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Special Issue "Information Theory Applications in Signal Processing"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (15 January 2019)

Special Issue Editors

Guest Editor
Dr. Sergio Cruces

Departamento de Teoría de la Señal y Comunicaciones, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Seville, Spain
Website | E-Mail
Interests: signal processing; information theory; machine learning; communications; audio
Guest Editor
Dr. Rubén Martín-Clemente

Departamento de Teoría de la Señal y Comunicaciones, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Seville, Spain
Website | E-Mail
Interests: digital signal processing; biomedical engineering; digital communications
Guest Editor
Dr. Wojciech Samek

Fraunhofer Heinrich Hertz Institute HHI, 10587 Berlin, Germany
Website | E-Mail
Interests: machine learning; interpretability; deep learning; artificial intelligence; robust signal processing

Special Issue Information

Dear Colleagues,

Information theory plays a fundamental role in the determination of theoretical performance limits for statistical estimation, detection, and compression. Its remarkable history of success during the last few decades has fueled research on information-guided principles for data analysis and signal processing. These dynamic and fast-growing fields have to cope with increasingly complex scenarios and novel applications in component analysis, machine learning, and communications. Hence, there is a need for specific information theoretic criteria and algorithms that work in each of the considered situations and attain a set of desired goals, for instance, an enhancement in the interpretability of the solutions, improvements in performance, robustness with respect to the model uncertainties and possible data perturbations, a reliable convergence for the algorithms and any other kind of theoretical guarantees.

In this Special Issue, we encourage researchers to present their original and recent developments in information theory for advanced methods in signal processing. Possible topics include, but are not limited to, the following:

  • Information criteria, divergence measures and algorithms for source separation, independent component analysis, matrix/tensor decompositions, data approximation and completion, low-rank and sparse based methods.
  • Applications in machine learning, including supervised and unsupervised methods, data representation, dimensionality reduction, feature extraction, Bayesian approaches and deep learning.
  • Applications in statistical signal processing, including parameter estimation, system identification, pattern classification, signal approximation and compressed sensing, signal analysis and restoration.
  • Applications in biomedical engineering, speech/audio processing, and communications.

Dr. Sergio Cruces
Dr. Rubén Martín-Clemente
Dr. Wojciech Samek
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (14 papers)

