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In this paper, we focus on decoding nonbinary low-density parity-check (LDPC) codes in Galois fields of characteristic two via the proximal alternating direction method of multipliers (proximal-ADMM). By exploiting Flanagan/Constant-Weighting embedding techniques and the decomposition technique based on three-variables parity-check equations, two efficient proximal-ADMM decoders for nonbinary LDPC codes are proposed. We show that both of them are theoretically guaranteed convergent to some stationary point of the decoding model and either of their computational complexities in each proximal-ADMM iteration scales linearly with LDPC code’s length and the size of the considered Galois field. Moreover, the decoder based on the Constant-Weight embedding technique satisfies the favorable property of codeword symmetry. Simulation results demonstrate their effectiveness in comparison with state-of-the-art LDPC decoders. [ABSTRACT FROM AUTHOR]

Recent deep convolutional neural networks have achieved great reconstruction accuracy for single image super-resolution (SISR). Most of them, however, need to train a specific set of parameters for a single scaling factor or a particular group of scaling factors. This means, multiple sets of model parameters have to be used for different scaling factors, each of which can be already very large. In this paper, we study a new problem of fine-grained scale space learning of SISR, which uses one set of parameters while achieving varying scales. Specifically, we aim to use an arbitrary base SISR × 2 model to realize high-quality SISR for a continuous-integer spectrum of scaling factors, e.g., 2 ∼ 8 . To this end, first for the base scaling factor 2, we propose low-resolution reconstruction, blind kernel estimation and recursive error compensation, to generate three loss functions, helping to boost the training quality of the base model. Then, we cascade the boosted SISR × 2 model and extend the low-resolution reconstruction to incorporate multiple LR loss functions covering { 3 , 4 , ... , 2 n } scales. By this way, the SISR × 2 model can be effectively tuned to work well for continuous-integer scaling factors, with exactly the same set of parameters. Extensive experiments verify the capability of our approach to enable state-of-the-art methods to realize fine-grained scale space learning of SISR, with higher accuracy and much less parameters. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability and stabilization problems for T-S fuzzy systems with two additive time-varying delays. Firstly, a novel Lyapounov-Krasovskii functional (LKF) is constructed by delay-product-type functional method together with the state vector augmentation. In order to handle time-delay square terms introduced into the derivative of LKF, an extended binary quadratic function negative-determination lemma is proposed. A less conservative delay-dependent stability condition is developed since not only some new bounding technologies are employed to deal with integral terms, but also the proposed lemma is employed to dispose nonlinear time-delay terms in derivative of constructed function. Then, the corresponding controller design method for closed-loop delayed fuzzy system is derived based on parallel distributed compensation scheme. Finally, four numerical examples are given to illustrate the superiority and effectiveness of the proposed criteria. [ABSTRACT FROM AUTHOR]

Let G = (V , E) be a simple graph with vertex set as V and edge set as E. Within the framework of graph-based binary coding, a graph G is a threshold graph if and only if it can be generated by a binary code of the type 0 s 1 1 t 1 ... 0 s k 1 t k , where s i and t i are positive integers with 1 ≤ i ≤ k. This type of binary code is called a binary generating code of G. In this paper, we address a problem originally posed by Harary and Schwenk in [10] titled "Which graphs have integral spectra?" in which the main focus of our investigations lies in the Seidel Laplacian spectrum of G generated by 0 s 1 1 t 1 ... 0 s k 1 t k . We establish that all eigenvalues of G are integers and multiplicities of eigenvalues are equal to powers of bits 0 and 1 (sizes of strings of 0's and 1's) involved in a binary generating code of G. We exhibit a necessary and sufficient condition in terms of eigenvalues of the matrix associated with a graph-based G binary code to be Seidel Laplacian integral. Furthermore, for any prime p , we explore the Seidel Laplacian spectrum of zero-divisor graphs associated with the ring Z p m (where m is a positive integer) and the polynomial ring Z p [ x ] / (x p). [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel surface reconstruction method for unoriented points by establishing and solving a nonlinear equation system. By treating normals as unknown parameters and imposing the conditions that the implicit field is constant and its gradients parallel to the normals on the input point cloud, we establish a nonlinear equation system involving the oriented normals. To simplify the system, we transform it into a 0-1 integer programming problem solely focusing on orientation by incorporating inconsistent oriented normal information through PCA. We solve the simplified problem using flipping-based iterative algorithms and propose two novel criteria for flipping based on theoretical analysis. Extensive experiments on renowned datasets demonstrate that our flipping-based method with wavelet surface reconstruction achieves state-of-the-art results in orientation and reconstruction. Furthermore, it exhibits linear computational and storage complexity by leveraging the orthogonality and compact support properties of wavelet bases. The source code is available at https://github.com/mayueji/FISR_code. • We propose a novel surface reconstruction method by establishing and solving nonlinear equation systems numerically. • To tackle the nonlinear equation system, we innovatively propose the gradient-based criterion and value-based criterion. • Our method achieves state-of-the-art performance in orientation and reconstruction. Its linear complexity overcomes computational and storage bottlenecks. [ABSTRACT FROM AUTHOR]

Cross-modal hashing has attracted a lot of attention and achieved remarkable success in large-scale cross-media similarity retrieval applications because of its superior computational efficiency and low storage overhead. However, constructing similarity relationship among samples in cross-modal unsupervised hashing is challenging because of the lack of manual annotation. Most existing unsupervised methods directly use the representations extracted from the backbone of their respective modality to construct instance similarity matrices, leading to inaccurate similarity matrices and resulting in suboptimal hash codes. To address this issue, a novel unsupervised hashing model, named Structure-aware Contrastive Hashing for Unsupervised Cross-modal Retrieval (SACH), is proposed in this paper. Specifically, we concurrently employ both high-dimensional representations and discriminative representations learned by the network to construct a more informative semantic correlative matrix across modalities. Moreover, we design a multimodal structure-aware alignment network to minimize heterogeneous gap in the high-order semantic space of each modality, effectively reducing disparities within heterogeneous data sources and enhancing the consistency of semantic information across modalities. Extensive experimental results on two widely utilized datasets demonstrate the superiority of our proposed SACH method in cross-modal retrieval tasks over existing state-of-the-art methods. • We propose an informative multimodal correlation matrix construction approach. • We propose a multimodal structure-aware alignment network to bridge heterogeneous gaps. • Extensive experiments show SACH's superiority in cross-modal retrieval. [ABSTRACT FROM AUTHOR]

