the GC-content of its length-i prefix falls between$i/2-\delta $and$i/2+\delta $for any$i \in \{1, 2, \ldots , n\}$, where$\delta $is a positive integer. In this paper, we realize the first enumerative coding for the capacity-achieving$(\epsilon ,\ell)$-constrained codes and$(\delta ,\ell)$-prefix-constrained codes with polynomial encoding/decoding complexity. Meanwhile, we propose an efficient pseudo-random construction of capacity-approaching$(\epsilon ,\ell)$-constrained codes and$(\epsilon ,\ell)$-constrained error correction codes. We further generalize the idea and establish a systematic framework of pseudo-random construction for a wide range of codes.

Maximum distance separable (MDS) codes in distributed storage systems provide the optimal tradeoff between fault tolerance and storage overhead. As a kind of MDS codes, minimum storage regenerating (MSR) codes have attracted a lot of attention since they are also optimal in terms of repair bandwidth. However, MSR codes suffer from a high repair degree, meaning many helper nodes are needed in the node repair process. Compared to MSR codes, locally repairable codes (LRCs) can significantly reduce the repair degree at the cost of increased storage overhead. The recently introduced concept of vector LRCs combines the advantages of MSR codes and LRCs, providing a tradeoff between repair degree/repair bandwidth and storage overhead. Most existing vector LRCs are built on MSR codes or their shortened versions. However, existing MSR codes have an unavoidably large sub-packetization levels, which also result in large sub-packetization levels in the corresponding vector LRCs. In this paper, we propose a new vector LRC structure, where MDS array codes (without shortening) can be employed as the local codes. Based this new structure, we propose three constructions of vector LRCs with small sub-packetization levels and small repair bandwidth, whose required field sizes are comparable to the code lengths. Additionally, the first two constructions offer a flexible tradeoff between the sub-packetization level and the repair bandwidth, while the third construction has a sub-packetization level of 2, making it easy to implement. Compared to existing vector LRCs, the new vector LRCs provide significantly smaller sub-packetization levels and support a wider range of parameters.

In this paper, the repair problem for erasures beyond locality in locally repairable codes is explored under a practical system setting, where a rack-aware storage system consists of racks, each containing a few parity checks. This is referred to as a rack-aware system with locality. Two repair schemes are devised to reduce the repair bandwidth for Tamo-Barg codes under the rack-aware model by setting each repair set as a rack. Additionally, a cut-set bound for locally repairable codes under the rack-aware model with locality is introduced. Using this bound, the second repair scheme is proven to be optimal. Furthermore, the partial-repair problem is considered for locally repairable codes under the rack-aware model with locality, and both repair schemes and bounds are introduced for this scenario.n this paper, the repair problem for erasures beyond locality in locally repairable codes is explored under a practical system setting, where a rack-aware storage system consists of racks, each containing a few parity checks. This is referred to as a rack-aware system with locality. Two repair schemes are devised to reduce the repair bandwidth for Tamo-Barg codes under the rack-aware model by setting each repair set as a rack. Additionally, a cut-set bound for locally repairable codes under the rack-aware model with locality is introduced. Using this bound, the second repair scheme is proven to be optimal. Furthermore, the partial-repair problem is considered for locally repairable codes under the rack-aware model with locality, and both repair schemes and bounds are introduced for this scenario.

Twisted generalized Reed-Solomon (TGRS) codes are an extension of generalized Reed-Solomon (GRS) codes, and have recently attracted significant attention due to their potential for constructing non-GRS MDS codes. This paper presents an in-depth and comprehensive investigation of TGRS codes in their most general form, allowing arbitrary twists at arbitrary positions. First, we introduce a more precise definition of TGRS codes, namely (L,P)-TGRS codes, and provide a concise necessary and sufficient condition for them to be MDS, thereby generalizing previous results. Second, we explicitly characterize the parity check matrices of (L,P)-TGRS codes, and provide a sufficient condition for them to be self-dual. Finally, we investigate the non-GRS properties of (L,P)-TGRS codes via two approaches: the dimensions of Schur squares and combinatorial techniques. As a result, we obtain an infinite family of non-GRS MDS codes.

We consider the problem of symmetric private linear computation (SPLC) over a replicated storage system with colluding and straggler constraints. The SPLC problem allows the user to privately compute a linear combination of multiple files from a set of replicated servers, even in the presence of straggler servers that can bottleneck the entire computation. It is guaranteed that a certain number of colluding servers learn nothing about the coefficients of the linear combination, and the user must not learn any information about the files other than the desired linear computation. Unlike previous private computation literature that mainly focused on decreasing download cost from servers, we aim to establish a flexible tradeoff between communication costs and computational complexities. In particular, we propose a novel SPLC scheme under the assumption of a fixed number of stragglers. Additionally, by generalizing this SPLC scheme, we construct an adaptive SPLC scheme capable of tolerating the presence of a varying number of stragglers, even if their identities and numbers are unknown in advance. Compared to the SPLC scheme with a fixed number of stragglers, the adaptive SPLC scheme achieves a lower communication cost based on the actual number of stragglers, albeit at the cost of increased computational complexities. Both types of SPLC schemes achieve flexible performance tradeoffs and can be employed to optimize system efficiency in practice.

The problem ofT-colluding private information retrieval (PIR) enables the user to retrieve one out ofMfiles from a distributed storage system withNservers without revealing anything about the index of the desired file to any group of up toTcolluding servers. In the considered storage system, theMfiles are stored across theNdistributed servers in anX-secureK-coded manner such that any group of up toXcolluding servers learns nothing about the files; the storage overhead at each server is reduced by a factor of 1/Kcompared to the total size of the files; and the files can be reconstructed from anyK+Xservers. However, in practical scenarios, when the user retrieves the desired file from the distributed system, some servers may respond to the user very slowly or not respond at all. These servers are referred to asstragglers, and particularly their identities and numbers are unknown in advance and may change over time. This paper considers the adaptive PIR problem that can be capable of tolerating the presence of a varying number of stragglers. We propose a general coding method for designing adaptive PIR schemes by introducing the concept of afeasible PIR coding framework. We demonstrate that anyfeasible PIR coding frameworkover a finite field Fqwith sizeqcan be used to construct an adaptive PIR scheme that achieves a retrieval rate of 1 −K+X+T−1/N−Ssimultaneously for all numbers of stragglers 0 ≤S≤N−(K+X+T) over the same finite field. Additionally, we provide an implementation of thefeasible PIR coding framework, ensuring that the adaptive PIR scheme operates over any finite field Fqwith sizeq≥N+max{K,N−(K+X+T−1)}.

We study the problem of repairing erasures in locally repairable codes beyond the code locality under the rack-aware model. We devise two repair schemes to reduce the repair bandwidth for Tamo-Barg codes under the rack-aware model, by setting each repair set as a rack. The first repair scheme provides optimal repair bandwidth for one rack erasure. We then establish a cut-set bound for locally repairable codes under the rack-aware model. Using this bound we show that our second repair scheme is optimal. Furthermore, we consider the partial-repair problem for locally repairable codes under the rack-aware model, and introduce both repair schemes and bounds for this scenario.

In this paper, we discuss codes for distributed storage systems with hierarchical repair properties. Specifically, we devote attention to the repair problem of the rack-aware storage model with locality, aiming to enhance the system's ability to repair a small number of erasures within each rack by locality and efficiently handling a rack erasure with a small repair bandwidth. By employing the regenerating coding technique, we construct a family of array codes with$(r,\ u-r+1)$-locality, where the$u$nodes of each repair set are systematically organized into a rack. When the number of failures is less than$u-r+1$, these failures can be repaired without counting the system bandwidth. In cases where the number of failures exceeds the locality, the failed nodes within a single rack can be recovered with optimal cross-rack bandwidth.

We consider the problem of private multiple linear computation (PMLC) over a replicated storage system with colluding and unresponsive constraints. In this scenario, the user wishes to privately compute$P$linear combinations of$M$files from a set of$N$replicated servers without revealing any information about the coefficients of these linear combinations to any$T$colluding servers, in the presence of$S$unresponsive servers that do not provide any information in response to user queries. Our focus is on more general performance metrics where the communication and computational overheads incurred by the user are not neglected. Additionally, the communication and computational overheads for servers are also taken into consideration. Unlike most previous literature that primarily focused on download cost from servers as a performance metric, we propose a novel PMLC scheme to establish a flexible tradeoff between communication costs and computational complexities.

Motion compensated temporal filter (MCTF) is a pre-filtering technology for video encoding, which employs bilateral filtering to enhance temporal correlations among adjacent frames. In this paper, a spatial neighbor information assisted MCTF method is proposed, which introduces the spatial information into the motion estimation and bilateral filtering processes in MCTF to improve the coding efficiency. For the motion estimation process, the spatial neighbor information is involved in preventing motion estimation from capturing a local optimum. For the bilateral filtering process, the spatial neighbor information is employed as well to reduce the block boundary effect. The proposed method is implemented on top of the Fraunhofer Versatile Video Encoder (VVenC). Experimental results show that the proposed method can achieve 1.05% bitrate saving on average compared to the current MCTF scheme, and 10.33% bitrate saving compared with MCTF disabled.

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.

The partially cooperative repair model is an available technology to deal with multiple node failures in a distributed storage system, which does not depend on the heavy assumption of exchanging data with all new nodes, increasing the flexibility of the system. In this paper, constructions and repair schemes for codes with minimum storage overhead and optimal repair bandwidth, i.e., minimum storage partially cooperative regenerating codes are proposed. These constructions show that the theoretic bound on the repair bandwidth of the partially cooperative repair model is tight for the minimum storage cases. Notably, these codes with optimal repair bandwidth may have smaller sub-packetization compared with the known codes for this model.

In this paper, we address the node repair problem of Reed-Solomon (RS) coded distributed storage systems. Specifically, to overcome the challenges of multiple-node failures of RS codes under the rack-aware storage model, we employ good polynomials to guide the placement of the conventional RS codes into racks and then propose a novel repair framework for the resultant rack-aware RS codes, which can transform its repair to that under the homogeneous storage model. As applications of our repair framework, firstly we present the repair scheme of multiple-node failures for some existing constructions, which only have non-trivial solutions for repairing a single-node failure before. Secondly, we deduce several new constructions of rack-aware RS codes supporting the repair of multiple-node failures within a single rack and across multiple racks respectively.

Product codes (PCs) are typically decoded using iterative bounded distance decoding (iBDD) to ensure a low decoding complexity. To obtain further performance gain, a soft-aided decoding algorithm, termed the iBDD with scaled reliability (iBDD-SR), was proposed for PCs. In this paper, we propose an enhanced iBDD-SR by introducing threshold and memory when passing messages between the component decoders. The resulting algorithm is referred to as the threshold-based binary message passing (TB-BMP) with memory. In the proposed decoding algorithm, the soft reliability of the BDD output at the current half-iteration is a weighted sum of the BDD output, the channel reliability, and the content of the memory unit, where the content of the memory unit at the current half-iteration is related to the selected threshold and the BDD output at last half-iteration. Due to the existence of memory, the Bayesian network is used to model the decoding process of the TB-BMP. Based on the Bayesian network, we derive the density evolution (DE) equations for the TB-BMP under the constraint of extrinsic message passing (EMP). The analytical results of the DE analysis can be used to guide the selection of the parameters of the TB-BMP decoder. Extensive simulation results show that the TB-BMP decoder outperforms the iBDD-SR over the binary-input additive white Gaussian noise (Bi-AWGN) channels. In particular, for a PC based on a two-error-correcting extended Bose-Chaudhuri-Hocquenghem (BCH) code of length 256, the TB-BMP decoder performs about 0.28 dB better than the iBDD-SR at a bit error rate (BER) of 10-7.

