Code Matrix Research Articles

A new efficient sensing matrix for cluster structured sparse signals recovery

Compressive sensing is a new sensing technique aiming to recover the original sparse signal from a much fewer number of samples compared to the conventional sensing technique of Shannon-Nyquist. Recently, several works have considered the problem of recovering sparse signals when their nonzero coefficients tend to cluster into blocks. We refer to this new type of signals as cluster structured sparse signals. In this paper, we deal with the problem of cluster structured sparse signals recovery by proposing a novel sensing matrix based on Bernoulli sensing matrix and full-orthogonal Hadamard codes. We demonstrate theoretically and experimentally that the proposed sensing matrix performs well in the case of cluster structured sparse signals recovery. Indeed, the new sensing matrix provides a considerable gain in terms of the rate of exact recovery and error support rate. Also, an application on natural images is conducted exploiting their cluster structured sparse property in the discrete cosine transform domain.

A new Gaussian Fibonacci matrices and its applications

In this paper, we introduced a new Gaussian Fibonacci matrix, $G^{n}$ whose elements are Gaussian Fibonacci numbers and we developed a new coding and decoding method followed from this Gaussian Fibonacci matrix, $G^{n}$. We established the relations between the code matrix elements, error detection and correction for this coding theory. Correction ability of this method is $93.33$%.

High-payload secret hiding mechanism for QR codes

QR code is an important approach of information transmission and is widely used in our daily life. As a public patent, the message embeded in a QR code can be easily decoded by any QR code reader, thus can lead to information leaks when delivering the secret message with QR code. To overcome this weakness, we exploited the characteristics of Reed-Solomon code and turtle shell matrix to propose a simple yet efficient data embedding mechanism to hide secret messages in the QR code while maintaining the marked QR code valid. Different from the traditional schemes, the proposed scheme of this paper hides the secret messages without sacrificing the error correction capacity of QR code and is able to achieve a higher secret payload. Meanwhile, the public message of generated marked QR code still can be decoded by standard QR code reader. Such nature will reduce the risk due to the curiosity of the malicious users. Experiments were performed to evaluate the performance of the proposed scheme. Experimental results showed that the proposed scheme is robust to several common image attacks.

A discrete information coding matrix algorithm based on image features for tracking circulation of commodities

AbstractFor fast‐consumed‐commodities industry, it is usually difficult for producers to track the commodities in their circulation process, especially, when their labels have been damaged. In this paper, we develop a novel method based on channel coding theory of forward error correction (FEC) to prevent the flooding of counterfeit products with a very low cost and easy implementation. This anti‐interference matrix information coding method has a strong ability to resist damage and high recovery rate, and can produce a large number of nonrepeated codes in terms of different characteristics of demand, yielding a great enhancement of anti‐counterfeiting trace capacity. However, the process of reading information strongly relies on artificial means that requires a high cost and reduces the efficiency. For this reason, we propose an efficient approach for image feature extraction based on discrete information coding matrix. It takes the advantage of wearing perspective clipping method to obtain the revised image with printed matrix information and then extract the regions of interest (ROI) that carry the information about the coding matrix by working out its row and column coordinates with the center of gravity method. The matrix code recognition software is implemented. The simulation and experimental results show that the method is effective and robust.

Combining the Burrows-Wheeler Transform and RCM-LDGM Codes for the Transmission of Sources with Memory at High Spectral Efficiencies.

In this paper, we look at the problem of implementing high-throughput Joint Source- Channel (JSC) coding schemes for the transmission of binary sources with memory over AWGN channels. The sources are modeled either by a Markov chain (MC) or a hidden Markov model (HMM). We propose a coding scheme based on the Burrows-Wheeler Transform (BWT) and the parallel concatenation of Rate-Compatible Modulation and Low-Density Generator Matrix (RCM-LDGM) codes. The proposed scheme uses the BWT to convert the original source with memory into a set of independent non-uniform Discrete Memoryless (DMS) binary sources, which are then separately encoded, with optimal rates, using RCM-LDGM codes.

The generalized relations among the code elements for a new complex Fibonacci matrix

In this paper, we introduce a new complex Fibonacci matrix [Formula: see text] whose elements are complex Fibonacci numbers and we developed a new coding and decoding method followed from this complex Fibonacci matrix [Formula: see text]. We establish the relations among the code matrix elements, error detection and correction for this coding theory.