Session-based recommendations (SBR) aim to predict the user's next choice of items based on historical data. It is hard to access the interaction information between users and we can only analyze the user's behavioral preferences based on the current session characteristics, which makes the recommendation task in this field quite challenging. Recently, considerable research has grown up around the theme of SBR. Previous works apply attention mechanisms and Graph Neural Networks (GNN) to achieve remarkable results. However, these methods ignore two main points: one is losing sight of the specific position of items in the session; the other is to drive global preference with local preference without considering the offset of the target preference among items in the session. This paper proposes a Global Target Preference Attention Network (GTPAN) Model with position information for the session-based recommendation. We introduce a position-aware embedding module to eliminate the effect of position missing. Considering that each item in the session is potentially rich in latent information of target preference, we use a target preference attention layer to learn the target preference vector of the session. Extensive experiments on three real datasets show that the proposed GTPAN model outperforms state-of-the-art session-based recommendation methods, especially on datasets with long sessions. [ABSTRACT FROM AUTHOR]

This paper takes a fresh look at the image authentication problem and proposes an alternative framework for personalized authentication based on the hash learning technology. Conventional image authentication methods tend to provide a general authentication framework for all images with the fixed quantization strategy and fixed control parameters determined based on given limited images and attacks. However, they may suffer from more or less misjudgments in practice, not to mention performance degradation when encountering out-of-sample images. Instead of proposing a new feature extraction algorithm, a novel personalized authentication framework which incorporates the distance metric learning technology and supervised quantization strategy to the process of image authentication is proposed in this paper. The tamper detection task is reformulated as a new supervised manipulation classification problem. For each input image, various content-preserving and content-changing samples are generated automatically firstly. Then, feature representations of all samples can be obtained by existing feature extraction methods. After that, a weighted large margin for manipulation classification (WLMMC) scheme is proposed to learn an effective feature mapping space to improve the classification performance between content-changing samples and content-preserving samples. During the quantization stage, a novel supervised personalized quantization strategy (SPQ), which is motivated by the observation that different attacks have different degrees of influence on feature components, is proposed to learn more compact yet discriminative binary codes for each input image. Effectiveness of the proposed framework is qualitatively and quantitatively demonstrated on a variety of images. Extensive experiments show that the proposed framework can significantly improve the authentication performance over the state-of-the-art techniques while achieve more compact hash codes flexibly as required. [ABSTRACT FROM AUTHOR]

In this paper, we present a variable-length binary code for permutations of degree n, where n is a power of 2. The Lehmer code and its variants provide a bijection between permutations and the indexes in lexicographic ordering. They provide compression of permutations approaching Shannon bound at the expense of structural information. The variable-length code proposed in this paper has asymptotically optimal compression capability while preserving structural information of permutations. In other words, the code encodes the way a permutation is organized, and is optimal in the sense that the ratio of average codeword length and the entropy of permutations approaches 1 as n tends to infinity. The encoding and decoding are efficient. Like the Lehmer code and other enumerative codes, it is not necessary to construct look-up tables. The code is complete and satisfies the prefix condition. Furthermore, the codeword length indicates how “well shuffled” a permutation is. Permutations with longer codewords seem more “random.” An enumeration method of the variable-length code is also given by using T. Cover’s enumerative coding scheme and Schalkwijk code. This gives a different indexing from the Lehmer code. This work can be extended to the case of arbitrary $n$ in a straightforward way. [ABSTRACT FROM AUTHOR]

Based on the relaxation digital‐to‐analog converter (ReDAC) architecture and the capacitor charge/discharge function under discrete time conditions, this paper proposes a new mathematical model for the output voltage of the ReDAC to implement the unconstrained relaxation DAC (Uc‐ReDAC). The system clock calibration is not required. An adaptive probabilistic binary particle swarm optimization (AP‐BPSO) algorithm is proposed for solving the binary coding configuration problem under the Uc‐ReDAC model. Simulation results show that the 8‐bit (10‐bit) Uc‐ReDAC has an average sampling rate of 7.9 MS/s (6.76 MS/s). [ABSTRACT FROM AUTHOR]

The family of Goppa codes is one of the most interesting subclasses of linear codes. As the McEliece cryptosystem often chooses a random Goppa code as its key, knowledge of the number of inequivalent Goppa codes for fixed parameters may facilitate in the evaluation of the security of such a cryptosystem. In this paper we present a new approach to give an upper bound on the number of inequivalent extended irreducible binary Goppa codes. To be more specific, let $n>3$ be an odd prime number and $q=2^{n}$ ; let $r\geq 3$ be a positive integer satisfying $\gcd (r,n)=1$ and $\gcd \big (r,q(q^{2}-1)\big)=1$. We obtain an upper bound for the number of inequivalent extended irreducible binary Goppa codes of length $q+1$ and degree $r$. [ABSTRACT FROM AUTHOR]