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Research

Open AccessArticle A New Dictionary Construction Based Multimodal Medical Image Fusion Framework
Entropy 2019, 21(3), 267; https://doi.org/10.3390/e21030267
Received: 12 January 2019 / Revised: 22 February 2019 / Accepted: 4 March 2019 / Published: 9 March 2019
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Abstract
Training a good dictionary is the key to a successful image fusion method of sparse representation based models. In this paper, we propose a novel dictionary learning scheme for medical image fusion. First, we reinforce the weak information of images by extracting and [...] Read more.
Training a good dictionary is the key to a successful image fusion method of sparse representation based models. In this paper, we propose a novel dictionary learning scheme for medical image fusion. First, we reinforce the weak information of images by extracting and adding their multi-layer details to generate the informative patches. Meanwhile, we introduce a simple and effective multi-scale sampling to implement a multi-scale representation of patches while reducing the computational cost. Second, we design a neighborhood energy metric and a multi-scale spatial frequency metric for clustering the image patches with a similar brightness and detail information into each respective patch group. Then, we train the energy sub-dictionary and detail sub-dictionary, respectively by K-SVD. Finally, we combine the sub-dictionaries to construct a final, complete, compact and informative dictionary. As a main contribution, the proposed online dictionary learning can not only obtain an informative as well as compact dictionary, but can also address the defects, such as superfluous patch issues and low computation efficiency, in traditional dictionary learning algorithms. The experimental results show that our algorithm is superior to some state-of-the-art dictionary learning based techniques in both subjective visual effects and objective evaluation criteria. Full article
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Open AccessArticle Efficient Low-PAR Waveform Design Method for Extended Target Estimation Based on Information Theory in Cognitive Radar
Entropy 2019, 21(3), 261; https://doi.org/10.3390/e21030261
Received: 29 December 2018 / Revised: 14 February 2019 / Accepted: 5 March 2019 / Published: 7 March 2019
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Abstract
This paper addresses the waveform design problem of cognitive radar for extended target estimation in the presence of signal-dependent clutter, subject to a peak-to-average power ratio (PAR) constraint. Owing to this kind of constraint and the convolution operation of the waveform in the [...] Read more.
This paper addresses the waveform design problem of cognitive radar for extended target estimation in the presence of signal-dependent clutter, subject to a peak-to-average power ratio (PAR) constraint. Owing to this kind of constraint and the convolution operation of the waveform in the time domain, the formulated optimization problem for maximizing the mutual information (MI) between the target and the received signal is a complex non-convex problem. To this end, an efficient waveform design method based on minimization–maximization (MM) technique is proposed. First, by using the MM approach, the original non-convex problem is converted to a convex problem concerning the matrix variable. Then a trick is used for replacing the matrix variable with the vector variable by utilizing the properties of the Toeplitz matrix. Based on this, the optimization problem can be solved efficiently combined with the nearest neighbor method. Finally, an acceleration scheme is used to improve the convergence speed of the proposed method. The simulation results illustrate that the proposed method is superior to the existing methods in terms of estimation performance when designing the constrained waveform. Full article
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Open AccessArticle Informed Weighted Non-Negative Matrix Factorization Using αβ-Divergence Applied to Source Apportionment
Entropy 2019, 21(3), 253; https://doi.org/10.3390/e21030253
Received: 19 January 2019 / Revised: 21 February 2019 / Accepted: 26 February 2019 / Published: 6 March 2019
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Abstract
In this paper, we propose informed weighted non-negative matrix factorization (NMF) methods using an αβ-divergence cost function. The available information comes from the exact knowledge/boundedness of some components of the factorization—which are used to structure the NMF parameterization—together with the row [...] Read more.
In this paper, we propose informed weighted non-negative matrix factorization (NMF) methods using an α β -divergence cost function. The available information comes from the exact knowledge/boundedness of some components of the factorization—which are used to structure the NMF parameterization—together with the row sum-to-one property of one matrix factor. In this contribution, we extend our previous work which partly involved some of these aspects to α β -divergence cost functions. We derive new update rules which are extendthe previous ones and take into account the available information. Experiments conducted for several operating conditions on realistic simulated mixtures of particulate matter sources show the relevance of these approaches. Results from a real dataset campaign are also presented and validated with expert knowledge. Full article
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Open AccessFeature PaperArticle Centroid-Based Clustering with αβ-Divergences
Entropy 2019, 21(2), 196; https://doi.org/10.3390/e21020196
Received: 18 January 2019 / Revised: 6 February 2019 / Accepted: 14 February 2019 / Published: 19 February 2019
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Abstract
Centroid-based clustering is a widely used technique within unsupervised learning algorithms in many research fields. The success of any centroid-based clustering relies on the choice of the similarity measure under use. In recent years, most studies focused on including several divergence measures in [...] Read more.