In this paper, we construct a large family of projective linear codes over${\mathbb F}_{q}$from the general simplicial complexes of${\mathbb F}_{q}^{m}$via the defining-set construction, which generalizes the results of [IEEE Trans. Inf. Theory 66(11):6762-6773, 2020]. The parameters and weight distributions of this class of codes are completely determined. By using the Griesmer bound, we give a necessary and sufficient condition such that the codes are Griesmer codes and a sufficient condition such that the codes are distance-optimal. For a special case, we also present a necessary and sufficient condition for the codes to be near Griesmer codes. Moreover, by discussing the cases of simplicial complexes with one, two and three maximal elements respectively, the parameters and weight distributions of the codes are given more explicitly, which shows that the codes are at most 2-weight, 5-weight and 19-weight respectively. By studying the optimality of the codes for the three cases in detail, many infinite families of optimal linear codes with few weights over${\mathbb F}_{q}$are obtained, including Griesmer codes, near Griesmer codes and distance-optimal codes.

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.

In light of the emergence of privacy breaches in federated learning, secure aggregation protocols, which mainly adopt either homomorphic encryption or threshold secret sharing techniques, have been extensively developed to preserve the privacy of each client's local gradient. Nevertheless, many existing schemes suffer from either poor capability of privacy protection or expensive computational and communication overheads. Accordingly, in this paper, we propose an efficient and multi-private key secure aggregation scheme for federated learning. Specifically, we skillfully design a multi-private key secure aggregation algorithm that achieves homomorphic addition operation, with two important benefits: 1) both the server and each client can freely select public and private keys without introducing a trusted third party, and 2) the plaintext space is relatively large, making it more suitable for deep models. Besides, for dealing with the high dimensional deep model parameter, we introduce a super-increasing sequence to compress multi-dimensional data into one dimension, which greatly reduces encryption and decryption times as well as communication for ciphertext transmission. Detailed security analyses show that our proposed scheme can achieve semantic security of both individual local gradients and the aggregated result while achieving optimal robustness in tolerating client collusion. Extensive simulations demonstrate that the accuracy of our scheme is almost the same as the non-private approach, while the efficiency of our scheme is much better than the state-of-the-art baselines. More importantly, the efficiency advantages of our scheme will become increasingly prominent as the number of model parameters increases.

A robust transmission scheme for intelligent reflecting surface (IRS) aided cognitive radio systems is designed to provide security against internal eavesdropping. By considering the secondary receiver as an internal eavesdropper, a total transmit power (TTP) minimization problem is formulated. Through a novel optimization strategy which jointly considers the transmit beamforming vector at the primary transmitter, the transmit beamforming vector at the secondary transmitter and the phase shifts at the IRS, a solution to the formulated problem is presented. By considering perfect channel state information (CSI) and imperfect CSI scenarios, two optimization algorithms are proposed both aiming at reducing the TTP. For the former scenario, instead of applying the commonly used inner approximation (IA) algorithm which cannot handle maximum allowable leaked rate constraint, a novel penalty-based IA algorithm is proposed. For the latter scenario, a non-convex robust optimization problem is formulated. Because of its non-convex nature, a novel upper-bounding technique and S-procedure are used to transform it into a more tractable form which is then solved by deriving of a penalty convex-concave procedure based alternating optimization algorithm. Performance results show that, as compared to other baseline schemes, the proposed algorithms significantly reduce the TTP.

User-centric cell-free massive MIMO (CFmMIMO), where only partial access points (APs) are selected to serve a specific user equipment (UE), is a scalable extension of CFmMIMO. Existing works have studied the spectral efficiency of large-scale fading decoding (LSFD) aided user-centric CFmMIMO that includes local combining at each AP and statistical channel state information (S-CSI) based fusion in the central processing unit (CPU). However, few efforts have so far been paid to analyze the error probability bound, and existing detectors fail to balance the error probability and fusion complexity. In this paper, we analyze the symbol error rate (SER) and design low-complexity near-optimal detectors for uplink user-centric CFmMIMO systems. Considering non-identical large-scale fading coefficients and local channel estimation errors, we first leverage the pairwise error probability to derive an SER upper bound for optimal linear fusion (OLF) in the CPU, which is suitable to different local combining methods at the APs. Then, by combining local normalization methods and S-CSI based UE grouping or error correction, we design improved detectors for local maximum-ratio and local minimum mean squared error combining successively. Simulation results verify the correctness of the derived SER bound, and show that the proposed detectors are capable of approaching the SER performance of conventional OLF based counterparts with reduced fusion complexity even in scenarios with pilot contamination.

In this paper, we consider a cooperative communication network where multiple low-Earth-orbit (LEO) satellites provide services to multiple ground users (GUs) cooperatively at the same time and on the same frequency. The multi-satellite cooperation has great potential in extending communication coverage and increasing spectral efficiency. Considering that the on-board radio-frequency circuit resources and computation resources on each satellite are restricted, we aim to propose a low-complexity yet efficient multi-satellite cooperative transmission framework. Specifically, we first propose a hybrid beamforming method consisting of analog beamforming for beam alignment and digital beamforming for interference mitigation. Then, to establish appropriate connections between the satellites and GUs, we propose a heuristic user scheduling algorithm which determines the connections according to the total spectral efficiency increment of the multi-satellite cooperative network. Next, considering the intrinsic connection between beamforming and user scheduling, a joint hybrid beamforming and user scheduling (JHU) scheme is proposed to dramatically improve the performance of the multi-satellite cooperative network. In addition to the single-connection scenario, we also consider the multi-connection case using the JHU scheme. Extensive simulations conducted over different LEO satellite constellations and across various GU locations demonstrate the superiority of the proposed schemes in both overall and per-user spectral efficiencies.

Inter prediction is a key technology in video coding standards. In natural videos, moving objects lead to complex motion fields that are difficult to represent, potentially limiting the coding efficiency. In view of this, we propose a multi-zone division-based inter prediction (MDIP) framework to improve the partitioning precision of moving objects and achieve the flexible description of the complex motion field. For each coding block, four multi-zone division modes are supported to adapt to the different motion situations in the block. With the guidance of division mode, motion compensation and motion information coding are separately performed for different zones to achieve higher prediction accuracy and economize the bits consumed for motion information signalling. The proposed algorithm is implemented into the Versatile Video Coding (VVC) reference software, VTM version 6.0. Experimental results show that the proposed method achieves up to 2.90% and on average 0.49% BD-rate reduction compared to the VTM anchor, under the low-delay P configuration, without any increase in time complexity.

In this paper, we consider a cooperative communication network where multiple satellites provide services for ground users (GUs) (at the same time and on the same frequency). The communication and computational resources on satellites are usually restricted and the satellite-GU link determination affects the communication performance significantly when multiple satellites provide services for multiple GUs in a collaborative manner. Therefore, considering the limitation of the on-board radio-frequency chains, we first propose a hybrid beamforming method consisting of analog beamforming for beam alignment and digital beamforming for interference mitigation. Then, to establish appropriate connections between satellites and GUs, we propose a heuristic user scheduling algorithm which determines the connections according to the total spectral efficiency (SE) increment of the multi-satellite cooperative network. Next, a joint hybrid beamforming and user scheduling scheme is proposed to dramatically improve the performance of the multi-satellite cooperative network. Moreover, simulations are conducted to compare the proposed schemes with representative baselines and analyze the key factors influencing the performance of the multi-satellite cooperative network. It is shown that the proposed joint beamforming and user scheduling approach can provide 47.2% SE improvement on average as compared with its non-joint counterpart.

Abundant high-rate$(n, k)$minimum storage regenerating (MSR) codes have been reported in the literature. However, most of them require contacting all the surviving nodes during a node repair process, resulting in a repair degree of$d=n-1$. In practical systems, it may not always be feasible to connect and download data from all surviving nodes, as some nodes may be unavailable. Therefore, there is a need for MSR code constructions with a repair degree of$d < n-1$. Up to now, only a few$(n, k)$MSR code constructions with repair degree$d < n-1$have been reported, some have a large sub-packetization level, a large finite field, or restrictions on the repair degree$d$. In this paper, we propose a new$(n, k)$MSR code construction that works for any repair degree$d>k$, and has a smaller sub-packetization level or finite field than some existing constructions. Additionally, in conjunction with a previous generic transformation to reduce the sub-packetization level, we obtain an MDS array code with a small sub-packetization level and$(1+\epsilon)$-optimal repair bandwidth (i.e.,$(1+\epsilon)$times the optimal repair bandwidth) for repair degree$d=n-1$. This code outperforms some existing ones in terms of either the sub-packetization level or the field size.

In this paper, we consider how to partition the parity-check matrices (PCMs) to reduce the hardware complexity and increase decoding throughput for the row layered decoding of quasi-cyclic low-density parity-check (QC-LDPC) codes. First, we formulate the PCM partitioning as an optimization problem, which targets to minimize the maximum column weight of each layer while maintaining a block cyclic shift property among different layers. As a result, we derive all the feasible solutions for the problem and propose a tight lower bound ωLBon the minimum possible maximum column weight to evaluate a solution. Second, we define a metric called layer distance to measure the data dependency between consecutive layers and further illustrate how to identify the solutions with desired layer distance from those achieving the minimum value of ωLB= 1, which is preferred to reduce computation delay. Next, we demonstrate that up-to-now, finding an optimal solution for the optimization problem with polynomial time complexity is unachievable. Therefore, both enumerative and greedy partition algorithms are proposed instead. After that, we modify the quasi-cyclic progressive edge-growth (QC-PEG) algorithm to directly construct PCMs that have a straightforward partition scheme to achieve ωLBor the desired layer distance. Simulation results showed that the constructed codes have better error correction performance and achieve less average number of iterations than the underlying 5G LDPC codes.

Reconfigurable intelligent surface (RIS) is able to create favorable reflecting channels for different users and piggyback additional data in the reflected signals. The former brings benefits to non-orthogonal multiple access (NOMA), while the latter enables a mechanism of symbiotic radio (SR). Inspired by these unique advantages, we consider a general SR-NOMA system model where an RIS is deployed to assist both the NOMA in an uplink multi-channel system and the Internet-of-Things (IoT) data transmission. This general model also allows for different performance objectives from the NOMA users. In particular, the users can be either energy-efficiency oriented or spectrum-efficiency oriented. To strike the performance trade-off between these two types of users, a performance metric called resource efficiency (RE) is leveraged to formulate the optimization problem. We jointly design the time-frequency resource allocation, multi-user power control and RIS phase shifts to maximize the weighted sum-RE of the system, subject to the quality-of-service constraints of the SR-NOMA system. An efficient alternating optimization framework with a series of algorithms, including matching theory, fractional programming method, and inner majorization-minimization method, is developed to solve this highly complex and non-convex problem.

Coded distributed computing can alleviate the communication load by leveraging the redundant storage and computation resources with coding techniques in distributed computing. In this paper, we study a MapReduce-type distributed computing framework over star topological network, where all the workers exchange information through a common access point. The optimal tradeoff among the normalized number of stored files (storage load), computed intermediate values (computation load), and transmitted bits in the uplink and downlink (communication loads) is characterized. A coded computing scheme is proposed to achieve the Pareto-optimal tradeoff surface, in which the access point only needs to perform simple chain coding between the signals it receives, and information- theoretical bound matching the surface is also provided.

This paper presents the first performance analysis of physical layer downlink secure transmissions in a scalable cell-free massive MIMO (SCF-mMIMO) system. A stochastic geometry approach is used to model the locations of the access points (APs), user equipments (UEs) and eavesdroppers (Eves) as independent homogeneous Poisson point processes (HPPPs). In addition to applying maximum ratio transmission (MRT) to send the confidential messages, null-space artificial noise is also injected for secrecy enhancement. We analytically characterize the secrecy performance in terms of both the outage-based secrecy transmission rate (STR) and the ergodic secrecy rate (ESR), appropriate for slow quasi-static fading channels and fast block-fading channels, respectively. By utilizing moment matching and Gil-Pelaez inversion theorem, we are able to obtain mathematically tractable approximations for the performance metrics. These approximations are shown to have high accuracy as compared to simulation results. Our numerical results reveal useful design insights that cannot be inferred from existing studies. These insights answer important questions such as whether it is best to deploy as many APs each with fewer antennas and to what extent the artificial noise insertion is beneficial.