Non-overlapping codes are a set of codewords in $\bigcup _{n \ge 2} \mathbb {Z}_{q}^{n}$ , where $\mathbb {Z}_{q} = \{0,1, {\dots },q-1\}$ , such that the prefix of each codeword is not a suffix of any codeword in the set, including itself; and for variable-length codes, a codeword does not contain any other codeword as a subword. In this paper, we investigate a generic method to generalize binary codes to $q$ -ary ones for $q > 2$ , and analyze this generalization on the two constructions given by Levenshtein (also by Gilbert; Chee, Kiah, Purkayastha, and Wang) and Bilotta, respectively. The generalization on the former construction gives large non-expandable fixed-length non-overlapping codes whose size can be explicitly determined; the generalization on the latter construction is the first attempt to generate $q$ -ary variable-length non-overlapping codes. More importantly, this generic method allows us to utilize the generating function approach to analyze the cardinality of the underlying $q$ -ary non-overlapping codes. The generating function approach not only enables us to derive new results, e.g., recurrence relations on their cardinalities, new combinatorial interpretations for the constructions, and the superior limit of their cardinalities for some special cases, but also greatly simplifies the arguments for these results. Furthermore, we give an exact formula for the number of fixed-length words that do not contain the codewords in a variable-length non-overlapping code as subwords. This thereby solves an open problem by Bilotta and induces a recursive upper bound on the maximum size of variable-length non-overlapping codes. [ABSTRACT FROM AUTHOR]

Low-density parity-check (LDPC) codes are among the most effective modern error-correcting codes due to their excellent correction performance and highly parallel decoding scheme. Moreover, the nonbinary extension of such codes further increases performance in the short-block regime. In this paper, we review the key elements for the construction of implementation-oriented binary and nonbinary codes. These quasi-cyclic LDPC (QC-LDPC) codes additionally feature efficient encoder and decoder implementation frameworks. We then present a versatile algorithm for the construction of both binary and nonbinary QC-LDPC codes that have low encoding complexity and an optimized corresponding graph structure. Our algorithm uses a progressive edge growth algorithm, modified for QC-LDPC graph construction, and then performs an iterative global search for optimized cyclic shift values within the QC-LDPC circulants. Strong error correction performance is achieved by minimizing the number of short cycles, and cycles with low external connectivity, within the code graph. We validate this approach via error rate simulations of a transmission system model featuring an LDPC coder-decoder, digital modulation, and additive white Gaussian noise channels. The obtained numerical results validate the effectiveness of the proposed construction algorithm, with a number of constructed codes exhibiting either similar or superior performance to industry standard binary codes and selected nonbinary codes from the literature. [ABSTRACT FROM AUTHOR]

Cross-modal hashing (CMH) has gained considerable attention due to its low storage and fast query speed. Most existing CMH research pursues the binary codes of each modality by preserving a similarity matrix which is computationally expensive. In this paper, we propose a Gaussian similarity preserving method for cross-modal hashing. By using the semantic transformation, our model can avoid computing the similarity matrix explicitly. We further employ the sequential learning approach to reduce the quantization error. Experimental results on three benchmark datasets clearly show that our proposed method can outperform the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Searching for the nearest neighbor is a fundamental problem in the computer vision field, and deep hashing has become one of the most representative and widely used methods, which learns to generate compact binary codes for visual data. In this paper, we first delve into the representation learning of deep hashing and surprisingly find that deep hashing could be a double-edged sword, i.e. , deep hashing can accelerate the query speed and decrease the storage cost in the nearest neighbor search progress, but it greatly sacrifices the discriminability of deep representations especially with extremely short target code lengths. To solve this problem, we propose a two-step deep hashing learning framework. The first step focuses on learning deep discriminative representations with metric learning. Subsequently, the learning framework concentrates on simultaneously learning compact binary codes and preserving representations learned in the former step from being sacrificed. Extensive experiments on two general image datasets and four challenging image datasets validate the effectiveness of our proposed learning framework. Moreover, the side effect of deep hashing is successfully mitigated with our learning framework. [ABSTRACT FROM AUTHOR]

The rth generalized Hamming weight of a linear [n, k] code C is the cardinality of the smallest support of any r-dimensional subcode of C. In this paper, we obtain the generalized Hamming weights of the binary linear codes whose parity check matrices are the incidence matrices of the Cartesian product of graphs. We also determine the rth generalized Hamming weights of their dual codes. [ABSTRACT FROM AUTHOR]

In entropy coding, universal coding of integers (UCI) is a binary universal prefix code, such that the ratio of the expected codeword length to $\max \{1, H(P)\}$ is less than or equal to a constant expansion factor $K_{\mathcal {C}}$ for any probability distribution $P$ , where $H(P)$ is the Shannon entropy of $P$. $K_{\mathcal {C}}^{*}$ is the infimum of the set of expansion factors. The optimal UCI is defined as a class of UCI possessing the smallest $K_{\mathcal {C}}^{*}$. Based on prior research, the range of $K_{\mathcal {C}}^{*}$ for the optimal UCI is $2\leq K_{\mathcal {C}}^{*}\leq 2.75$. Currently, the code constructions achieve $K_{\mathcal {C}}=2.75$ for UCI and $K_{\mathcal {C}}=3.5$ for asymptotically optimal UCI. In this paper, we construct a class of UCI, termed $\iota $ code, to achieve $K_{\mathcal {C}}=2.5$. This further narrows the range of $K_{\mathcal {C}}^{*}$ to $2\leq K_{\mathcal {C}}^{*}\leq 2.5$. Next, a family of asymptotically optimal UCIs is presented, where their expansion factor infinitely approaches 2.5. Then, tighter upper bounds of the expansion factors are derived for several classic UCIs. Finally, we prove that the length of the first codeword of optimal UCI is one. [ABSTRACT FROM AUTHOR]