Centroid-based clustering is a widely used technique within unsupervised learning algorithms in many research fields. The success of any centroid-based clustering relies on the choice of the similarity measure under use. In recent years, most studies focused on including several divergence measures in the traditional hard k-means algorithm. In this article, we consider the problem of centroid-based clustering using the family of α β -divergences, which is governed by two parameters, α and β . We propose a new iterative algorithm, α β -k-means, giving closed-form solutions for the computation of the sided centroids. The algorithm can be fine-tuned by means of this pair of values, yielding a wide range of the most frequently used divergences. Moreover, it is guaranteed to converge to local minima for a wide range of values of the pair ( α , β ). Our theoretical contribution has been validated by several experiments performed with synthetic and real data and exploring the ( α , β ) plane. The numerical results obtained confirm the quality of the algorithm and its suitability to be used in several practical applications. Full article
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Open AccessArticle New Construction of Maximum Distance Separable (MDS) Self-Dual Codes over Finite Fields
Entropy 2019, 21(2), 101; https://doi.org/10.3390/e21020101
Received: 24 December 2018 / Revised: 10 January 2019 / Accepted: 17 January 2019 / Published: 22 January 2019
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Abstract
Maximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality. MDS self-dual codes are completely determined by the length n, so the problem of constructing q-ary MDS self-dual codes [...] Read more.
Maximum distance separable (MDS) self-dual codes have useful properties due to their optimality with respect to the Singleton bound and its self-duality. MDS self-dual codes are completely determined by the length n , so the problem of constructing q-ary MDS self-dual codes with various lengths is a very interesting topic. Recently X. Fang et al. using a method given in previous research, where several classes of new MDS self-dual codes were constructed through (extended) generalized Reed-Solomon codes, in this paper, based on the method given in we achieve several classes of MDS self-dual codes. Full article
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
Open AccessArticle Quaternion Entropy for Analysis of Gait Data
Entropy 2019, 21(1), 79; https://doi.org/10.3390/e21010079
Received: 9 December 2018 / Revised: 9 January 2019 / Accepted: 15 January 2019 / Published: 17 January 2019
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Abstract
Nonlinear dynamical analysis is a powerful approach to understanding biological systems. One of the most used metrics of system complexities is the Kolmogorov entropy. Long input signals without noise are required for the calculation, which are very hard to obtain in real situations. [...] Read more.
Nonlinear dynamical analysis is a powerful approach to understanding biological systems. One of the most used metrics of system complexities is the Kolmogorov entropy. Long input signals without noise are required for the calculation, which are very hard to obtain in real situations. Techniques allowing the estimation of entropy directly from time signals are statistics like approximate and sample entropy. Based on that, the new measurement for quaternion signal is introduced. This work presents an example of application of a nonlinear time series analysis by using the new quaternion, approximate entropy to analyse human gait kinematic data. The quaternion entropy was applied to analyse the quaternion signal which represents the segments orientations in time during the human gait. The research was aimed at the assessment of the influence of both walking speed and ground slope on the gait control during treadmill walking. Gait data was obtained by the optical motion capture system. Full article
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Open AccessArticle A New Efficient Expression for the Conditional Expectation of the Blind Adaptive Deconvolution Problem Valid for the Entire Range ofSignal-to-Noise Ratio
Entropy 2019, 21(1), 72; https://doi.org/10.3390/e21010072
Received: 10 December 2018 / Revised: 9 January 2019 / Accepted: 14 January 2019 / Published: 15 January 2019
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Abstract
In the literature, we can find several blind adaptive deconvolution algorithms based on closed-form approximated expressions for the conditional expectation (the expectation of the source input given the equalized or deconvolutional output), involving the maximum entropy density approximation technique. The main drawback of [...] Read more.
In the literature, we can find several blind adaptive deconvolution algorithms based on closed-form approximated expressions for the conditional expectation (the expectation of the source input given the equalized or deconvolutional output), involving the maximum entropy density approximation technique. The main drawback of these algorithms is the heavy computational burden involved in calculating the expression for the conditional expectation. In addition, none of these techniques are applicable for signal-to-noise ratios lower than 7 dB. In this paper, I propose a new closed-form approximated expression for the conditional expectation based on a previously obtained expression where the equalized output probability density function is calculated via the approximated input probability density function which itself is approximated with the maximum entropy density approximation technique. This newly proposed expression has a reduced computational burden compared with the previously obtained expressions for the conditional expectation based on the maximum entropy approximation technique. The simulation results indicate that the newly proposed algorithm with the newly proposed Lagrange multipliers is suitable for signal-to-noise ratio values down to 0 dB and has an improved equalization performance from the residual inter-symbol-interference point of view compared to the previously obtained algorithms based on the conditional expectation obtained via the maximum entropy technique. Full article
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Open AccessArticle SINR- and MI-Based Maximin Robust Waveform Design
Entropy 2019, 21(1), 33; https://doi.org/10.3390/e21010033
Received: 27 September 2018 / Revised: 17 December 2018 / Accepted: 2 January 2019 / Published: 7 January 2019
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Abstract
Due to the uncertainties of radar target prior information in the actual scene, the waveform designed based on radar target prior information cannot meet the needs of detection and parameter estimation performance. In this paper, the optimal waveform design techniques under energy constraints [...] Read more.