Partial maximum distance separable (PMDS) codes are a kind of erasure codes where the nodes are divided into multiple groups with each forming an MDS code with a smaller code length, thus they allow repairing a failed node with only a few helper nodes and can correct all erasure patterns that are information-theoretically correctable. However, the repair of a failed node of PMDS codes still requires a large amount of communication if the group size is large. Recently, PMDS array codes with each local code being an MSR code were introduced to reduce the repair bandwidth further. However, they require extensive rebuilding access and unavoidably a significant sub-packetization level. In this paper, we first propose two constructions of PMDS array codes with two global parities that have smaller sub-packetization levels and much smaller finite fields than the existing one. One construction can support an arbitrary number of local parities and has$(1+\epsilon)$-optimal repair bandwidth (i.e.,$(1+\epsilon)$times the optimal repair bandwidth), while the other one is limited to two local parities but has significantly smaller rebuilding access and its sub-packetization level is only 2. In addition, we present a construction of PMDS array code with three global parities, which has a smaller sub-packetization level as well as$(1+\epsilon)$-optimal repair bandwidth, the required finite field is significantly smaller than existing ones.

The cooperative repair model is an available technology to deal with multiple node failures in distributed storage systems. Recently, explicit constructions of cooperative MSR codes were given by Ye (IEEE Transactions on Information Theory, 2020) with sub-packetization level$(d-k+h)(d-k+1)^{n}$. Specifically, the sub-packetization level is$(h+1)2^{n}$when$d=k+1$. In this paper, we propose a new cooperative repair scheme by means of the inter-instance pairing and intra-instance pairing inherited from the perfect code which reduces the sub-packetization to$2^{n}$when$(h+1)|2^{n}$and$(2\ell +1)2^{n}$when$h+1=(2\ell +1)2^{m}$for$\ell \ge 1$,$m\ge 0$with$d=k+1$helper nodes. That is to say, the sub-packetization is$h + 1 $times or$2^{m}$times less than Ye’s. It turned out to be the best result so far known.

In the literature, most of the known high-rate$(n,k)$MDS array codes with the optimal repair property only support a single repair degree (i.e., the number of helper nodes contacted during a repair process)$d$, where$k\le d\le n-1$. However, in practical storage systems, the number of available nodes changes frequently. Thus, it is preferred to construct$(n,k)$MDS array codes with multiple repair degrees and the optimal repair property for all nodes. To the best of our knowledge, only two high-rate MDS array codes have such properties in the literature, which were proposed by Ye and Barg (IEEE Trans. Inform. Theory, 63(10), 2001–2014, 2017). However, their sub-packetization levels are relatively large. In this paper, we present a generic construction method that can convert some MDS array codes with a single repair degree into ones with multiple repair degrees and optimal repair property for a set of nodes, while the repair efficiency/degrees of the remaining nodes can be kept. As an application of the generic construction method, an explicit construction of high-rate MDS array code with multiple repair degrees and the optimal access property for all nodes is obtained over a small finite field by choosing the code proposed by Vajha et al. as the base code. Especially, the sub-packetization level is much smaller than that of the two codes proposed by Ye and Barg concerning the same parameters$n$and$k$.

In this paper, we investigate the power function$F(x)=x^{d}$over the finite field$\mathbb {F}_{2^{4n}}$, where$n$is a positive integer and$d=2^{3n}+2^{2n}+2^{n}-1$. We prove that this power function is AP$c\text{N}$with respect to all$c\in \mathbb {F}_{2^{4n}}\setminus \{1\}$satisfying$c^{2^{2n}+1}=1$, and we determine its$c$-differential spectrum. To the best of our knowledge, this is the second class of AP$c\text{N}$power functions over finite fields of even characteristic. By the same proof ideas, we completely determine the differential spectrum of this function, and give an affirmative answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski.

The minimum storage rack-aware regenerating (MSRR) code is a variation of regenerating codes that achieves the optimal repair bandwidth for a single node failure in the rack-aware model. Some explicit constructions of MSRR codes for all parameters to repair a single failed node have been reported. This paper studies MSRR codes with error-correcting capability for multiple erasure tolerance. First, we propose a general repair model of maximum distance separable (MDS) codes with error-correcting capability for multiple erasure tolerance and derive lower bounds on the number of symbols downloaded and accessed, respectively from helper racks for the purpose of correction and repair. Then, we construct a class of MDS array codes and scalar Reed-Solomon (RS) codes with the optimal repair bandwidth and error resilient capability for multiple node failures. Further, our codes are shown to have the low-access property. In particular, they have the optimal access property for repairing$u$failed nodes when the dimension of the code is divisible by the rack size$u$.

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.

In this paper, we propose a mutual information-maximizing quantized layered min-sum (MIM-QLMS) decoder for quasi-cyclic low-density parity-check (QC-LDPC) codes. Our proposed decoder operates similarly to a layered min-sum decoder with additional reconstruction and quantization operations by using single-input lookup tables (LUTs). In particular, we first develop the protograph-based MIM density evolution to design the LUTs, which may differ for each iteration and each edge in the protograph of the QC-LDPC codes. Furthermore, to minimize the memory requirement for storing the LUTs, we propose an optimization method to unify all LUTs into only four distinct LUTs, which can be used for all decoding iterations. To the best of our knowledge, the proposed MIM-QLMS decoders are the first class of layered finite alphabet iterative decoders (FAIDs) that are designed based on accurately tracking the probability distributions of the exchanged messages. Simulation results show that for 3-bit (resp. 4-bit) exchanged message precision, the proposed MIM-QLMS decoders can reasonably (resp. generally) outperform the state-of-the-art layered FAIDs and the layered normalized min-sum decoder, in terms of both the error rate performance and the average number of iterations.

A scalable cell-free massive MIMO (SCF-mMIMO) system where all user equipments (UEs) and access points (APs) employ finite resolution digital-to-analog converters (DACs) and analog-to-digital converters (ADCs) over correlated Rician fading is presented and analysed in this paper. A closed-form expression for the uplink (UL) spectral efficiency (SE) using maximal-ratio combining (MRC) detection for centralized scheme is first derived. Moreover, a novel low complexity partial MMSE (P-MMSE) detector is proposed, which achieves very similar SE performance and maintains much less computational complexity in comparison with the original partial MMSE (P-MMSE) detector. In addition, a joint algorithm consisting of AP cluster formation, pilot assignment, and power control policy is proposed, which yields much higher SE performance than random pilot assignment and user-group based pilot assignment policies do, and meanwhile improves the quality of service (QoS) fairness for all accessing UEs as compared to the equal power transmit policy.

Partial maximum distance separable (PMDS) codes are a kind of erasure codes where the storage nodes are divided into multiple groups with each forming an MDS code of a smaller code length. They allow repairing a failed node by contacting only a few helper nodes and can correct all erasure patterns which are information-theoretically correctable. However, the repair of a failed node of PMDS codes still requires a large amount of communication if the group size is large. Recently, PMDS array codes with each local code being an MSR code were introduced to further reduce the repair bandwidth, but codes over small finite fields only exist for two global parities, and require large rebuilding access and unavoidably a large sub-packetization level. In this paper, we propose two constructions of PMDS array codes with two and three global parities, respectively. Both have a small sub-packetization level, small repair bandwidth, and much smaller finite fields than existing ones.

GC-content and homopolymer run are two constraints of interest in DNA storage systems. Extensive experiments showed that if GC-content is too high (low), or homopolymer run exceeds six in a DNA sequence, there will give rise to dramatical increase of insertion, deletion and substitution errors. Committing to study the DNA sequences with both constraints, a recent work (Nguyen et al. 2020) proposed a class of (ϵ, ℓ)-constrained codes that can only asymptotically approach the capacity, but may have reasonable loss for finite code lengths.In this paper, we design the first (ϵ, ℓ)-constrained codes based on the enumeration coding technique which can always achieve capacity regardless of code lengths. In addition, motivated by the influence of local GC-content, we consider a nontrivial case that the prefixes of a DNA sequence also hold GC-content constraint for the first time, called (δ,ℓ)-prefix constrained codes.

Although federated learning improves privacy of training data by exchanging local gradients or parameters rather than raw data, the adversary still can leverage local gradients and parameters to obtain local training data by launching reconstruction and membership inference attacks. To defend against such privacy attacks, many noises perturbed methods (like differential privacy or CountSketch matrix) have been widely designed. However, the strong defence ability and high learning accuracy of these schemes cannot be ensured at the same time, which will impede the wide application of FL in practice (especially for medical or financial institutions that require both high accuracy and strong privacy guarantee). To overcome this issue, we propose an efficient model perturbation method for federated learning to defend against reconstruction and membership inference attacks launched by curious clients. On the one hand, similar to the differential privacy, our method also selects random numbers as perturbed noises added to the global model parameters, and thus it is very efficient and easy to be integrated in practice. Meanwhile, the random selected noises are positive real numbers and the corresponding value can be arbitrarily large, and thus the strong defence ability can be ensured. On the other hand, unlike differential privacy or other perturbation methods that cannot eliminate added noises, our method allows the server to recover the true aggregated gradients by eliminating the added noises. Therefore, our method does not hinder learning accuracy at all. Extensive experiments demonstrate that for both regression and classification tasks, our method achieves the same accuracy as non-private approaches and outperforms the state-of-the-art defence schemes. Besides, the defence ability of our method against reconstruction and membership inference attack is significantly better than the state-of-the-art related defence schemes.

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 problem of Multi-user Blind$X$-secure$T$-colluding Symmetric Private Information Retrieval from Maximum Distance Separable (MDS) coded storage system with$B$Byzantine and$U$unresponsive servers (U-B-MDS-MB-XTSPIR) is studied in this paper. Specifically, a database consisting of multiple files, each labeled by$M$indices, is stored at the distributed system with$N$servers according to$(N,K+X)$MDS codes over$\mathbb {F}_{q}$such that any group of up to$X$colluding servers learn nothing about the data files. There are$M$users, in which each user$m,m=1,\ldots,M$privately selects an index$\theta _{m}$and wishes to jointly retrieve the file specified by the$M$users’ indices$(\theta _{1},\ldots,\theta _{M})$from the storage system, while keeping its index$\theta _{m}$private from any$T_{m}$colluding servers, where there exists$B$Byzantine servers that can send arbitrary responses maliciously to confuse the users retrieving the desired file and$U$unresponsive servers that will not respond any message at all. In addition, each user must not learn information about the other users’ indices and the database more than the desired file. An U-B-MDS-MB-XTSPIR scheme is constructed based on Lagrange encoding. The scheme achieves a retrieval rate of$1-\frac {K+X+T_{1}+\ldots +T_{M}+2B-1}{N-U}$with secrecy rate$\frac {K+X+T_{1}+\ldots +T_{M}-1}{ N-(K+X+T_{1}+\ldots +T_{M}+2B+U-1)}$on the finite field of size$q\geq N+\max \{K, N-(K+X+T_{1}+\ldots +T_{M}+2B+U-1)\}$for any number of files.

Secure data deduplication can significantly reduce the communication and storage overheads in cloud storage services, and has potential applications in our big data-driven society. Existing data deduplication schemes are generally designed to either resist brute-force attacks or ensure the efficiency and data availability, but not both conditions. We are also not aware of any existing scheme that achieves accountability, in the sense of reducing duplicate information disclosure (e.g., to determine whether plaintexts of two encrypted messages are identical). In this paper, we investigate a three-tier cross-domain architecture, and propose an efficient and privacy-preserving big data deduplication in cloud storage (hereafter referred to as EPCDD). EPCDD achieves both privacy-preserving and data availability, and resists brute-force attacks. In addition, we take accountability into consideration to offer better privacy assurances than existing schemes. We then demonstrate that EPCDD outperforms existing competing schemes, in terms of computation, communication and storage overheads. In addition, the time complexity of duplicate search in EPCDD is logarithmic.

For high-rate linear systematic maximum distance separable (MDS) codes, most early constructions could initially optimally repair all the systematic nodes but not all the parity nodes. Fortunately, this issue was first solved by Liet al.in (IEEE Trans. Inform. Theory, 64(9), 6257-6267, 2018), where a transformation that can convert any nonbinary MDS array code into another one with desired properties was proposed. However, the transformation does not work for binary MDS array codes. In this paper, we address this issue by proposing another generic transformation that can convert any$[n, k]$binary MDS array code into a new one, which endows any$r=n-k\ge 2$chosen nodes with optimal repair bandwidth and optimal rebuilding access properties, and at the same time, preserves the normalized repair bandwidth/rebuilding access for the remaining$k$nodes under some conditions. As two immediate applications, we show that 1) by applying the transformation multiple times, any binary MDS array code can be converted into one with optimal rebuilding access for all nodes, 2) any binary MDS array code with optimal repair bandwidth or optimal rebuilding access for the systematic nodes can be converted into one with the corresponding optimality property for all nodes.