In the last several years, deep learning has been introduced to recover a hyperspectral image (HSI) from a single RGB image and demonstrated good performance. In particular, attention mechanisms have further strengthened discriminative features, but most of them are learned by convolutions with limited receptive fields or require much computational cost, which hinders the function of attention modules. Furthermore, the performance of these deep learning methods is hampered by tackling multi-level features equally. To this end, in this paper, based on multiple lightweight densely residual modules, we propose a densely residual network with dual attention (DRN-DA), which utilizes advanced attention and adaptive fusion strategy for more efficient feature correlation learning and more powerful feature extraction. Specifically, an SE layer is applied to learn channel-wise dependencies, and dual downsampling spatial attention (DDSA) is developed to capture long-range spatial contextual information. All the intermediate-layer feature maps are adaptively fused. Experimental results on four data sets from the NTIRE 2018 and NTIRE 2020 Spectral Reconstruction Challenges demonstrate the superiority of the proposed DRN-DA over state-of-the-art methods (at least −6.19% and −1.43% on NTIRE 2018 "Clean" track and "Real World" track, −6.85% and −5.30% on NTIRE 2020 "Clean" track and "Real World" track) in terms of mean relative absolute error. [ABSTRACT FROM AUTHOR]

Maximum Distance Separable (MDS) matrices offer ideal diffusion properties and are of great importance in design of block ciphers and hash functions. A rhotrix as defined by Sani, is a coupled matrix which when used in a cryptosystem provides double security. Many authors constructed MDS Rhotrices over finite fields using matrices which are cryptographically significant. Hankel matrices have wide range of applications in engineering, coding theory and cryptography. In the present paper, we define block rhotrix and block Hankel-like rhotrix. Further, we construct MDS block Hankel-like rhotrices using self-dual basis and conjugate elements of Fp«. [ABSTRACT FROM AUTHOR]

With the dramatic increase in the amount of multimedia data, cross-modal similarity retrieval has become one of the most popular yet challenging problems. Hashing offers a promising solution for large-scale cross-modal data searching by embedding the high-dimensional data into the low-dimensional similarity preserving Hamming space. However, most existing cross-modal hashing usually seeks a semantic representation shared by multiple modalities, which cannot fully preserve and fuse the discriminative modal-specific features and heterogeneous similarity for cross-modal similarity searching. In this paper, we propose a joint specifics and consistency hash learning method for cross-modal retrieval. Specifically, we introduce an asymmetric learning framework to fully exploit the label information for discriminative hash code learning, where 1) each individual modality can be better converted into a meaningful subspace with specific information, 2) multiple subspaces are semantically connected to capture consistent information, and 3) the integration complexity of different subspaces is overcome so that the learned collaborative binary codes can merge the specifics with consistency. Then, we introduce an alternatively iterative optimization to tackle the specifics and consistency hashing learning problem, making it scalable for large-scale cross-modal retrieval. Extensive experiments on five widely used benchmark databases clearly demonstrate the effectiveness and efficiency of our proposed method on both one-cross-one and one-cross-two retrieval tasks. [ABSTRACT FROM AUTHOR]

Fine-grained hashing is a new topic in the field of hashing-based retrieval and has not been well explored up to now. In this paper, we raise three key issues that fine-grained hashing should address simultaneously, i.e., fine-grained feature extraction, feature refinement as well as a well-designed loss function. In order to address these issues, we propose a novel Fine-graIned haSHing method with a double-filtering mechanism and a proxy-based loss function, FISH for short. Specifically, the double-filtering mechanism consists of two modules, i.e., Space Filtering module and Feature Filtering module, which address the fine-grained feature extraction and feature refinement issues, respectively. Thereinto, the Space Filtering module is designed to highlight the critical regions in images and help the model to capture more subtle and discriminative details; the Feature Filtering module is the key of FISH and aims to further refine extracted features by supervised re- weighting and enhancing. Moreover, the proxy-based loss is adopted to train the model by preserving similarity relationships between data instances and proxy-vectors of each class rather than other data instances, further making FISH much efficient and effective. Experimental results demonstrate that FISH achieves much better retrieval performance compared with state-of-the-art fine-grained hashing methods, and converges very fast. The source code is publicly available: https://github.com/chenzhenduo/FISH. [ABSTRACT FROM AUTHOR]

Recommendation efficiency and data sparsity problems have been regarded as two challenges of improving performance for online recommendation. Most of the previous related work focus on improving recommendation accuracy instead of efficiency. In this paper, we propose a Deep Pairwise Hashing (DPH) to map users and items to binary vectors in Hamming space, where a user's preference for an item can be efficiently calculated by Hamming distance, which significantly improves the efficiency of online recommendation. To alleviate data sparsity and cold-start problems, the user-item interactive information and item content information are unified to learn effective representations of items and users. Specifically, we first pre-train robust item representation from item content data by a Denoising Auto-encoder instead of other deterministic deep learning frameworks; then we finetune the entire framework by adding a pairwise loss objective with discrete constraints; moreover, DPH aims to minimize a pairwise ranking loss that is consistent with the ultimate goal of recommendation. Finally, we adopt the alternating optimization method to optimize the proposed model with discrete constraints. Extensive experiments on three different datasets show that DPH can significantly advance the state-of-the-art frameworks regarding data sparsity and item cold-start recommendation. [ABSTRACT FROM AUTHOR]

The probability Jaccard similarity was recently proposed as a natural generalization of the Jaccard similarity to measure the proximity of sets whose elements are associated with relative frequencies or probabilities. In combination with a hash algorithm that maps those weighted sets to compact signatures which allow fast estimation of pairwise similarities, it constitutes a valuable method for big data applications such as near-duplicate detection, nearest neighbor search, or clustering. This paper introduces a class of one-pass locality-sensitive hash algorithms that are orders of magnitude faster than the original approach. The performance gain is achieved by calculating signature components not independently, but collectively. Four different algorithms are proposed based on this idea. Two of them are statistically equivalent to the original approach and can be used as drop-in replacements. The other two may even improve the estimation error by introducing statistical dependence between signature components. Moreover, the presented techniques can be specialized for the conventional Jaccard similarity, resulting in highly efficient algorithms that outperform traditional minwise hashing and that are able to compete with the state of the art. [ABSTRACT FROM AUTHOR]