Due to the uncertainties of radar target prior information in the actual scene, the waveform designed based on radar target prior information cannot meet the needs of detection and parameter estimation performance. In this paper, the optimal waveform design techniques under energy constraints for different tasks are considered. To improve the detection performance of radar systems, a novel waveform design method which can maximize the signal-to-interference-plus-noise ratio (SINR) for known and random extended targets is proposed. To improve the performance of parameter estimation, another waveform design method which can maximize the mutual information (MI) between the radar echo and the random-target spectrum response is also considered. Most of the previous waveform design researches assumed that the prior information of the target spectrum is completely known. However, in the actual scene, the real target spectrum cannot be accurately captured. To simulate this scenario, the real target spectrum was assumed to be within an uncertainty range where the upper and lower bounds are known. Then, the SINR- and MI-based maximin robust waveforms were designed, which could optimize the performance under the most unfavorable conditions. The simulation results show that the designed optimal waveforms based on these two criteria are different, which provides useful guidance for waveform energy allocation in different transmission tasks. However, under the constraint of limited energy, we also found that the performance improvement of SINR or MI in the worst case for single targets is less significant than that of multiple targets. Full article
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Open AccessArticle Computing the Partial Correlation of ICA Models for Non-Gaussian Graph Signal Processing
Entropy 2019, 21(1), 22; https://doi.org/10.3390/e21010022
Received: 23 November 2018 / Revised: 23 December 2018 / Accepted: 24 December 2018 / Published: 29 December 2018
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Abstract
Conventional partial correlation coefficients (PCC) were extended to the non-Gaussian case, in particular to independent component analysis (ICA) models of the observed multivariate samples. Thus, the usual methods that define the pairwise connections of a graph from the precision matrix were correspondingly extended. [...] Read more.
Conventional partial correlation coefficients (PCC) were extended to the non-Gaussian case, in particular to independent component analysis (ICA) models of the observed multivariate samples. Thus, the usual methods that define the pairwise connections of a graph from the precision matrix were correspondingly extended. The basic concept involved replacing the implicit linear estimation of conventional PCC with a nonlinear estimation (conditional mean) assuming ICA. Thus, it is better eliminated the correlation between a given pair of nodes induced by the rest of nodes, and hence the specific connectivity weights can be better estimated. Some synthetic and real data examples illustrate the approach in a graph signal processing context. Full article
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Open AccessArticle Auditory Inspired Convolutional Neural Networks for Ship Type Classification with Raw Hydrophone Data
Entropy 2018, 20(12), 990; https://doi.org/10.3390/e20120990
Received: 26 October 2018 / Revised: 13 December 2018 / Accepted: 14 December 2018 / Published: 19 December 2018
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Abstract
Detecting and classifying ships based on radiated noise provide practical guidelines for the reduction of underwater noise footprint of shipping. In this paper, the detection and classification are implemented by auditory inspired convolutional neural networks trained from raw underwater acoustic signal. The proposed [...] Read more.
Detecting and classifying ships based on radiated noise provide practical guidelines for the reduction of underwater noise footprint of shipping. In this paper, the detection and classification are implemented by auditory inspired convolutional neural networks trained from raw underwater acoustic signal. The proposed model includes three parts. The first part is performed by a multi-scale 1D time convolutional layer initialized by auditory filter banks. Signals are decomposed into frequency components by convolution operation. In the second part, the decomposed signals are converted into frequency domain by permute layer and energy pooling layer to form frequency distribution in auditory cortex. Then, 2D frequency convolutional layers are applied to discover spectro-temporal patterns, as well as preserve locality and reduce spectral variations in ship noise. In the third part, the whole model is optimized with an objective function of classification to obtain appropriate auditory filters and feature representations that are correlative with ship categories. The optimization reflects the plasticity of auditory system. Experiments on five ship types and background noise show that the proposed approach achieved an overall classification accuracy of 79.2%, which improved by 6% compared to conventional approaches. Auditory filter banks were adaptive in shape to improve accuracy of classification. Full article
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Open AccessArticle A Novel Image Encryption Scheme Based on Collatz Conjecture
Entropy 2018, 20(12), 901; https://doi.org/10.3390/e20120901
Received: 24 October 2018 / Revised: 11 November 2018 / Accepted: 21 November 2018 / Published: 25 November 2018
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Abstract
Image encryption methods aim to protect content privacy. Typically, they encompass scrambling and diffusion. Every pixel of the image is permuted (scrambling) and its value is transformed according to a key (diffusion). Although several methods have been proposed in the literature, some of [...] Read more.