Recently, some high-rate maximum distance separable (MDS) array codes were designed to optimally repair a single failed node by connecting all the surviving nodes. However, in practical systems, sometimes not all the surviving nodes are available. To facilitate the practical storage system, a few constructions of$(n,k)$MDS array codes with the property that any single failed node can be optimally repaired by accessing any$d$surviving nodes (i.e., minimum-storage regenerating (MSR) codes) have been proposed, where$d\in [k+1:n-1)$. However, all high-rate MDS array codes with this property either have large sub-packetization levels or are not explicit for all the parameters. To address these issues, we propose a generic transformation that can convert any$(n',k')$MDS array/scalar code to another$(n=n'-\delta,k=k'-\delta)$MDS array code with the optimal repair property and optimal access property for an arbitrary set of two nodes, while the repair efficiency of the remaining$n-2$nodes can be kept, where$2\le \delta \le n'-k'$. By recursively applying the generic transformation to an MDS scalar code multiple times, we get a high-rate MDS array code with the optimal repair property and the optimal access property for all nodes, which outperforms previous known high-rate MDS array codes in terms of either the sub-packetization level or the flexibility of the parameters.

Cloud storage as one of the most important services of cloud computing which significantly facilitates cloud users to outsource their data to the cloud for storage and share them with authorized users. In cloud storage, secure deduplication has been widely investigated as it can eliminate the redundancy over the encrypted data to reduce storage space and communication overhead. Regarding the security and privacy, many existing secure deduplication schemes generally focus on achieving the following properties: data confidentiality, tag consistency, access control, and resistance to brute-force attacks. However, as far as we know, none of them can achieve these four requirements at the same time. To overcome this shortcoming, in this article, we propose an efficient secure deduplication scheme that supports user-defined access control. Specifically, by allowing only the cloud service provider to authorize data access on behalf of data owners, our scheme can maximally eliminate duplicates without violating the security and privacy of cloud users. Detailed security analysis shows that our authorized secure deduplication scheme achieves data confidentiality and tag consistency while resisting brute-force attacks. Furthermore, extensive simulations demonstrate that our scheme outperforms the existing competing schemes, in terms of computational, communication and storage overheads as well as the effectiveness of deduplication.

We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. We then also provide explicit constructions of optimal codes which show that for certain parameters the new bound is sharp. Additionally, as a byproduct, some previously known codes are shown to attain the new bound and are thus proved to be optimal.

We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic regimes, the constructed codes have order-optimal alphabet size, asymptotically matching the known lower bound.

In this paper, we construct four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including infinite families of (near) Griesmer codes. We also characterize the optimality of these four families of linear codes with an explicit computable criterion using the Griesmer bound and obtain many distance-optimal linear codes. In addition, by a more in-depth discussion on some special cases of these four families of linear codes, we obtain several classes of (distance-)optimal linear codes with few weights and completely determine their weight distributions. It is shown that most of our linear codes are self-orthogonal or minimal which are useful in applications.

The problem of$X$-secure$T$-colluding symmetric Private Polynomial Computation (PPC) from coded storage system with$B$Byzantine and$U$unresponsive servers is studied in this paper. Specifically, a dataset consisting of$M$files is stored across$N$distributed servers according to$(N,K+X)$Maximum Distance Separable (MDS) codes such that any group of up to$X$colluding servers can not learn anything about the data files. A user wishes to privately evaluate one out of a set of candidate polynomial functions over the$M$files from the system, while guaranteeing that any$T$colluding servers can not learn anything about the identity of the desired function and the user can not learn anything about the$M$data files more than the desired polynomial function evaluations, in the presence of$B$Byzantine servers that can send arbitrary responses maliciously to confuse the user and$U$unresponsive servers that will not respond any information at all. A novel symmetric PPC scheme using Lagrange encoding is proposed. This scheme achieves a PPC rate of$1-\frac {G(K+X-1)+T+2B}{N-U}$with secrecy rate$\frac {G(K+X-1)+T}{N-(G(K+X-1)+T+2B+U)}$and finite field size$N+\max \{K,N-(G(K+X-1)+T+2B+U)\}$, where$G$is the maximum degree over all the candidate polynomial functions. Moreover, to further measure the efficiency of PPC schemes, upload cost, query complexity, server computation complexity and decoding complexity required to implement the scheme are analyzed. Remarkably, the PPC setup studied in this paper generalizes all the previous MDS coded PPC setups and the degraded schemes strictly outperform the best known schemes in terms of (asymptotical) PPC rate, which is the main concern of the PPC schemes.

This paper focuses on mitigating the impact of stragglers in distributed learning system. Unlike the existing results designated for a fixed number of stragglers, we develop a new scheme calledAdaptive Gradient Coding (AGC)with flexible communication cost for varying number of stragglers. Our scheme gives an optimal tradeoff between computation load, straggler tolerance and communication cost by allowing workers to send multiple signals sequentially to the master. In particular, it can minimize the communication cost according to the unknown real-time number of stragglers in practical environments. In addition, we present aGroup AGC (G-AGC)by combining the group idea with AGC to resist more stragglers in some situations. The numerical and simulation results demonstrate that our adaptive schemes can achieve the smallest average running time.

The Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes is studied. An improved bound is presented by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. Additionally, as a byproduct, some previously known codes are shown to attain the new bound and are thus proved to be optimal.

This paper investigates the problem of Secure Multi-party Batch Matrix Multiplication (SMBMM), where a user aims to compute the pairwise products$\mathbf {A}\divideontimes \mathbf {B}\triangleq (\mathbf {A}^{(1)}\mathbf {B}^{(1)},\ldots,\mathbf {A}^{(M)}\mathbf {B}^{(M)})$of two batch of massive matrices$\mathbf {A}$and$\mathbf {B}$that are generated from two sources, through$N$honest but curious servers which share some common randomness. The matrices$\mathbf {A}$(resp.$\mathbf {B}$) must be kept secure from any subset of up to$X_{\mathbf {A}}$(resp.$X_{\mathbf {B}}$) servers even if they collude, and the user must not obtain any information about$(\mathbf {A},\mathbf {B})$beyond the products$\mathbf {A}\divideontimes \mathbf {B}$. A novel computation strategy for single secure matrix multiplication problem (i.e., the case$M=1$) is first proposed, and then is generalized to the strategy for SMBMM by means of cross subspace alignment. The SMBMM strategy focuses on the tradeoff between recovery threshold (the number of successful computing servers that the user needs to wait for), system cost (upload cost, the amount of common randomness, and download cost) and system complexity (encoding, computing, and decoding complexities). Notably, compared with the known result by Chenet al., the strategy for the degraded case$X= X_{\mathbf {A}}=X_{\mathbf {B}}$achieves better recovery threshold, amount of common randomness, download cost and decoding complexity when$X$is less than some parameter threshold, while the performance with respect to other measures remain identical.

Coded caching systems have been widely studied to reduce the data transmission during the peak traffic time. In practice, two important parameters of a coded caching system should be considered, i.e., the transmission rate which is the maximum amount of the data transmission during the peak traffic time, and the subpacketization level, the number of divided packets of each file when we implement a coded caching scheme. Although there exists a tradeoff between transmission rate and subpacketization, we prefer to design a scheme with transmission rate and subpacketization as small as possible since they reflect the transmission efficiency and complexity of the caching scheme, respectively. In this paper, we first characterize a coded caching scheme from the viewpoint of linear algebra and show that designing a linear coded caching scheme is equivalent to constructing three classes of matrices satisfying some rank conditions. Then based on the invariant subspaces in linear algebra and combinatorial design theory, a new class of coded caching schemes over F2is obtained by constructing these three classes of matrices. It turns out that the transmission rate of our new scheme is the same as the scheme construct by Yan et al. (IEEE Trans. Inf. Theory 63, 5821-5833, 2017), but the subpacketization is significantly reduced. Finally by means of these matrices, we show that the minimum storage regenerating codes can also be used to construct coded caching schemes.

In the literature, all the known high-rate MDS codes with the optimal repair bandwidth possess a significantly large sub-packetization level, which may prevent the codes to be implemented in practical systems. To build MDS codes with small sub-packetization level, existing constructions and theoretical bounds imply that one may sacrifice the optimality of the repair bandwidth. Partly motivated by the work of Tamo et al. (IEEE Trans. Inform. Theory, 59(3), 1597-1616, 2013), in this paper, we present a transformation that can greatly reduce the sub-packetization level of MDS codes with the optimal repair bandwidth with respect to the same code length n. As applications of the transformation, four high-rate MDS codes having both small sub-packetization level and near-optimal repair bandwidth can be obtained, where three of them are explicit and the required field sizes are around or even smaller than the code length n. Additionally, we propose another explicit MDS code which has a similar structure as that of the first resultant code obtained by the generic transformation, but can be built on a smaller finite field.

This paper investigates reducing sub-packetization of capacity-achieving schemes for uncoded Storage Constrained Private Information Retrieval (SC-PIR) systems. In the SC-PIR system, a user aims to download one out of K files from N servers while revealing nothing about the identity of the requested file to any individual server, in which the K files are stored at the N servers in an uncoded form and each server can store up to μK equivalent files, where μ is the normalized storage capacity of each server. We first prove that there exists a capacity-achieving SC-PIR scheme for a given storage design if and only if all the packets are stored exactly at M\triangleq μN servers for μ such that M=μN ∈ {2,3,...,N}. Then, the optimal sub-packetization for capacity-achieving linear SC-PIR schemes is characterized as the solution to an optimization problem, which is typically hard to solve since it involves non-continuous indicator functions. Moreover, a new notion of array called Storage Design Array (SDA) is introduced for the SC-PIR system. With any given SDA, an associated capacity-achieving SC-PIR scheme is constructed. Next, the SC-PIR schemes that have equal-size packets are investigated. Furthermore, the optimal equal-size sub-packetization among all capacity-achieving linear SC-PIR schemes characterized by Woolsey et al. is proved to be \frac N(M-1)gcd(N,M), which is achieved by a construction of SDA. Finally, by allowing unequal size of packets, a greedy SDA construction is proposed, where the sub-packetization of the associated SC-PIR scheme is upper bounded by \frac N(M-1)gcd(N,M). Among all capacity-achieving linear SC-PIR schemes, the sub-packetization is optimal when min{M,N-M}|N or M=N, and within a multiplicative gap \frac min{M,N-M}gcd(N,M) of the optimal one in general. In particular, for the special case N=d·M±1 where the positive integer d ≥ 2, we propose another SDA construction to obtain lower sub-packetization.

Secure data deduplication, as it can eliminate redundancies over encrypted data, has been widely developed in cloud storage to reduce storage space and communication overheads. Among them, the convergent encryption has been extensively adopted. However, it is vulnerable to brute-force attacks that can determine which plaintext in a message space corresponds to a given ciphertext. Many existing schemes have to sacrifice efficiency to resist brute-force attacks, especially for cross-domain deduplication, which is inevitably contrary to practical applications. Moreover, few existing schemes consider protecting the message equality information (i.e., whether two different ciphertexts correspond to an identical plaintext). To address the above challenges, in this paper, we propose an efficient and privacy-preserving big data deduplication scheme for a two-level multi-domain architecture. Specifically, by generating a random tag and a constant number of random ciphertexts for each data, our scheme not only ensures data confidentiality under multi-domain deduplication but also resists brute-force attacks. By allowing only the agent and cloud service provider to perform intra-deduplication and inter-deduplication, respectively, our scheme can protect the message equality information from disclosure as much as possible. Detailed security analysis shows that our scheme achieves privacy-preservation for both data content and the message equality information and data integrity while resisting brute-force attacks. Furthermore, extensive simulations demonstrate that our scheme significantly outperforms the existing competing schemes, especially the computational cost and the time complexity of the duplicate search.