Asymptotic BER EXIT chart analysis for high rate codes based on the parallel concatenation of analog RCM and digital LDGM codes

This paper proposes an extrinsic information transfer (EXIT) chart analysis and an asymptotic bit error rate (BER) prediction method to speed up the design of high rate RCM-LDGM hybrid codes over AWGN and fast Rayleigh channels. These codes are based on a parallel concatenation of a rate compatible modulation (RCM) code with a low-density generator matrix (LDGM) code. The decoder uses the iterative sum-product algorithm to exchange information between the variable nodes (VNs) and the two types of constituent check nodes: RCM-CN and LDGM-CN. The novelty of the proposed EXIT chart procedure lies on the fact that it mixes together the analog RCM check nodes with the digital LDGM check nodes, something not possible in previous multi-edge EXIT charts proposed in the literature.

Advanced Modulation Scheme for Visible Light Communication

In this paper, an improved version of existing modulation schemes is investigated by inserting Hadamard codes (HC) at the peak slot of each symbol for the Visible Light Communication (VLC) system. The performance of the proposed scheme is analyzed and compared with existing schemes On-Off Keying (OOK), Pulse Position Modulation (PPM), Differential PPM (DPPM), Pulse Amplitude Modulation (PAM), Differential Amplitude PPM (DAPPM) and Differential Pulse Interval Modulation (DPIM). Moreover, the symbol error rate (SER) for kth PAM is derived for ds distances between symbols. The performance in Symbol Error Rate (SER) is improved by introducing the Positive and Negative Amplitudes (PNA) levels with respect to DC-bias. The theoretical and simulation results show that the proposed scheme outperforms the existing schemes in terms of bandwidth, and transmission capacity. Keywords: Hadamard Code Matrix, Modulation, Visible Light Communication

Bayesian Electromagnetic Spatio-Temporal Imaging of Extended Sources Based on Matrix Factorization.

Accurate estimation of the locations and extents of neural sources from electroencephalography and magnetoencephalography (E/MEG) is challenging, especially for deep and highly correlated neural activities. In this study, we proposed a new fully data-driven source imaging method, source imaging based on spatio-temporal basis function (SI-STBF), which is built upon a Bayesian framework, to address this issue. The SI-STBF is based on the factorization of a source matrix as a product of a sparse coding matrix and a temporal basis function (TBF) matrix, which includes a few TBFs. The prior of the TBF is set in the empirical Bayesian manner. Similarly, for the spatial constraint, the SI-STBF assumes the prior covariance of the coding matrix as a weighted sum of several spatial covariance components. Both the TBFs and the coding matrix are learned from E/MEG simultaneously through variational Bayesian inference. To enable inference on high-resolution source space, we derived a scalable algorithm using convex analysis. The performance of the SI-STBF was assessed using both simulated and experimental E/MEG recordings. Compared with L2-norm constrained methods, the SI-STBF is superior in reconstructing extended sources with less spatial diffusion and less localization error. By virtue of the spatio-temporal factorization of source matrix, the SI-STBF also produces more accurate estimations than spatial-only constraint method for high correlated and deep sources.

New Non-binary Quantum Codes Over <i>F<sub>q</sub>+uF<sub>q</sub>+vF<sub>q</sub>+uvF<sub>q</sub></i>

Let R= Fq+uFq+vFq+uvFq be a commutative ring with u2=u, v2=v, uv=vu, where q is a power of an odd prime. Ashraf and Mohammad constructed some new quantum codes from cyclic codes. Under this background, another Gray map from R to Fq4 is given. This map can be naturally extended to Rn. The problem on the ring turns to the field by this isomorphic map now. Therefore, This mapping is obviously a weight-preserving and distance-preserving map. The results show that the codes after mapping are self-orthogonal codes over Fq if they are self-orthogonal codes over R. Some computational examples show that some better non-binary quantum codes can be obtained under this Gray map. We discuss the structure of linear codes. On this basis, the structure of the generating matrix of linear codes is obtained. The structure of their dual codes is also obtained. The CSS construction guarantees the existence of quantum codes. Finally, with the help of the CSS construction, we get some good quantum codes. By comparison, our quantum codes have better parameters.