The improvement of photovoltaic (PV) power prediction precision plays a crucial role in the new energy consumption. This paper proposes a composite prediction framework (DC (DWT-DAE)-CNN) consisting of dual clustering and convolutional neural network to achieve day-ahead prediction of PV power. To avoid the temporal uncertainty of PV power and the high-dimensional complexity of numerical weather prediction, the raw data are processed by Discrete Wavelet Transform (DWT) and Deep Autoencoder respectively (DAE) to reduce the data redundancy. Secondly, a dual clustering pattern based on dynamic time warping distance clustering and Fuzzy C-Mean (FCM) clustering is proposed to progressively realize the dynamic characteristics of the power curve and numerical clustering of the weather information data. Finally, the data from PV plants in northeast China are used for validation. The results show that the annual average day-ahead prediction AR of the DC (DWT-DAE)-CNN model can reach 90.17%, which is better than other competing models. In addition, the dual clustering pattern performs better than other traditional clustering patterns with the same predictor. Using this method to predict the PV output power can provide better theoretical guidance for the stable and safe operation of grid-connected PV. • A dual clustering model based on numerical variation and curve morphology variation is proposed. • The power data and NWP data were processed separately using Discrete Wavelet Transform and Deep Autoencoder. • Building multiple convolutional neural network predictors for PV power day-ahead prediction. • The proposed model was shown to outperform the comparison model under different seasons. [ABSTRACT FROM AUTHOR]

Linear codes over $\mathbb {Z}_{p^{s}}$ of length $n$ are subgroups of $\mathbb {Z}_{p^{s}}^{n}$. These codes are also called $\mathbb {Z}_{p^{s}}$ -additive codes and can be seen as a generalization of linear codes over $\mathbb {Z}_{2}$ and $\mathbb {Z}_{4}$. A $\mathbb {Z}_{p^{s}}$ -linear code is a code over $\mathbb {Z}_{p}$ , not necessarily linear, which is the generalized Gray map image of a $\mathbb {Z}_{p^{s}}$ -additive code. In 2015, a systematic encoding was found for $\mathbb {Z}_{4}$ -linear codes. Moreover, an alternative permutation decoding method, which is suitable for any binary code (not necessarily linear) with a systematic encoding, was established. In this paper, we generalize these results by presenting a systematic encoding for any $\mathbb {Z}_{p^{s}}$ -linear code with $s\geq 2$ and $p$ prime. We also describe a permutation decoding method for any systematic code over $\mathbb {Z}_{p}$ , not necessarily linear, and show some examples of how to use this systematic encoding in this decoding method. [ABSTRACT FROM AUTHOR]

In this paper, the design of all-optical gray code converter for binary and BCD inputs using two-dimensional photonic crystal is proposed. The proposed design contains square lattice which includes silicon rods in air in the form of point defect, line defect and nano resonators. The plane wave expansion and finite difference time domain method is used in the simulation to calculate the band gap and system performance. All-optical OR and XOR logic outputs are achieved by introducing suitable phase difference between two input data to interfere appropriately. The proposed design exhibits acceptable performance with time delay of 0.154 ps, contrast ratio of 12.01 dB, foot print of 658 µm2 for the considered BCD and binary inputs. [ABSTRACT FROM AUTHOR]

On the premise of satisfying the design conditions and practical engineering needs, it is of practical significance to optimize the design of assembly components. Therefore, in this paper, based on the improved immune genetic algorithm, the structural optimization of prefabricated components is deeply studied, where it is converted into binary gene code, and the structural design requirements are introduced into the algorithm through structural layout vaccine and concrete strength vaccine. In addition, the section size of components is designed according to economic indicators, which has proved that the research is effective for the structural optimization method of prefabricated components. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of correcting multiple criss-cross insertions and deletions in arrays. More precisely, we study the unique recovery of $n \times n$ arrays affected by ${t}$ -criss-cross deletions defined as any combination of ${t_{\mathrm {r}}}$ row and ${t_{\mathrm {c}}}$ column deletions such that ${t_{\mathrm {r}}}+ {t_{\mathrm {c}}}= {t}$ for a given $t$. We show an equivalence between correcting ${t}$ -criss-cross deletions and ${t}$ -criss-cross insertions and show that a code correcting ${t}$ -criss-cross insertions/deletions has redundancy at least ${t} n + {t}\log n - \log ({t}!)$. Then, we present an existential construction of a ${t}$ -criss-cross insertion/deletion correcting code with redundancy bounded from above by ${t} n + \mathcal {O}({t}^{2} \log ^{2} n)$. The main ingredients of the presented code construction are systematic binary ${t}$ -deletion correcting codes and Gabidulin codes. The first ingredient helps locating the indices of the inserted/deleted rows and columns, thus transforming the insertion/deletion-correction problem into a row/column erasure-correction problem which is then solved using the second ingredient. [ABSTRACT FROM AUTHOR]

Self-supervised representation learning for videos has been very attractive recently because these methods exploit the information inherently obtained from the video itself instead of annotated labels that is quite time-consuming. However, existing methods ignore the importance of global observation while performing spatio-temporal transformation perception, which highly limits the expression capabilities of the video representation. This paper proposes a novel pretext task that combines the temporal information perception of the video with the motion amplitude perception of moving objects to learn the spatio-temporal representation of the video. Specifically, given a video clip containing several video segments, each video segment is sampled by different sampling rates and the order of video segments is disrupted. Then, the network is used to regress the sampling rate of each video segment and classify the order of input video segments. In the pre-training stage, the network can learn rich spatio-temporal semantic information where content-related contrastive learning is introduced to make the learned video representation more discriminative. To alleviate the appearance dependency caused by contrastive learning, we design a novel and robust vector similarity measurement approach, which can take feature alignment into consideration. Moreover, a view synthesis framework is proposed to further improve the performance of contrastive learning by automatically generating reasonable transformed views. We conduct benchmark experiments with several 3D backbone networks on two datasets. The results show that our proposed method outperforms the existing state-of-the-art methods across the three backbones on two downstream tasks of human action recognition and video retrieval. [ABSTRACT FROM AUTHOR]