Traffic demand forecasting is essential to intelligent transportation systems and is widely used to support urban planning, traffic management and vehicle dispatching. One challenge of this problem is to model the complex spatial-temporal correlation. Although both factors have been studied, many of the existing works have strong limitations. They rely too heavily on the locality assumption (i.e., the local area is more relevant than the remote area) and only use a distance-based correlation measurement. However, the spatial correlation is also global (i.e., areas far away may also be relevant) and sparse. And it's insufficient to measure the spatial correlation using only the distance measurement. In this paper, a sparsity and diversity driven correlation network is proposed to tackle these issues. Firstly, Multiple sparse correlation graphs are carefully generated to encode sparsity and diversity. Then a newly designed hybrid graph filtering module (HGFM) leverages them to learn a more expressive node representation. Finally, the HGFM-based recurrent filtering module (RFM) is introduced to handle the spatial-temporal correlation. Extensive experiments conducted on real-world datasets demonstrate the competitiveness of our model while showing the significance of sparsity and diversity.

In coded caching system, we prefer to design a scheme with the rate R and the packet number F of each file split as small as possible since the efficiency of transmission in the peak traffic times increases with the decreasing of R and the realizing complexity increases with the increasing of F. Up to now, almost all of the previously known schemes can be realized by the combinatorial structure which is called placement delivery array (PDA). In this paper, we also study the schemes by means of PDAs. We first show that given the minimum rate, the scheme proposed by Maddah-Ali and Niesen (MN scheme) has the minimum packet number which is too large in practice. From the view point of combinatorial design, two variant MN schemes, which can significantly reduce the packet number by increasing some rate, are obtained. Especially one of these schemes has better performance than the scheme generated by the well known grouping method.

Placement delivery arrays for distributed computing (Comp-PDAs) have recently been proposed as a framework to construct universal computing schemes for MapReduce-like systems. In this work, we extend this concept to systems with straggling nodes, i.e., to systems where a subset of the nodes cannot accomplish the assigned map computations in due time. Unlike most previous works that focused on computing linear functions, our results are universal and apply for arbitrary map and reduce functions. Our contributions are as follows. Firstly, we show how to construct a universal coded computing scheme for MapReduce-like systems with straggling nodes from any given Comp-PDA. We also characterize the storage and communication loads of the resulting scheme in terms of the Comp-PDA parameters. Then, we prove an information-theoretic converse bound on the storage-communication (SC) tradeoff achieved by universal computing schemes with straggling nodes. We show that the information-theoretic bound matches the performance achieved by the coded computing schemes with straggling nodes corresponding to the Maddah-Ali and Niesen (MAN) PDAs, i.e., to the Comp-PDAs describing Maddah-Ali and Niesen's coded caching scheme. Interestingly, the MAN-PDAs are optimal for any number of straggling nodes. This implies that the map phase of optimal coded computing schemes does not need to be adapted to the number of stragglers in the system. We show that the points that lie exactly on the fundamental SC tradeoff cannot be achieved with Comp-PDAs that require smaller number of files than the MAN-PDAs. This is however possible for some of the points that lie close to the SC tradeoff. For these latter points, the decrease in the requested number of files can be exponential in the number of nodes of the system. We also model the total execution time, and numerically show that the active set size should be chosen to balance the duration of the map phase and the durations of the shuffle and reduce phases.

In a distributed storage system, private information retrieval (PIR) guarantees that a user retrieves one file from the system without revealing any information about the identity of its interested file to any individual server. In this paper, we investigate an (N, K, M) coded server model of PIR, where each of M files is distributed to N servers in the form of (N, K) maximum distance separable (MDS) code for some N > K and M > 1. As a result, we propose a new capacity-achieving (N, K, M) coded linear PIR scheme such that it can be implemented with file length (K(N-K)/(gcd(N,K)), which is much smaller than the previous best result K(N/(gcd(N,K)))M-1. Notably, among all the capacity-achieving coded linear PIR schemes, we show that the file length is optimal if M > ⌊K/(gcd(N,K)) - K/(N-K)⌋ + 1 or min(K, N - K)|N, and within a multiplicative gap (min(K,N-K))/(gcd(N,K) ) of a lower bound on the minimum file length otherwise.

In this paper, locally repairable codes which have optimal minimum Hamming distance with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds apply to more general cases, and have weaker requirements compared with the known ones. In this sense, they both improve and generalize previously known bounds. Further, optimal codes are constructed, whose length is order-optimal with respect to the new upper bounds. Notably, the length of the codes is super-linear in the alphabet size.

Locally repairable codes are desirable for distributed storage systems to improve the repair efficiency. In this paper, a new combination of codes with locality and codes with multiple disjoint repair sets (also called availability) is introduced. Accordingly, a Singleton-type bound is derived for the new code, which contains those bounds in [9], [20], [28] as special cases. Optimal constructions are proposed with respect to the new bound. In addition, these constructions can also generate optimal codes with multiple disjoint repair sets with respect to the bound in [28], which to the best of our knowledge, are the first explicit constructions that can achieve the bound in [28].

In the literature, all the known high-rate MDS codes with the optimal repair bandwidth possess a significantly large sub-packetization level, which may prevent the codes to be implemented in practical systems. To build MDS codes with small sub-packetization level, existing constructions and theoretical bounds imply that one may sacrifice the optimality of the repair bandwidth. Partly motivated by the work of Tamo et al. (IEEE Trans. Inform. Theory, 59(3), 1597-1616, 2013), in this paper, we present a powerful transformation that can greatly reduce the sub-packetization level of any MDS codes with respect to the same code length n. As applications of the transformation, four high-rate MDS codes having both small sub-packetization level and near optimal repair bandwidth can be obtained, where two of them are also explicit and the required field sizes are comparable to the code length n.

Optimal locally repairable codes with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds both improve and generalize previously known bounds. Optimal codes are constructed, whose length is order optimal when compared with the new upper bounds. The length of the codes is super linear in the alphabet size.

The optimal storage-computation tradeoff is characterized for a MapReduce-like distributed computing system with straggling nodes, where only a part of the nodes can be utilized to compute the desired output functions. The result holds for arbitrary output functions and thus generalizes previous results that restricted to linear functions. Specifically, in this work, we propose a new information-theoretical converse and a new matching coded computing scheme, that we call coded computing for straggling systems (CCS).

Big data mining-driven disease risk prediction has become one of the important topics in the field of e-healthcare. However, without the security and privacy assurances, disease risk prediction cannot continue to flourish. To address this challenge, in this paper, an efficient and privacy-preserving disease risk prediction scheme for e-healthcare is proposed, hereafter referred to as EPDP. Compared with the up-to-date works, the proposed EPDP comprehensively achieves two phases of disease risk prediction, i.e., disease model training and disease prediction, while ensuring the privacy preservation. Specifically, a super-increasing sequence is combined with a homomorphic cryptographic algorithm to efficiently extract the symptom set of each disease in the phase of disease model training. Bloom filter technique is introduced to compute the prediction result in the phase of disease risk prediction. Besides, extensive performance evaluations demonstrate that our proposed EPDP attains outstanding efficiency advantage over the state-of-the-art in terms of both computational and communication overheads, and hence our EPDP is more suitable for real-time e-healthcare, especially medical emergency.

Locally repairable codes are desirable for distributed storage systems to improve the repair efficiency. In this paper, a connection between locally repairable codes with multiple disjoint repair sets and packings is derived under the condition that each repair set contains exactly one check symbol. Particularly, conditions under which an optimal locally repairable code corresponds to a packing are also characterized. As an application of this connection, some optimal locally repairable codes can be obtained by packings. Specifically, two constructions of locally repairable codes are proposed which not only generalize some known explicit constructions but also give optimal locally repairable codes with flexible new parameters.

Coded caching scheme recently has become quite popular in the wireless network, since the maximum transmission amount R reduces effectively during the peak-traffic times. To realize a coded caching scheme, each file must be divided into F packets, which usually increases the computation complexity of a coded caching scheme. So we prefer to design a scheme with R and F as small as possible in practice. However, there exists a tradeoff between R and F. In this paper, we generalize the schemes constructed by Shangguan et al. (IEEE TRANSACTIONS ON INFORMATION THEORY, 64, 5755-5766, 2018) and Yan et al. (IEEE TRANSACTIONS ON INFORMATION THEORY 63, 5821-5833, 2017), respectively. These two classes of schemes have a wider range of application due to the more flexible memory size than the original ones. By comparing with the previous known deterministic schemes, our new schemes have advantages on R or F.

As a kind of erasure code, piggybacking has been applied in practice since it can significantly reduce the repair bandwidth of distributed storage systems. Currently, several efficient piggybacking designs have been proposed. In this paper, we propose a more efficient “one-to-one” piggybacking design (OOP) to further reduce the repair bandwidth. Different from the existing piggybacking designs, OOP adopts a simple encoding principle that one parity node only piggybacks symbols from one substripe. Particularly, OOP takes into account the efficient repair of systematic nodes and parity nodes simultaneously. It is shown that for OOP design, the optimal number of substripes is (√r-1+r-1), the average repair bandwidth ratio of systematic nodes can be as low as 2√r-1+1/2√r-1+r, and the average repair bandwidth ratio of parity nodes reaches √r-1+r-1/r + (r-1)2-√(r-1)3rk). In contrast to the existing piggybacking designs, OOP can further reduce the repair bandwidth of both system nodes and parity nodes.

Ji et al. (IEEE TRANSACTIONS ON INFORMATION THEORY, 62(2): 849-869, 2016) first studied coded caching in device-to-device (D2D) networks, and proposed a D2D coded caching scheme, which is referred to as the JCM scheme. In practice, we prefer to design a scheme with its two important targets, i.e., the rate (the maximal total amount of transmission) and packet number F, as small as possible. In this paper, we first propose a simple array called D2D placement delivery array (DPDA) to characterize the placement phase and the delivery phase in D2D networks. Consequently, some D2D coded caching schemes can be realized by an appropriate DPDA. Second, a lower bound on the rate of a DPDA is derived. And, we show that the JCM scheme achieves our lower bound. However, it is well known that its packet number F increases exponentially with the number of users K. So, we propose two classes of new schemes by constructing DPDAs. One reduces the packet number exponentially with K compared with the JCM scheme while keeping the rate near to our lower bound. The other further reduces F to increasing sub-exponentially with K.

In many applications, including integer-forcing linear multiple-input and multiple-output (MIMO) receiver design, one needs to solve a successive minima problem (SMP) on an n-dimensional lattice to get an optimal integer coefficient matrix A* ∈ Zn×n. In this paper, we first propose an efficient optimal SMP algorithm with an O(n2) memory complexity. The main idea behind the new algorithm is it first initializes with a suitable suboptimal solution, which is then updated via a novel algorithm with only O(n2) flops in each updating, until A* is obtained. Different from existing algorithms which find A* column by column through using a sphere decoding search strategy n times, the new algorithm uses a search strategy once only. We then rigorously prove the optimality of the proposed algorithm. Furthermore, we theoretically analyze its complexity. In particular, we not only show that the new algorithm is Ω(n) times faster than the most efficient existing algorithm with polynomial memory complexity, but also assert that it is even more efficient than the most efficient existing algorithm with exponential memory complexity. Finally, numerical simulations are presented to illustrate the optimality and efficiency of our novel SMP algorithm.

In last ISIT, we reported a generic transformation on maximum distance separable (MDS) codes, which can convert any non-binary (k+r, k) MDS code into another (k+r, k) MDS code such that an arbitrarily chosen r nodes will have the optimal repair bandwidth and the optimal rebuilding access by modifying their data. However, the resultant code thus obtained is no longer in a systematic form if we wish to optimal repair r systematic nodes, and another linear transformation is needed to convert it into one, which may break the inherent simplicity in the decoding and repair procedure. In this work, we propose an alternative generic transformation to solve this issue. In the alternative generic transformation, any r systematic nodes can be optimally repaired with their data keeping unchanged through instead modifying the data on the r parity nodes. As a result, by applying multiple times the two transformations in combination, we can directly obtain systematic MDS codes with optimal rebuilding access for all nodes or for a subset of nodes from any non-binary scalar MDS codes, which have the optimal sub-packatization level as well.