Image encryption methods aim to protect content privacy. Typically, they encompass scrambling and diffusion. Every pixel of the image is permuted (scrambling) and its value is transformed according to a key (diffusion). Although several methods have been proposed in the literature, some of them have been cryptanalyzed. In this paper, we present a novel method that deviates the traditional schemes. We use variable length codes based on Collatz conjecture for transforming the content of the image into non-intelligible audio; therefore, scrambling and diffusion processes are performed simultaneously in a non-linear way. With our method, different ciphered audio is obtained every time, and it depends exclusively on the selected key (the size of the key space equal to 8 . 57 × 10 506 ). Several tests were performed in order to analyze randomness of the ciphered audio signals and the sensitivity of the key. Firstly, it was found that entropy and the level of disorder of ciphered audio signals are very close to the maximum value of randomness. Secondly, fractal behavior was detected into scatter plots of adjacent samples, altering completely the behavior of natural images. Finally, if the key was slightly modified, the image could not be recovered. With the above results, it was concluded that our method is very useful in image privacy protection applications. Full article
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Open AccessArticle Sparse Optimistic Based on Lasso-LSQR and Minimum Entropy De-Convolution with FARIMA for the Remaining Useful Life Prediction of Machinery
Entropy 2018, 20(10), 747; https://doi.org/10.3390/e20100747
Received: 11 September 2018 / Revised: 28 September 2018 / Accepted: 28 September 2018 / Published: 29 September 2018
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Abstract
To reduce the maintenance cost and safeguard machinery operation, remaining useful life (RUL) prediction is very important for long term health monitoring. In this paper, we introduce a novel hybrid method to deal with the RUL prediction for health management. Firstly, the sparse [...] Read more.
To reduce the maintenance cost and safeguard machinery operation, remaining useful life (RUL) prediction is very important for long term health monitoring. In this paper, we introduce a novel hybrid method to deal with the RUL prediction for health management. Firstly, the sparse reconstruction algorithm of the optimized Lasso and the Least Square QR-factorization (Lasso-LSQR) is applied to compressed sensing (CS), which can realize the sparse optimization for long term health monitoring data. After the sparse signal is reconstructed, the minimum entropy de-convolution (MED) is used to identify the fault characteristics and to obtain significant fault information from the machinery operation. Health indicators with Skip-over, sample entropy and approximate entropy are then performed to track the degradation of the machinery process. The performance analysis of the Skip-over is superior to other indicators. Finally, Fractal Autoregressive Integrated Moving Average model (FARIMA) is employed to predict the Skip-over using the R/S method. The analysis results evidence that the novel hybrid method yields a good performance, and such method can achieve highly accurate RUL prediction and safeguard machinery operation for long term monitoring. Full article
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Open AccessArticle Dynamic Rounds Chaotic Block Cipher Based on Keyword Abstract Extraction
Entropy 2018, 20(9), 693; https://doi.org/10.3390/e20090693
Received: 5 July 2018 / Revised: 28 August 2018 / Accepted: 8 September 2018 / Published: 11 September 2018
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Abstract
According to the keyword abstract extraction function in the Natural Language Processing and Information Retrieval Sharing Platform (NLPIR), the design method of a dynamic rounds chaotic block cipher is presented in this paper, which takes into account both the security and efficiency. The [...] Read more.
According to the keyword abstract extraction function in the Natural Language Processing and Information Retrieval Sharing Platform (NLPIR), the design method of a dynamic rounds chaotic block cipher is presented in this paper, which takes into account both the security and efficiency. The cipher combines chaotic theory with the Feistel structure block cipher, and uses the randomness of chaotic sequence and the nonlinearity of chaotic S-box to dynamically generate encrypted rounds, realizing more numbers of dynamic rounds encryption for the important information marked by NLPIR, while less numbers of dynamic rounds encryption for the non-important information that is not marked. Through linear and differential cryptographic analysis, ciphertext information entropy, “0–1” balance and National Institute of Science and Technology (NIST) tests and the comparison with other traditional and lightweight block ciphers, the results indicate that the dynamic variety of encrypted rounds can achieve different levels of encryption for different information, which can achieve the purpose of enhancing the anti-attack ability and reducing the number of encrypted rounds. Therefore, the dynamic rounds chaotic block cipher can guarantee the security of information transmission and realize the lightweight of the cryptographic algorithm. Full article
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Open AccessArticle Achievable Rate Region under Linear Beamforming for Dual-Hop Multiple-Access Relay Network
Entropy 2018, 20(8), 547; https://doi.org/10.3390/e20080547
Received: 20 May 2018 / Revised: 18 July 2018 / Accepted: 21 July 2018 / Published: 24 July 2018
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Abstract
Consider a network consisting of two independent single-antenna sources, a single-antenna destination and a helping multiple-antenna relay. This network is called a dual-hop multiple access relay network (MARN). In this network, sources transmit to the relay simultaneously in the first time slot. The [...] Read more.
Consider a network consisting of two independent single-antenna sources, a single-antenna destination and a helping multiple-antenna relay. This network is called a dual-hop multiple access relay network (MARN). In this network, sources transmit to the relay simultaneously in the first time slot. The relay retransmits the received sum-signal to the destination using a linear beamforming scheme in the second time slot. In this paper, we characterize the achievable rate region of MARN under linear beamforming. The achievable rate region characterization problem is first transformed to an equivalent “corner point” optimization problem with respect to linear beamforming matrix at the relay. Then, we present an efficient algorithm to solve it via only semi-definite programming (SDP). We further derive the mathematical close-forms of the maximum individual rates and the sum-rate. Finally, numerical results demonstrate the performance of the proposed schemes. Full article
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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