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, two classes of cyclic codes whose duals have two zeros are presented. The weight distributions of these cyclic codes are settled with the help of Gaussian periods. The duals of one class of cyclic codes are also studied. Some of the cyclic codes presented in this paper are optimal in the sense that they meet some bounds of linear codes. [ABSTRACT FROM AUTHOR]

Context. In earlier papers, we aimed to reconstruct the progenitor systems of Algol-type semi-detached binaries. To this end, we developed a binary evolutionary code for the purpose of reproducing the orbital parameters, masses, and location in the HRD of well-observed Algol systems. In this code, the effects of mass and angular momentum losses and tidal coupling were included, but not magnetic braking at that point. In the present paper, we study the effects of magnetic braking on the rotation of the mass gainers in these systems. Aims. Equatorial velocities have been measured for a number of mass-gaining stars in interacting binaries. Tides tend to synchronize the rotation of the gainer, but many observed low equatorial velocities cannot be explained by tidal interactions alone. Methods. We added magnetic braking to our code to better reproduce the observed equatorial velocities. Results. Large equatorial velocities of mass-gaining stars are lowered by tidal interaction and magnetic braking. Tides are mainly at work at short orbital periods, leaving magnetic braking alone at work during longer orbital periods. Conclusions. Slow rotation of mass gainers in Algol-type binaries is mostly well reproduced by our code. However, (not observed) critical rotation of the gainer in some systems cannot be avoided by our calculations. [ABSTRACT FROM AUTHOR]

The paper deals with state-of-the-art trends in the field of automated hardware development, specifically development of digital systems using programmable logic integrated circuits, as exemplified by field-programmable logic arrays. The paper suggests a modeling method of development using an algebraic model of design specifications, requirements and binary codes in order to apply formal methods of verification, model-based testing, as well as methods of algebraic matching. The specifications of the algebraic hardware model are behavior algebra determined on a set of actions and behaviors. [ABSTRACT FROM AUTHOR]

With the rapid growth of image and video data on the web, hashing has been extensively studied for image or video search in recent years. Benefiting from recent advances in deep learning, deep hashing methods have shown superior performance over the traditional hashing methods. However, there are some limitations of previous deep hashing methods (e.g., the semantic information is not fully exploited). In this paper, we develop a general deep supervised discrete hashing framework based on the assumption that the learned binary codes should be ideal for classification. Both the similarity information and the classification information are used to learn the hash codes within one stream framework. We constrain the outputs of the last layer to be binary codes directly, which is rarely investigated in deep hashing algorithms. Besides, both the pairwise similarity information and the triplet ranking information are exploited in this paper. In addition, two different loss functions are presented: l 2 loss and hinge loss, which are carefully designed for the classification term under the one stream framework. Because of the discrete nature of hash codes, an alternating minimization method is used to optimize the objective function. Experimental results have shown that our approach outperforms current state-of-the-art methods on benchmark datasets. [ABSTRACT FROM AUTHOR]

The generalized Pareto (GP) distribution model is often used to describe the amplitude statistical feature of sea clutter. Generally, the parameters of GP distribution are estimated by moments estimators. However, when the sea state is high, the appearance of sea spikes will increase the echo of the anomalous scattering units, which leads to a decrease in the parameter estimation accuracy and target detection performance. To improve the parameter estimation accuracy, this paper proposes a novel parameter estimation method based on variable intervals. Considering the local properties of sea clutter, we take a variable interval of the entire sea clutter series for parameter estimation, where the interval position is selected according to the sea state conditions. For contrast, the bipercentile parameter estimation and truncate moment estimation are also introduced. Finally, the experiment based on the real measured X-band sea clutter datasets indicates that the proposed method outperforms the state-of-the-art moments estimators. [ABSTRACT FROM AUTHOR]

Online image hashing has received increasing research attention recently, which processes large-scale data in a streaming fashion to update the hash functions on-the-fly. To this end, most existing works exploit this problem under a supervised setting, i.e., using class labels to boost the hashing performance, which suffers from the defects in both adaptivity and efficiency: First, large amounts of training batches are required to learn up-to-date hash functions, which leads to poor online adaptivity. Second, the training is time-consuming, which contradicts with the core need of online learning. In this paper, a novel supervised online hashing scheme, termed Fast Class-wise Updating for Online Hashing (FCOH), is proposed to address the above two challenges by introducing a novel and efficient inner product operation. To achieve fast online adaptivity, a class-wise updating method is developed to decompose the binary code learning and alternatively renew the hash functions in a class-wise fashion, which well addresses the burden on large amounts of training batches. Quantitatively, such a decomposition further leads to at least 75 percent storage saving. To further achieve online efficiency, we propose a semi-relaxation optimization, which accelerates the online training by treating different binary constraints independently. Without additional constraints and variables, the time complexity is significantly reduced. Such a scheme is also quantitatively shown to well preserve past information during updating hashing functions. We have quantitatively demonstrated that the collective effort of class-wise updating and semi-relaxation optimization provides a superior performance comparing to various state-of-the-art methods, which is verified through extensive experiments on three widely-used datasets. [ABSTRACT FROM AUTHOR]