Recently, placement delivery array (PDA) was formulated to describe the placement and delivery phases with a single array for centralized coded caching scheme in an error-free shared link. In this paper, we explore PDA characterizations for two other models: device-to-device (D2D) network and distributed computing system. The inherent connections between these systems and the shared link caching system are displayed through PDA, which allows us to transform the PDA based schemes originally designated for shared link to those networks. As a result, combining with existing constructions, we can obtain schemes requiring low subpacketization level for D2D network or smaller number of files for distributed computing system.

Heterogeneous computing powered by remote clouds and local fogs is a promising technology to improve the performance of user terminals in the Internet of Things. In this paper, two semi-Markov decision process (SMDP)-based coordinated virtual machine (VM) allocation methods are proposed to balance the tradeoff between the high cost of providing services by the remote cloud and the limited computing capacity of the local fog. We first present a model-based planning method in which it is necessary to train the state transition probabilities and the expected time intervals between adjacent decision epochs. To facilitate training them, the SMDP is degraded into a continuous-time Markov decision process (CTMDP) in which the service requests and ongoing service completions follow a continuous-time Markov chain. The relative value iterative algorithm for the CTMDP is used to find an asymptotically optimal VM allocation policy. In addition, we also propose a model-free reinforcement learning (RL) method, where an optimal coordinated VM allocation policy is approximated by learning from the states and rewards of feedback. The simulation results show that the performance of the model-free RL method can converge to a level similar to that of the model-based planning method and outperform the greedy VM allocation method.

Recently, it has been shown that the time-varying multiple-access channel (MAC) with perfect channel state information (CSI) at the receiver and delayed feedback CSI at the transmitters can be modeled as the finite state MAC (FS-MAC) with delayed state feedback, where the time variation of the channel is characterized by the statistics of the underlying state process. To study the fundamental limit of the secure transmission over multi-user wireless communication systems, we re-visit the FS-MAC with delayed state feedback by considering an external eavesdropper, which we call the finite state multiple-access wiretap channel (FS-MAC-WT) with delayed feedback. The main contribution of this paper is to show that taking full advantage of the delayed channel output feedback helps to increase the secrecy rate region of the FS-MAC-WT with delayed state feedback. Moreover, by a degraded Gaussian fading example, we show the effects of feedback delay and channel memory on the secrecy sum rate of the FS-MAC-WT with delayed feedback.

Up to now, many (k + r, k, N) minimum-storage regenerating (MSR) codes with k information nodes, r parity nodes, and node capacity N have been proposed. However, most of them are constructed over a relatively large finite field. In this paper, we propose three high-rate MSR codes over small finite fields. First, the new MSR code C1with the optimal access property for all nodes is constructed over small finite field Fq, for example q = 3 for even r or q ≥ r + 1 for odd r, which is much smaller than that of the known one given by Ye and Barg. Further, considering to reduce the node capacity, another new MSR code C2over Fqwith q ≥ r + 2 is generated based on C1, which can effectively reduce the node capacity of C1by a factor of rr-1. However, only the first k nodes of C2have the optimal access property. Therefore, the new MSR code C3over Fqwith q ≥ r + 2 which has the optimal access property for all nodes is proposed by modifying C2. Notably, in contrast to C1, the node capacity of C3is decreased by a factor of rr-2.

Being able to provide a relatively easy and inexpensive way to collect data, portable readers have gained increasing popularity in wide-ranging RFID applications. In order to maximize the reader’s battery life, efficient tag identification protocols are of paramount importance in large-scale passive radio frequency identification (RFID) systems. This paper proposes a time- and energy-aware protocol based on$M$-ary collision tree (MCT) for efficient RFID tag identification. Thanks to Manchester encoding, the proposed MCT protocol recursively divides colliding tags into$M$subsets with at least two nonempty ones according to the information of$\log _2 M$colliding bits. Through the new MCT recognition process, MCT can effectively identify all the tags within its reading range. Theoretic analysis demonstrates that it takes the proposed MCT protocol fewer numbers of collision slots and message bits to identify all the tags, which reduces not only the identification time but also the energy cost. Simulation results are also presented to show that compared with other benchmark works, the proposed MCT protocol is able to reduce the average identification time and energy cost by at least 16.12% and 15.73%, respectively.

We propose a generic transformation that can convert any nonbinary (n = k + r, k) maximum distance separable (MDS) code into another (n, k) MDS code over the same field such that: 1) some arbitrarily chosen r nodes have the optimal repair bandwidth and the optimal rebuilding access; 2) for the remaining k nodes, the normalized repair bandwidth and the normalized rebuilding access (over the file size) are preserved; and 3) the sub-packetization level is increased only by a factor of r. Two immediate applications of this generic transformation are then presented. The first application is that we can transform any nonbinary MDS code with the optimal repair bandwidth or the optimal rebuilding access for the systematic nodes only, into a new MDS code which possesses the corresponding repair optimality for all nodes. The second application is that by applying the transformation multiple times, any nonbinary (n, k) scalar MDS code can be converted into an (n, k) MDS code with the optimal repair bandwidth and the optimal rebuilding access for all nodes, or only a subset of nodes, whose sub-packetization level is also optimal.

Binary sequences with low odd correlation have important applications in communication systems to reduce interference. In this paper, using the interleaving technique, we present a generic connection between binary sequences with low odd correlation and quaternary sequences with low even correlation. As a result, some new binary sequences with optimal odd auto-correlation magnitude are obtained. Besides, two sets consisting of 2n+1 binary sequences of period 2(2n-1) with the maximum odd correlation magnitude 2((n+1)/2)+ 2 are derived, which are the first two optimal classes of binary sequence sets achieving the Sarwate bound on the odd correlation magnitude in the literature.

In a mobile RFID system, a large number of tags move in and out of the system continuously, so that the reader has very limited time to recognize all the tags. As a result, the effective and efficient identification of tags in mobile environments is a more challenging problem compared to conventional static RFID systems. In this paper, we propose an efficient bit-detecting (EBD) protocol to accelerate the reading process of large-scale mobile RFID systems. In these systems, some previously recognized tags, i.e., known tags, may stay in the reader's reading range for two consecutive reading cycles, and some unknown tags may newly participate in the current reading cycle. In the proposed EBD protocol, a new bit monitoring method is proposed to detect the presence of known tags using a small number of slots, and to retrieve their IDs from the back-end database. Next, an$M$-ary bit-detecting tree recognition method is proposed to rapidly recognize unknown tags without generating any idle slots. This new protocol is shown to perform better than existing methods reported in the literature. Both theoretic and simulation results are present to demonstrate that the proposed protocol is superior to existing protocols in terms of lower time cost.

The integer-forcing (IF) linear multiple-input and multiple-output (MIMO) receiver is a recently proposed suboptimal receiver which nearly reaches the performance of the optimal maximum likelihood receiver for the entire signal-to-noise ratio (SNR) range and achieves the optimal diversity multiplexing tradeoff for the standard MIMO channel with no coding across transmit antennas in the high SNR regime. The optimal integer coefficient matrix A* ϵ ZNt×Ntfor IF maximizes the total achievable rate, where Nt is the column dimension of the channel matrix. To obtain A*, a successive minima problem (SMP) on an Nt-dimensional lattice that is suspected to be NP-hard needs to be solved. In this paper, an efficient exact algorithm for the SMP is proposed. For efficiency, our algorithm first uses the LLL reduction to reduce the SMP. Then, different from existing SMP algorithms which form the transformed A*column by column in Ntiterations, it first initializes with a suboptimal matrix which is the Nt× Ntidentity matrix with certain column permutations that guarantee this suboptimal matrix is a good initial solution of the reduced SMP. The suboptimal matrix is then updated, by utilizing the integer vectors obtained by employing an improved Schnorr-Euchner search algorithm to search the candidate integer vectors within a certain hyper-ellipsoid, via a novel and efficient algorithm until the transformed A*is obtained in only one iteration. Finally, the algorithm returns the matrix obtained by left multiplying the solution of the reduced SMP with the unimodular matrix that is generated by the LLL reduction. Simulation results show the optimality of our novel algorithm and indicates that the new one is much more efficient than existing optimal algorithms.

We propose a generic transformation on maximum distance separable (MDS) codes, which can convert any non-binary (k+r, k) MDS code into another (k+r, k) MDS code with the following properties: 1) An arbitrarily chosen r nodes will have the optimal repair bandwidth and the optimal rebuilding access, 2) the repair bandwidth and rebuilding access efficiencies of all other nodes are maintained as in the code before the transformation, 3) it uses the same finite field as the code before the transformation, and 4) the sub-packetization is increased only by a factor of r. As two immediate applications of this powerful transformation, we show that 1) any non-binary MDS code with optimal repair bandwidth, or optimal rebuilding access, for only systematic nodes can be converted into an MDS code with the corresponding repair optimality for all nodes; and 2) any non-binary scalar MDS code can be converted to an MDS code with optimal repair bandwidth and rebuilding access for all nodes, or to an MDS code with optimal rebuilding access for all systematic nodes and moreover with the optimal sub-packatization, by applying the transformation multiple times.

Radio frequency identification (RFID) technology has been employed in wide-raging application domains. In most RFID applications, time-efficient identification of missing tags is one of the most fundamental objectives, especially for asset management and anti-theft purposes. In this paper, we propose a time-efficient pair-wise collision-resolving missing tag identification (PCMTI) protocol for large-scale RFID systems. In the protocol, two novel strategies, i.e., the pair-reply and two-collision slot (i.e., a slot with two exact tag responses) resolving strategies, are proposed. The pair-reply strategy can verify two tags in one short response slot simultaneously, while the two-collision slot resolving strategy further increases the number of tags verified in each frame. Both theoretical analysis and simulated results are presented to demonstrate the superiority of the proposed PCMTI protocol, which is capable of outperforming the state-of-the-art comparative protocols with at least a 30% reduction in average identification time for verifying one tag.

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.

A family IP8of sequences over the 8-ary quadrature-pulse amplitude modulation (Q-PAM) constellation with asymptotically optimal correlation property was presented by Anand and Kumar in 2008. This is the only known family of sequences over the quadrature amplitude modulation (QAM) constellation whose correlation magnitude asymptotically achieves the Welch bound. In this paper, a larger family IP8newof sequences with the same correlation magnitude as that of IP8but double family size is obtained. Moreover, the correlation distributions of IP8and IP8neware also determined for two particular cases in terms of the property of a class of exponential sums over Galois rings. It is also shown that more classes of QAM and Q-PAM sequences with low correlation and larger family size can be obtained from our approach.

Rotation symmetric bent functions and their generation two-rotation symmetric bent functions are two classes of cryptographically significant Boolean functions. However, few constructions have been presented in the literature, which either have restriction on integer n or have algebraic degree no more than 4. In this paper, for any even integer n ≥ 4, three classes of bent functions are presented respectively. Most notably, the proposed n-variable rotation symmetric bent functions and two-rotation symmetric bent functions can have any possible algebraic degree ranging from 2 to n/2. Besides, we obtain bent idempotent functions with the maximal algebraic degree n/2.

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.

Caching is a promising solution to satisfy the ever-increasing demands for the multi-media traffics. In caching networks, coded caching is a recently proposed technique that achieves significant performance gains over the uncoded caching schemes. However, to implement the coded caching schemes, each file has to be split into F packets, which usually increases exponentially with the number of users K. Thus, designing caching schemes that decrease the order of F is meaningful for practical implementations. In this paper, by reviewing the Ali-Niesen caching scheme, the placement delivery array (PDA) design problem is first formulated to characterize the placement issue and the delivery issue with a single array. Moreover, we show that, through designing appropriate PDA, new centralized coded caching schemes can be discovered. Second, it is shown that the Ali-Niesen scheme corresponds to a special class of PDA, which realizes the best coding gain with the least F. Third, we present a new construction of PDA for the centralized coded caching system, wherein the cache size M at each user (identical cache size is assumed at all users) and the number of files N satisfies M/N = 1/q or (q - 1)/q (q is an integer, such that q ≥ 2). The new construction can decrease the required F from the order O(eK·((M/N) ln(N/M)+(1-(M/N)) ln (N/(N-M))) of Ali-Niesen scheme to O(eK·(M/N) ln(N/M)) or O(eK·(1-(M/N)) ln(N/(N-M))), respectively, while the coding gain loss is only 1.