Improving the Signal-to-Noise Ratio of Time Domain Fiber Bragg Grating Sensor Based on Hybrid Simplex and Golay Coding Technique

We report on the experimental results of the combination of unique auto-correlation properties of Golay complementary code and Hadamard matrix properties of standard simplex code. The combination of the two coding techniques results in improvement of the signal-to-noise ratio (SNR) of time domain multiplexed fiber Bragg grating (TDM-FBG) sensor for temperature measurement. Previously, we have analyzed the properties of both coding techniques when deployed separately in the TDM-FBG sensor. In this case, both coding techniques result in the same amount of SNR improvement for code length longer than 31 bits. In this paper, we demonstrate the combination and simultaneous deployment of the two techniques to measure multiple FBGs under room condition (25 °C) and 50 °C temperature. The two schemes combination results in remarkable improvement of SNR and still retains the original spatial property of the decoded FBG signals, confirming the successful deployment of the hybrid codes. From the measurement of two FBG sensors located after 16 km of fiber, the combination of 31 bits of simplex- and 64 bits of Golay codes has resulted in a total of 10.5 dB improvement of SNR.

Tensor Representation of Rank-Metric Codes

We present the theory of rank-metric codes with respect to the 3-tensors that generate them. We define the generator tensor and the parity check tensor of a matrix code, and describe the properties...

On Privacy Amplification, Lossy Compression, and Their Duality to Channel Coding

We examine the task of privacy amplification from information-theoretic and coding-theoretic points of view. In the former, we give a one-shot characterization of the optimal rate of privacy amplification against classical adversaries in terms of the optimal type-II error in asymmetric hypothesis testing. This formulation can be easily computed to give finite-blocklength bounds and turns out to be equivalent to smooth min-entropy bounds by Renner and Wolf [Asiacrypt 2005] and Watanabe and Hayashi [ISIT 2013], as well as a bound in terms of the $E_\gamma$ divergence by Yang, Schaefer, and Poor [arXiv:1706.03866 [cs.IT]]. In the latter, we show that protocols for privacy amplification based on linear codes can be easily repurposed for channel simulation. Combined with known relations between channel simulation and lossy source coding, this implies that privacy amplification can be understood as a basic primitive for both channel simulation and lossy compression. Applied to symmetric channels or lossy compression settings, our construction leads to proto- cols of optimal rate in the asymptotic i.i.d. limit. Finally, appealing to the notion of channel duality recently detailed by us in [IEEE Trans. Info. Theory 64, 577 (2018)], we show that linear error-correcting codes for symmetric channels with quantum output can be transformed into linear lossy source coding schemes for classical variables arising from the dual channel. This explains a "curious duality" in these problems for the (self-dual) erasure channel observed by Martinian and Yedidia [Allerton 2003; arXiv:cs/0408008] and partly anticipates recent results on optimal lossy compression by polar and low-density generator matrix codes.

High-Rate Spatially Modulated Space Time Block Code

A high-rate spatially modulated space-time block code (HRSM-STBC) based on golden code is presented in which the spatial constellation (SC) codewords and the core STBC code matrix are designed for two active antennas. In addition to the high rate of the core STBC, the number of SC codewords offered by the HRSM-STBC scheme is the largest as compared to existing schemes that have the same antenna configuration. Consequently, the proposed scheme can provide the highest spectral efficiency to date. To maximize the achievable coding gain and diversity, the optimization of the HRSM-STBC is carried out. Performance advantages of our proposed scheme over its existing counterparts such as STBC-SM, H-STBC-SM, STBC-CSM, and DT-SM are demonstrated.

Options to Use Data Matrix Codes in Production Engineering

Abstract The paper deals with the possibilities of using Data Matrix codes in production engineering. We designed and tested the computationally efficient method for locating the Data Matrix code in the images. The location search procedure consists of identification of candidate regions using image binarization, then joining adjacent points into continuous regions and also examining outer boundaries of the regions. Afterwards we verify the presence of the Finder Pattern (as two perpendicular line segments) and Timing Pattern (as alternating sequence of black and white modules) in these candidate regions. Such procedure is invariant to shift rotation and scale change of Data Matrix codes. The method we have proposed has been verified on a set of real industrial images and compared to other commercial algorithms. We are also convinced that such technique is also suitable for real-time processing and has achieved better results than comparable commercial algorithms.