This paper considers generalized quasi-cyclic (GQC) codes with no restriction on their block lengths. By relaxing the condition on its block lengths, we find some new optimal codes of small length. Also, we generalize the decomposition of codes and dimension formula given by Güneri et al, Séguin, and Siap et al. We use two different approaches to describe GQC codes: first, by torsion module structure, and second, by injection into classes of QC codes. Using the first approach, we can determine the dimension and give a formula for the minimum distance of the corresponding GQC code. In the second approach, we use structural properties of QC codes with one specific length. This approach gives us a way to construct GQC codes, dual code for a given GQC code, and a criterion for a GQC code to be a Euclidean self-dual code. Moreover, we also consider GQC codes over a family of finite rings, called the ring B k , and its relation to GQC codes over finite fields using a collection of Gray maps. [ABSTRACT FROM AUTHOR]

A class of network codes have been proposed in the literature where the symbols transmitted on network edges are binary vectors and the coding operation performed in network nodes consists of the application of (possibly several) permutations on each incoming vector and XOR-ing the results to obtain the outgoing vector. These network codes, which we will refer to as permute-and-add network codes, involve simpler operations and are known to provide lower complexity solutions than scalar linear network codes. The complexity of these codes is determined by their degree which is the number of permutations applied on each incoming vector to compute an outgoing vector. Constructions of permute-and-add network codes for multicast networks are known. In this paper, we provide a new framework based on group algebras to design permute-and-add network codes for arbitrary (not necessarily multicast) networks. Our framework allows the use of any finite group of permutations (including circular shifts, proposed in prior works) and admits a trade-off between coding rate and the degree of the code. Further, our technique permits elegant recovery and generalizations of the key results on permute-and-add network codes known in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and defining sets. Second, we construct quaternary linear codes via simplicial complexes and determine the weight distributions of these codes. Third, the weight distributions of the binary subfield codes of these quaternary codes are also computed by employing the general characterization. Furthermore, we present two infinite families of optimal linear codes with respect to the Griesmer Bound, and a class of binary almost optimal codes with respect to the Sphere Packing Bound. We also need to emphasize that we obtain at least 9 new quaternary linear codes. [ABSTRACT FROM AUTHOR]

Neural Network Coding and Representation (NNR) is the first international standard for efficient compression of neural networks (NNs). The standard is designed as a toolbox of compression methods, which can be used to create coding pipelines. It can be either used as an independent coding framework (with its own bitstream format) or together with external neural network formats and frameworks. For providing the highest degree of flexibility, the network compression methods operate per parameter tensor in order to always ensure proper decoding, even if no structure information is provided. The NNR standard contains compression-efficient quantization and deep context-adaptive binary arithmetic coding (DeepCABAC) as core encoding and decoding technologies, as well as neural network parameter pre-processing methods like sparsification, pruning, low-rank decomposition, unification, local scaling and batch norm folding. NNR achieves a compression efficiency of more than 97% for transparent coding cases, i.e. without degrading classification quality, such as top-1 or top-5 accuracies. This paper provides an overview of the technical features and characteristics of NNR. [ABSTRACT FROM AUTHOR]

Approximate Nearest Neighbor(ANN) search is the core problem in many large-scale machine learning and computer vision applications such as multimodal retrieval. Hashing is becoming increasingly popular, since it can provide efficient similarity search and compact data representations suitable for handling such large-scale ANN search problems. Most hashing algorithms concentrate on learning more effective projection functions. However, the accuracy loss in the quantization step has been ignored and barely studied. In this paper, we analyse the importance of various projected dimensions, distribute them into several groups and quantize them with two types of values which can both better preserve the neighborhood structure among data. One is Variable Integer-based Quantization (VIQ) that quantizes each projected dimension with integer values. The other is Variable Codebook-based Quantization (VCQ) that quantizes each projected dimension with corresponding codebook values. We conduct experiments on five common public data sets containing up to one million vectors. The results show that the proposed VCQ and VIQ algorithms can both achieve much higher accuracy than state-of-the-art quantization methods. Furthermore, although VCQ performs better than VIQ, ANN search with VIQ provides much higher search efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a more robust supervised hashing framework based on the Cauchy loss function and Supervised Discrete Hashing (SDH) called Robust Supervised Discrete Hashing (RSDH), which can learn a robust subspace consisted of binary codes. The Cauchy loss is used to measure the error between the label matrix and the product of the decomposed matrices. RSDH can not only reduce the outliers and noise of the hashing codes, but also achieve the more satisfactory retrieval effect. Image retrieval experiments demonstrate that RSDH performs better than the other hashing methods. [ABSTRACT FROM AUTHOR]

Let n, k, t be positive integers. What is the maximum number of arcs in a digraph on n vertices in which there are at most t distinct walks of length k with the same endpoints? Denote f (t) = max { 2 t + 1 , 2 2 t + 9 / 4 + 1 / 2 + 3 } . In this paper, we prove that the maximum number is equal to n (n - 1) / 2 and the extremal digraph are the transitive tournaments when k ≥ n - 1 ≥ f (t) . Based on this result, we may determine the maximum numbers and the extremal digraphs when k ≥ f (t) and n is sufficiently large, which generalizes the existing results. A conjecture is also presented. [ABSTRACT FROM AUTHOR]

This paper develops a non-coherent index modulation (IM) system in which activation patterns are characterized by multi-level block codes. We analyze performance of such a system under the maximum-likelihood (ML) receiver and when the set of activation patterns follows a multi-level code generated from asymptotically optimal alphabets. An asymptotic analysis of the pair-wise error probability (PEP) shows that the system can exploit a diversity order that is determined by the distance of the worst codeword pair in the $l_{1}$ metric, known as the Manhattan norm. We then explore the rate-diversity tradeoff for the developed non-coherent IM system as a function of the code length. Specifically, Gilbert-style bounds on the data rates for systems based on binary and ternary codes are obtained that can ensure a given diversity order. We approach the problem of packing in the $l_{1}$ metric by partitioning codes into permutation modulation codes (PMCs) and obtaining Gilbert-style bounds on PMCs. Several achievable rates for non-coherent binary and ternary IM systems, as well as a tradeoff between the information rate and codeword error probability (CEP) are also derived. Finally, simulation results are provided to corroborate the theoretical analysis. [ABSTRACT FROM AUTHOR]