In this paper, we study a buffer-aided collaborative relaying framework for cooperative communication system composed of one source node, multiple half-duplex DF relays with buffers, and one destination node. A two-phase adaptive relaying scheme is proposed,i.e., the source transmits data and the relay buffers receive data in the first phase, and all relays collaboratively transmit the buffered data to the destination node in the second phase. To achieve higher temporal and spatial diversity gains, time slots are dynamically allocated according to the state information of wireless channel (CSI), each node’s energy consumption (ESI), and each relay’s buffer (BSI). Lyapunov optimization theory is utilized to maximize the average achievable throughput under buffer stability and power consumption constraints, and an online buffer-energy-aware adaptive (BEAA) scheduling scheme is proposed to jointly consider relay selection, power allocation, and time allocation. It is disclosed that the proposed BEAA scheduling scheme is able to achieve a higher average network throughput by adapting the transmissions according to the CSI, ESI, and BSI. Moreover, it is unveiled that there exists inherent tradeoff among the transmission delay, power consumption, and the achievable throughput. Extensive simulations are presented to validate the efficiency of the proposed adaptive collaborative relaying protocol.

In this paper, we consider wireless-powered relay network consisting of one source, one wireless powered relay and one sink, where the relay is provisioned with both data buffer and energy storage. Firstly, a novel time-switching transmission scheme is proposed to divide the transmission from source to sink into three phases, namely, the relay energy harvesting phase, the relay receiving phase and the relay forwarding phase. And the achievable end to end (E2E) throughput and optimal timeswitching parameter are derived. Secondly, the transmission scheme is reformulated as a stochastic optimization problem to take into considerations of all the dynamic characteristics of the energy harvesting status, the data buffer status and the underlying time-varying channel conditions. By employing the Lyapunov optimization theory, an online buffer-energy aware adaptive transmission scheme is proposed to adjust the transmission at both source and relay according to the channel state information(CSI), the data buffer state information (BSI) and the energy state information (ESI). Moreover, the tradeoff between the average E2E throughput and the transmission delay is presented to show the great potential of the proposed adaptive transmission design to improve the achievable transmission throughput. Finally, simulations are presented to validate the efficiency of the proposed relaying protocols.

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.

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.

Frequency-hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. Strictly optimal FHSs are those FHSs with optimal partial Hamming autocorrelation irrespective of the correlation window length. In this paper, strictly optimal FHSs are investigated from a combinatorial approach. A generic connection between strictly optimal FHSs and disjoint cyclic perfect Mendelsohn difference families is established. By virtue of this connection, new strictly optimal FHSs are generated from some disjoint CPMDFs. These strictly optimal FHSs have new parameters not covered in the literature.

In this paper, we reinterpret the (k+2, k) zigzag code in coding matrix and then propose an optimal exact repair strategy for its parity nodes, whose repair disk I/O approaches a lower bound derived in this paper.

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.

Optical orthogonal codes (OOCs) are widely used as spreading codes in optical fiber networks. In this paper, a bound on the code size of 2-D OOCs with both at most one-pulse per wavelength (AM-OPPW) and at most one-pulse per time slot (AM-OPPTS) is derived. Accordingly, two constructions of optimal 2-D OOCs with both AM-OPPW and AM-OPPTS are proposed via the generalized cyclotomic classes. Furthermore, optimal 2-D OOC with AM-OPPW can be also constructed by adding more codewords into the 2-D OOCs with both AM-OPPW and AM-OPPTS.

In this paper, we present a generic framework for constructing systematic minimum storage regenerating codes with two parity nodes based on the invariant subspace technique. Codes constructed in our framework not only contain some best known codes as special cases, but also include some new codes with key properties, such as the optimal access property and the optimal update property. In particular, for a given storage capacity of an individual node, one of the new codes has the largest number of systematic nodes and two of the new codes have the largest number of systematic nodes with the optimal update property.

The newly presented (k + m, k) Hadamard minimum storage regenerating (MSR) codes are a class of high rate storage codes with optimal repair property for single node failure. In this paper, we propose a new simple optimal repair strategy for (k + m, k) Hadamard MSR codes, which can considerably reduce the computation compared with the original one during the node repair.

Piggybacking is an efficient method to decrease the repair bandwidth of maximum distance separable codes. In this paper, in order to reduce the repair bandwidth of parity nodes of the known minimum storage regenerating (MSR) codes with high rate, which is usually the whole amount of the original data, i.e., the maximal, a new systematic piggybacking design is proposed through an in-depth analysis of the design of piggybacking. As a result, new MSR codes are obtained with almost optimal repair bandwidth of parity nodes while retaining the optimal repair bandwidth of systematic nodes. Furthermore, MSR codes with balanced download during node repair process are presented based on the new piggybacking design.

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.

New quadratic bent functions in polynomial form are constructed in this paper. The constructions give new Boolean bent, generalized Boolean bent and p-ary bent functions. Based on Z4-valued quadratic forms, a simple method provides several new constructions of generalized Boolean bent functions. From these generalized Boolean bent functions a method is presented to transform them into Boolean bent and semi-bent functions. Moreover, many new p-ary bent functions can also be obtained by applying similar methods.

In this paper, a new construction of zero-difference balanced functions defined on is given, where is an odd positive integer. Based on the generic constructions proposed by Ding, optimal constant composition codes and perfect difference systems of sets with new parameters can be generated from the zero-difference balanced functions constructed in this paper.

In this paper, a class of functions from Niho exponents with four-valued Walsh transform is obtained for any prime by a uniform method, and the distribution of the Walsh transform values is also completely determined. In particular, this class of functions is proven to be bent for a special case. Although it is shown that the obtained bent functions are equivalent to the Leander-Kholosha's class of bent functions, a direct and much simpler proof for the bentness of this kind of Niho functions is provided.

Several new classes of binary andp-ary regular bent functions are obtained in this paper. The bentness of all these functions is determined by some exponential sums over finite fields, most of which have close relations with the well-known Kloosterman sums.

In this paper, we revisit a method to produce binary sequences using the most significant bit map fromZ4to the binary field. This method is useful for the construction of binary sequences with low correlation and large family size. There may be more cases where starting withZ4could help researchers design new low correlation sequences for code-division multiple access application.

We present necessary and sufficient conditions for a Boolean function to be a negabent function for both an even and an odd number of variables, which demonstrates the relationship between negabent functions and bent functions. By using these necessary and sufficient conditions for Boolean functions to be negabent, we obtain that the nega spectrum of a negabent function has at most four values. We determine the nega spectrum distribution of negabent functions. Further, we provide a method to construct bent-negabent functions innvariables (neven) of algebraic degree ranging from 2 to [(n)/2], which implies that the maximum algebraic degree of ann-variable bent-negabent function is equal to [(n)/2]. Thus, we answer two open problems proposed by Parker and Pott and by Stănică et al.

In 2008, Cusick et al conjectured that certain elementary symmetric Boolean functions of the form σ(2t+1)l-1, (2t) are the only nonlinear balanced ones, wheret,lare any positive integers, and σn,d=⊕1≤( i1)d≤ n xi1xi2⋯xid) for positive integersn, 1 ≤d≤n. In this paper, by analyzing the weight of σn,(2t) and σn, d, we prove that wt σn,dn-1holds in most cases, and so does the conjecture. According to the remainder modulo 4, we also consider the weight of σn, dfrom two aspects: n ≠ 3(mod 4) and n not ≡ 3(mod 4). In particular, our results not only cover the most known results, but also contain some new cases. Thus, we can reduce the conjecture to few remaining cases. We do not fully solve the conjecture, but we also consider the weight of σn, (2t+2s) and also give some experimental results on it.

Inspired by the previous work of Tu and Deng, we propose two infinite classes of Boolean functions of 2kvariables wherek≥ 2. The first class contains unbalanced functions having high algebraic degree and nonlinearity. The functions in the second one are balanced and have maximal algebraic degree and high nonlinearity (as shown by a lower bound that we prove; as a byproduct we also prove a better lower bound on the nonlinearity of the Carlet-Feng function). Thanks to a combinatorial fact, first conjectured by the authors and later proved by Cohen and Flori, we are able to show that they both possess optimal algebraic immunity. It is also checked that, at least for numbers of variablesn≤ 16, functions in both classes have a good behavior against fast algebraic attacks. Compared with the known Boolean functions resisting algebraic attacks and fast algebraic attacks, both of them possess the highest lower bounds on nonlinearity. These bounds are however not enough for ensuring a sufficient nonlinearity for allowing resistance to fast correlation attack. Nevertheless, as for previously found functions with the same features, there is a gap between the bound that we can prove and the actual values computed for bounded numbers of variables (n≤ 38). Moreover, these values are very good. The infinite class of functions we propose in Construction 2 presents, among all currently known constructions, the best provable tradeoff between all the important cryptographic criteria.

In this paper, a new generalized cyclotomy with respect to a positive odd integer is introduced, and a construction of frequency hopping sequence sets and two constructions of frequency hopping sequences are proposed as its applications. The frequency hopping sequence sets and frequency hopping sequences obtained in this paper can be optimal with respect to the Peng-Fan bound and Lempel-Greenberger bound, respectively. Further, the length of sequences in the optimal frequency hopping sequence sets can be any odd integer larger than 3. Some of them have new parameters.

New quadratic bent functions in polynomial forms are constructed in this paper. The constructions give new boolean bent and generalized boolean bent functions. Based on Z4-valued quadratic forms, a simple method provides several new constructions of generalized boolean bent functions. From these generalized boolean bent functions a method is presented to transform them into binary bent and semi-bent functions.

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, we propose an interleaving construction of new sets of frequency hopping sequences from the known ones. By choosing suitable known optimal frequency hopping sequences and sets of frequency hopping sequences and then recursively applying the proposed construction, optimal frequency hopping sequences and sets of frequency hopping sequences with new parameters can be obtained.

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.

The conventional binary complementary pairs exist only for very limited lengths, while binaryZ-complementary pairs exist for many more lengths. In this letter, an upper bound on zero correlation zone (ZCZ) width of binaryZ-complementary pairs of odd length is established. The existence conjecture of binaryZ-complementary pairs with ZCZ widths 2, 3, 4, 5 and 6 is completely solved, and a new recursive construction of binaryZ-complementary pairs is proposed.

Three classes of binary sequences of period 4Nwith optimal autocorrelation value/magnitude have been constructed by Tang and Gong based on interleaving certain kinds of sequences of periodN, i.e., the Legendre sequence, twin-prime sequence and generalized GMW sequence. In this paper, by means of sequence polynomials of the underlying sequences, the properties of roots of the corresponding sequence polynomials of the interleaved sequences with period 4Nand optimal autocorrelation value/magnitude are discussed in the splitting field ofxN-1 . As a consequence, both the minimal polynomials and linear complexities of these three classes of sequences are completely determined except for the case of the sequences obtained from the generalized GMW sequences. For the latter, the minimal polynomial and linear complexity can be specially obtained if the sequence is constructed based onm-sequences instead of generalized GMW sequences.

Let$m$and$k$be positive integers with$m/{\rm gcd}(m,k)$being odd, for$a\in \BBR$and$b\in \BBL$, the exponential sum$\sum_{x\in \BBL}i^{Tr(ax+2bx^{2^{k}+1})}$is studied systematically in this paper, where$i=\sqrt {-1}$,$\BBR =\BBG \BBR (4,m)$is a Galois ring,$\BBL$is the Teichmüller set of$\BBR$and$Tr(\cdot)$is the trace function from the Galois ring$\BBR$to$\BBZ_{4}$. Through the discussions on the solutions of certain equations and the newly developed theory of$\BBZ_{4}$-valued quadratic forms, the distribution of the exponential sum is completely determined. As its applications, we can determine the Lee weight and Hamming weight distributions of a class of codes${\cal C}^{k}$over$\BBZ_{4}$and the correlation distribution of a quaternary sequence family${\cal U}^{k}$, respectively. Furthermore, the Hamming weight distributions of the binary codes obtained from${\cal C}^{k}$under the most significant bit (MSB) and Gray maps are also determined. For the MSB map sequences of${\cal U}^{k}$, the nontrivial maximal correlation value is given and the correlation distribution is determined for the Gray map sequences of${\cal U}^{k}$. It should be noted that the distribution of the exponential sum for the case$\gcd (m,k)\ne 1$is obtained for the first time, and then the corresponding codes and sequences are novel.