Multi-task hybrid dictionary learning for vehicle classification in sensor networks

In this article, we propose a novel multi-task hybrid dictionary learning approach for moving vehicle classification tasks using multi-sensor networks to improve the classification accuracy in complex scenes with low time complexity, which considers both correlations and complementary information among multiple heterogeneous sensors simultaneously to learn a hybrid dictionary within observations of each sensor. The efficient hybrid dictionary consists of a synthesis dictionary and an analysis dictionary, where discriminative codes can be generated by the trained analysis dictionary and class-specific discriminative reconstruction can be achieved by the trained synthesis dictionary. Extensive experiments are conducted on real data sets captured by the multiple heterogeneous sensors, and the results demonstrate that the proposed method can use the multi-feature fusion method to improve the vehicle classification accuracy, and it can learn a hybrid dictionary to make sure that the sparse coding matrix is obtained by simple linear mapping function. Moreover, the problem of [Formula: see text]-norm[Formula: see text] sparse coding can been solved, to reduce the time complexity of this algorithm, compared with support vector machine, sparse representation classification, label consistent KSVD, Fisher discrimination dictionary learning, hybrid dictionary learning, multi-task sparse representation classification, and multi-task Fisher discrimination dictionary learning algorithms.

On quantum SPC product codes

Some methods have been proposed to construct quantum codes out of classical codes. There is a relationship between quantum codes and codes on the quaternary field. The structure of CSS codes has been raised to construct quantum codes. Most of them are based on the fact that a classical code is self-orthogonal. In this paper, a quantum code is constructed using a suitable permutation-based technique on the parity check matrix of classical codes. Several examples of the new quantum error correcting codes are provided. Single parity check (SPC) product codes have simple decoding algorithms, as well as good decoding efficiency. With this technique, the SPC product codes are used to construct quantum codes.

Improving Error Correction Codes for Multiple-Cell Upsets in Space Applications

Currently, faults suffered by SRAM memory systems have increased due to the aggressive CMOS integration density. Thus, the probability of occurrence of single-cell upsets (SCUs) or multiple-cell upsets (MCUs) augments. One of the main causes of MCUs in space applications is cosmic radiation. A common solution is the use of error correction codes (ECCs). Nevertheless, when using ECCs in space applications, they must achieve a good balance between error coverage and redundancy, and their encoding/decoding circuits must be efficient in terms of area, power, and delay. Different codes have been proposed to tolerate MCUs. For instance, Matrix codes use Hamming codes and parity checks in a bi-dimensional layout to correct and detect some patterns of MCUs. Recently presented, column–line–code (CLC) has been designed to tolerate MCUs in space applications. CLC is a modified Matrix code, based on extended Hamming codes and parity checks. Nevertheless, a common property of these codes is the high redundancy introduced. In this paper, we present a series of new low-redundant ECCs able to correct MCUs with reduced area, power, and delay overheads. Also, these new codes maintain, or even improve, memory error coverage with respect to Matrix and CLC codes.

Unsupervised Feature Learning From Time-Series Data Using Linear Models

In the Internet of Things (IoT), heterogenous sensors generate time-series data with different properties. The problem of unsupervised feature learning from a time-series dataset poses two challenges. First, it is known that centroids obtained by clustering time-series with high overlap do not reflect their patterns, i.e., subsequence time-series clustering is meaningless . In this paper, we show that principal component analysis, sparse coding, and non-negative matrix factorization are also meaningless for the same task, and that the systematic approach to learning meaningful features from time-series is by using the shift-invariant versions of these algorithms. Second, by comparing their shift-invariant versions on different kinds of time-series for reconstruction, prediction and classification, we show that no one algorithm is best suited for all time-series. This comparison leads to a method for automatically selecting the suitable feature learning algorithm for a given time-series dataset based on its structural properties. Generality of the method and significance of the structural properties are examined using statistical tests. The method can be implemented as a simple logic circuit, convenient for embedding in IoT hardware.

Experimental investigation and optimisation of laser direct part marking of Inconel 718

Many industries need product identification; laser marking is suitable to produce any kind of symbol, data matrix or bar code on parts. Consequently, the most important requirement for marking acceptance is, doubtless, the mark readability. The present study deals on the effect of process parameters on the laser marking of Inconel 718, with the aim to find a relation between the process parameters and mark characteristics in term of both mark geometry and readability. To this aim, laser markings, under different process conditions, were performed on Inconel 718 sheets, adopting a 30 W Q-switched Yb:YAG laser. The mark geometry was acquired by a 3D surface profiling system. Optical microscopy and SEM analysis were also performed on groove sections. In order to evaluate the readability of the marks, Weber contrast was calculated and adopted. The mark characteristics have been investigated by mean of statistical methodology (ANalysis of VAriance and Response Surface Method) and related to the process parameters. Furthermore, Master Response Optimisation methodology was adopted to individuate the optimal process conditions. It was found that mark geometry and the Weber contrast are mainly affected by the average power and the energy input per mark-length. Moreover, operative conditions allowing for maximum readability, yet without excessive increase in burr height, were also determined.