One of the most important functions used in a quantum key distribution (QKD) network is universal hash functions, specially, (almost) strongly universal hash functions which are used in at least three steps of QKD, in particular, in error correction, privacy amplification, and authentication. Also, they have been recently used in several other quantum communication protocols like quantum secret sharing (QSS). These hash functions have also many other important applications from information security to data structures and parallel computing. Recently, Bibak et al. [Quantum Inf. Comput., 2021] introduced quadratic hash which gives much better collision bound than the well-known polynomial hash. In this paper, we define three new universal hash function families which strongly generalize all the previous families and have several advantages over them. Then, using highly influential and pioneering results of Schmidt and of Weil, we show that these new families are (almost) Δ -universal which can then be easily converted to (almost) strongly universal families. This makes them useful for applications in QKD and many other areas. [ABSTRACT FROM AUTHOR]

The nonlocal self-similarity in natural image provides an effective prior for single image super-resolution (SISR), which is beneficial to contextual information capture and performance improvement, as demonstrated by conventional SISR methods. However, it is little explored to utilize this property in deep neural networks. In this paper, we propose a self-similarity prior guided (SSPG) network to incorporate self-similarity-based nonlocal operation into deep neural network for SISR. Specifically, we design a cross-scale nearest-neighbor residual (CSNNR) block via introducing cross-scale $k$ -nearest neighbors (KNN) matching into a residual block, which can be flexibly integrated into deep networks to capture long-range correlations among multi-scale and multi-level features. Meanwhile, by stacking a CSNNR block and a sequence of wide-activated residual blocks with a local skip-connection, a multi-level residual self-similarity (MRSS) module is developed to effectively employ local and nonlocal information for detail recovery. Thus, through cascading multiple MRSS modules, the proposed SSPG network performs both self-similarity-based nonlocal operation and convolution-based local operation on multi-level features to reconstruct informative features for accurate SISR. In addition, for pursuing visually pleasing results, we apply our SSPG network to the perception-oriented SISR field by following the framework of generative adversarial networks. In particular, we explore a sample-discriminating learning mechanism based on the statistical descriptions of training samples, and include it in optimization procedure to automatically tune the contributions of different samples according to their characteristics and then focus the network on creating realistic results. Extensive quantitative and qualitative evaluations on benchmark datasets illustrate the superiority of our proposed models over the state-of-the-art methods for both distortion-oriented and perception-oriented image super-resolution tasks. [ABSTRACT FROM AUTHOR]

• A deep neural network architecture is proposed to learn binary hash codes from physiological time series. • High utility, similarity preserving and temporal relationship are jointly learned with multiple designed objectives. • Experiments on ECG and EEG datasets show the effectiveness of the proposed method. In this paper, we aim to transform numerical physiological time series into binary hash codes, that can be further used for indexing large-scale dataset, or accelerating downstream tasks such as instance-based classification. We propose HITS to learn binary H ash codes from phys I ological T ime S eries. HITS first builds a very deep one-dimensional convolutional neural network to learn lower-dimensional representations from raw physiological time series. Then, HITS jointly learns high utility, similarity preserving, and temporal related compact binary codes by corresponding objectives with imposed. Finally, given a new physiological time series, HITS can encode it to a binary hash code. Experiments are performed on two real-world Electrocardiogram and Electroencephalogram datasets. The accuracy of a k-nearest classifier is used to evaluate the quality of codes. HITS outperforms the second-best baseline 7.42% on average of k = { 1 , 2 , 4 , 8 , 16 , 32 } with code length c = 48 , while reducing 45.51% searching time than the same length numerical vectors on average of c = { 16 , 24 , 32 , 48 , 64 }. HITS consistently achieve higher classification accuracy than compared methods using k-nearest classifier varying different k and code length. Thus, HITS learns better binary hash codes than compared methods. [ABSTRACT FROM AUTHOR]

Wenchuang product is the abbreviation of cultural and creative products, which is a modern extension of traditional culture. Its dissemination is conducive to enhancing the popularity, appeal, and influence of Chinese traditional culture. As an important carrier and manifestation of cultural and creative industries, Wenchuang products are the integration of regional cultural industry development and the dominant presentation of regional politics, culture, and economy. As a highly parallel, random, and adaptive search algorithm, genetic algorithm has been widely used in personalized product design, conceptual design, product optimization design, and intelligent design, etc. Based on the genetic algorithm, this paper studies the image representation of regional cultural and creative products. In the field of image representation design of regional cultural and creative products, tree structure coding, real number coding, binary coding, etc. are widely used in this field, and these coding methods all meet the innovative requirements of designers. In the field of image representation design of regional cultural and creative products, genetic coding, as a very important part of applying genetic algorithm, plays a very important role in its research and application. [ABSTRACT FROM AUTHOR]

In any transmission scheme, security against eavesdroppers is of importance. Contrary to classical encryption, security directly at the physical layer can be achieved by applying suited coding and modulation schemes. In this paper, coded modulation schemes, i.e., the use of higher-order constellations, is studied for generating both security against a wiretapper and reliability for the legitimate user. Specifically, a multilevel coding (MLC) scheme is considered. The influence of the constellation, in particular its cardinality and its dimensionality, on the gained security is assessed. As LSB component code, a practical secure coding scheme based on punctured LDPC codes is used. The security level for the employed LDPC code ensembles within MLC constructions is examined with an adapted density evolution technique. Results from numerical simulations cover the theoretical considerations and match with the derived asymptotic behavior. The results are compared to the situation when straightforwardly applying a binary code according to the BICM approach. [ABSTRACT FROM AUTHOR]