Recently, new optimal Families${\cal S}$and${\cal U}$of quaternary sequences have been presented, and the optimal binary sequence Family${\cal V}$obtained from Family${\cal S}$under Gray map has been investigated as well. The two sequence Families${\cal U}$and${\cal V}$are optimal with respect to the well-known Sidelnikov bound and Welch bound, but their exact correlation distributions are not known until now. In this paper, their exact correlation distributions are completely determined in some cases by making use of exponential sums and the theory of${\bf Z}_4$-valued quadratic forms.

In this paper, a simple but generic method is proposed for transforming any family of quaternary sequences, with low correlation, of any odd periodNto another family of quaternary sequences of period 2N with low correlation. As an application of the generic method to sequence Family A, a new optimal quaternary sequence family with length 2(2n-1), family size 2n+1 , and maximal nontrivial correlation value 2[(n+1)/2]+2, wherenis an odd integer, is obtained. Most notably, unlike all the known optimal quaternary sequence families, the new family has a unique property that the odd integers 1, 3 and the even integers 0, 2 are allocated alternatively in all the sequences.

In this paper, we derive a new bound on maximum nontrivial Hamming correlation of frequency hopping (FH) sequences from the Singleton bound in error correcting code literature, and we discuss the relation between the new bound and the known ones on FH sequences. Further, we construct two classes of FH sequences from punctured Reed–Solomon codes and one class of FH sequences from polynomial functions, which meet the new bound.

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 paper we revisit a method to produce binary sequences using a non-linear polynomial mapping from Z4to the binary field. This method is useful to construct binary sequences with low correlation with large sizes. We conclude that Z4may be the best starting ring to generate large binary families for code-division multiple access (CDMA) application.

Key distribution plays an important role in wireless sensor networks (WSNs), for information must be kept secure, even in an environment with limited storage ability and low data processing speed. However, it is a challenge to work in such a harsh requirement environment, the traditional key management scheme such as key distribution center (KDC) and public key cannot be used. Key pre-distribution is a good way to address this problem in WSNs, and while several schemes have been presented before, they cannot perform well in a large scale network. In this paper, we first use node's deployment knowledge to propose a hexagon scheme, and then combine it with the bivariate-polynomial to realize a new key agreement scheme. The simulation results show that our new scheme can be used in a large scale network, is attack resistant with low memory overhead, and achieves good network connectivity. We also introduce the measure how to effectively use key pre-distribution skills in the routing protocols.

In this letter, we introduce a simple approach to generate Z-periodic complementary set (ZPCS) by performing phase shift operation on periodic complementary sequence set (PCS). Favorable correlation properties of ZPCS enable its applications not only in MIMO channel estimation as optimal training sequences, but also in MC-CDMA system as spreading sequences to efficiently handle multipath interference (MI) and multiple access interference (MAI). Our approach provides flexible choices for zero correlation zone (ZCZ) length and set size. The resultant ZPCS is optimal with respect to the theoretical bound.

Binary sequences with low correlation have applications in communication systems and cryptography. Though binary sequences with optimal autocorrelation were constructed in the literature, no pair of binary sequences with optimal autocorrelation are known to have also best possible cross correlation. In this paper, new bounds on the cross correlation of binary sequences with optimal autocorrelation are derived, and pairs of binary sequences having optimal autocorrelation and meeting some of these bounds are presented. These new bounds are better than the Sarwate bounds on the cross correlation of binary sequences with optimal autocorrelation.

In communication systems, frequency hopping spread spectrum and direct sequence spread spectrum are two main spread coding technologies. Frequency hopping sequences are used in FH-CDMA systems. In this paper, an earlier idea of constructing optimal sets of frequency hopping sequences is further investigated. New optimal parameters of sets of frequency hopping sequences are obtained with subcodes of the Reed-Solomon codes. Optimal sets of frequency hopping sequences are constructed with a class of irreducible cyclic codes. As a byproduct, the weight distribution of a subclass of irreducible cyclic codes is determined.

Sequences with optimal autocorrelation property are needed in certain communication systems and cryptography. In this paper, a construction of balanced quaternary sequences with periodN≡ 2 (mod 4) and optimal autocorrelation value and a construction of almost balanced binary sequences with periodN≡ 0 (mod 4) and optimal autocorrelation value are presented. Both constructions are a generalization of earlier ones.

In this paper, two types of multiple binary zero correlation zone (ZCZ) sequence sets are constructed: 1. Each set is a binary(2n+1Zcz,2n,Zcz)-ZCZ sequence set, which is one of the best cases in the known constructions. 2. Among all the sets, the sequences still possess good cross-correlation property within the zone of lengthZ≤Zcz. In particular, the first type sequence sets have a common zero correlation zone of lengthZ, which solves the previous research problem. These multiple binary ZCZ sequence sets are suitable for multiuser environments.

In this paper, we give three new constructions of binary sequences of period AN with optimal autocorrelation value or optimal autocorrelation magnitude using N × 4 interleaved sequences. Yu and Gong recently found any binary sequence of period AN with optimal autocorrelation value constructed from an almost difference set by Arasu et al. is an N × 4 interleaved sequence for which all four columns in its N × 4 array are shift equivalent up to the complement. We found that it is not necessary that four columns are shift equivalent. Instead, it could be a pair of related sequences together with their shifts as the column sequences. The first construction is to use a generalized GMW sequence of period N = 2k- 1 and its modified version, the second construction is to use a twin prime sequence of length N = p(p + 2) and its modified version, and the third construction, a pair of Legendre sequences of period N = p (p odd prime) with their respective first terms complementary (the 2-level autocorrelation property is not needed for the Legendre sequence). The comparison with the known constructions are given. For the new sequences with optimal autocorrelation value, their corresponding new almost difference sets are also derived.

In this paper, we are concerned with Hadamard matrices with a certain noncyclic property. First we show that when the first column of a Sylvester Hadamard matrix of order 2m, m ≥ 2, a positive integer, is removed, the number of shift distinct row vectors in the matrix is given by 2m-m. Then, for m ≥ 4, we construct an infinite family of Hadamard matrices with a property that when the first column of the Hadamard matrix is removed, all the row vectors of the matrix are shift distinct. These Hadamard matrices are useful in constructing low correlation zone sequences.

In this letter, a new class of almost quadriphase sequences with a single zero element of period N, where N=1( mod 4) a prime, is presented. The new sequences have ideal autocorrelation property.

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.

In this paper, two new optimal families S and U of quadriphase sequences are presented. Compared to the family A constructed by Boztas and the family D investigated by Tang respectively, the proposed families have the same optimal correlation properties and family size, but larger linear spans.

In this paper, we present two optimal binary families of sequences of length 2n-1 and 2(2n-1) for odd integer n. They are obtained as the images of proposed optimal quaternary sequences under the most significant bit and the Gray maps. The first family has 2n+1 sequences of length 2n-1 and the identical correlation distribution to that of Gold sequences and Gold-like sequences, and the second family of sequences of length 2(2n-1) has 2nsequences and the same correlation values as those of Kerdock sequences.

An approach to generate generalized pairwise Z-complementary (GPZ) codes, which works in pairs in order to offer a zero correlation zone (ZCZ) in the vicinity of zero phase shift and fit extremely well in power efficient quadrature carrier modems, is introduced in this letter. Each GPZ code has MK sequences, each of length 4NK, where M is the number of Z-complementary mates, K is a factor to perform Walsh-Hadamard expansions, and N is the sequence length of the Z-complementary code. The proposed GPZ codes include the generalized pairwise complementary (GPC) codes as special cases.

Family A is a family of sequences of period 2n- 1 over Zi, the ring of integers modulo 4. This family has optimal correlation properties and its correlation distribution is well known. Two related families of quaternary sequences are the families B and C. These are families of sequences over Z4of period 2(2n- 1). In recent years, new families of quaternary sequences of period 2(2n- 1) have been constructed by modifying the sequence families B and C in a nonlinear way. This has resulted in a new family D of sequences of period 2(2n- 1) which has optimal correlation properties, but until now the correlation distribution of this family has not been known. In this paper, we completely determine the correlation distribution of family D by making use of properties of exponential sums.

In the literature, many constructions of zero correlation zone (ZCZ) sequences have been reported. While most of them are suboptimal with respect to the known upper bound, some constructed by Matsufuji et al. and Torii et al. respectively, are almost optimal (or even optimal). In this paper, we propose a systematic construction of almost optimal ZCZ sequence sets which generalizes the aforementioned constructions so that more flexible relationships between the set size and the sequence length are allowed. In particular, the obtained almost optimal ZCZ sequence sets of size m and length mn are new for 1 < gcd(m, n) < min(m, n). In addition, their alphabets can be binary or nonbinary since our construction is only based on interleaving perfect sequences according to a certain orthogonal matrix.

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.

In this paper, we construct two new families S and U of optimal quadriphase sequences. Compared to the family A constructed by Boztas et al and family D investigated by Tang et al respectively, the proposed families have the same optimal correlation properties and family size, but larger linear spans.

In this letter, a general construction of orthogonal variable spreading factor (OVSF) codes with zero correlation zone (ZCZ) property is presented based on orthogonal sequence sets and -complementary sets. It is shown that the proposed general construction includes the conventional binary and ternary OVSF codes as special cases and can accommodate more flexible rate assignment in direct sequence code division multiple access (DS-CDMA) systems.

In this note, by using a modification of the families B and C, we obtain a larger family of optimal quadriphase sequences, D over Z4. In contrast to the families B and C, the family D has the same length and the same maximal nontrival correlation value, but with double the size

In this correspondence, we present a family of binary 2nsequences of period 2(2n-1) where n is an integer, which can be seen as a generalization of nonlinear binary sequences obtained from Z4sequences and recently constructed GKW (Gold, Kasami, and Welch)-like sequences. The sequences have low correlations and are useful in code-division multiple-access (CDMA) communication systems and cryptography

The recently proposed loosely synchronized (LS) spreading code can in principle realize an intracell-interference-free quasi-synchronous code-division multiple-access (QS-CDMA) system by creating a wide enough interference-free window (IFW). However, the problem of minimizing intercell interference (ICI) in a cellular QS-CDMA system remains an open issue. Addressing the problem from a sequence design viewpoint, the key challenge is how to generalize the known construction of a single LS code to the design of many families of generalized LS (GLS) codes so that a desirable code family can be selected for the realization of a low-ICI cellular QS-CDMA system. Our main contribution is a systematic construction of new families of GLS codes with favorable intercode cross-correlation properties within a certain window, while maintaining the desirable IFW property. Many such code families can be obtained from our construction by choosing different Hadamard matrices and different uncorrelated complementary pairs. Their effectiveness with respect to some meaningful evaluation criteria are compared. In particular, by a simplified system bit-error rate analysis, it is demonstrated that a new GLS code family significantly outperforms the conventional scrambled LS codes.

In this paper we construct families of low correlation zone (LCZ) sequences derived from interleaved technique and Hadamard matrices. These sequences are useful in certain quasi-synchronous code-division multiple access (QS-CDMA) communication systems

In this correspondence, we present a new family of nonbinary sequences with three-level nontrivial correlations and large linear complexity. The sequences may be considered as nonlinear analogues of the well-known sequences by Trachtenberg and Helleseth. It is shown that the family is optimal with respect to the Welch bound in terms of root mean square of all nontrivial correlations. We also determine the correlation distribution of the new family.

This paper presents the generalized Udaya Sidiqi sequences which are the interleaved version of Gold like binary sequences of period satisfying the Welch bound maximum out of phase correlations. The sequences have large linear complexity and low correlations and are useful in code division multiple access (CDMA) communication systems and cryptography. A direct method to compute the correlation using the trace sequence representation and a sequence from a quadratic form are presented.

A new class of pseudonoise sequences over GF(p), based on Gordon-Mills-Welch (1962) sequences, is constructed. The sequences have the property that, in a specified zone, the out-of-phase autocorrelation and cross-correlation values are all equal to -1. Such sequences with low correlation zone (LCZ) are suitable for approximately synchronized code-division multiple-access (CDMA) system.