Time-Variant Decoding of Convolutional Network Codes

We propose an efficient Adaptive Random Convolutional Network Coding (ARCNC)\nalgorithm to address the issue of field size in random network coding. ARCNC\noperates as a convolutional code, with the coefficients of local encoding\nkernels chosen randomly over a small finite field. The lengths of local\nencoding kernels increase with time until the global encoding kernel matrices\nat related sink nodes all have full rank. Instead of estimating the necessary\nfield size a priori, ARCNC operates in a small finite field. It adapts to\nunknown network topologies without prior knowledge, by locally incrementing the\ndimensionality of the convolutional code. Because convolutional codes of\ndifferent constraint lengths can coexist in different portions of the network,\nreductions in decoding delay and memory overheads can be achieved with ARCNC.\nWe show through analysis that this method performs no worse than random linear\nnetwork codes in general networks, and can provide significant gains in terms\nof average decoding delay in combination networks.\n

结合卷积神经网络和稀疏编码的高光谱图像分类

In this article, we comment on the well known connection between noise and Q-Wiener processes. In physical applications, noise is usually given as a generalized Gaussian process and all assumptions are formulated in terms of the correlation functional. In contrast, the mathematical theory of stochastic partial differential equations on bounded domains is in many cases formulated with Q-Wiener processes. Our aim is to relate frequently made assumptions on the covariance operator Q to assumptions on the correlation function of the noise process, which is the kernel of Q. One of our main results gives necessary and sufficient conditions when the Wiener process is given as a series expansion in terms of eigenfunctions of the Laplacian.

To protect user privacy in wireless mesh networks (WMNs), it is important to address two major challenges, namely: flow untraceability and movement untraceability, which prevent malicious attackers from deducing the flow paths and the movement tracks of mobile devices. For these two privacy requirements, most existing approaches rely on encrypting the whole packet, appending random padding, and applying random delay for each message at every intermediate node, resulting in significant computational and communication overheads. Recently, linear network coding (LNC) has been introduced as an alternative but the global encoding vectors (GEVs) of coded messages have to be encrypted so as to conceal the relationships between the incoming and outgoing messages. In this paper, we aim to explore the potential of LNC to ensure the flow untraceability and movement untraceability. Specifically, we first determine the necessary and sufficient condition, with which the two privacy requirements can be achieved without encrypting either GEVs or message contents. We then design a deterministic untraceable LNC (ULNC) scheme to provide flow untraceability and movement untraceability when the sufficient and necessary condition is satisfied. Finally, we discuss the effectiveness of the proposed ULNC scheme against traffic analysis attacks in WMNs.

In two-way relay networks (TWRNs) with physical-layer network coding (PNC), introduction of convolutional codes is able to enhance the overall system reliability. In addition, the relay node has to determine a particular broadcast rate for coded packets transmission as the selected rate should be supported on the worst quality links to the intended receivers. Thus, the throughput gain brought by network coding is limited by capacity of the worst link in TWRNs. In this paper, a novel symbol-level rate diverse network coding (RDNC) scheme and reduced-state decoding scheme for convolutional codes are proposed to address the two problems. In this setup, for a given memory length constraint, two source nodes can adopt convolutional codes of different lengths and use reduced-state trellis to reduce decoding complexity. In this work, it is shown that the proposed approach is able to improve system throughput significantly, offer increased reliability, and reduce the complexity of convolutional codes decoding at the same time.

This paper deals with the performance of "Generalized Minimum Distance Decoding". In this method, a generalized distance taking into account of the reliability of the code symbol is used. We outline relationships between generalized minimum distance and correlation which are two criteria equivalent to Maximum Likelihood Decoding (MLD). A sufficient condition which guarantees the correct result of the GMD decoding algorithm is studied. For high signal-to-noise ratios, the GMD decoding algorithm enables to achieve MLD performance with a complexity O(n3). We present, by computer simulation, the behavior of the GMD algorithm for different error-correcting codes, in particular, the results for concatenated schemes (Reed-Solomon outer codes with inner convolutional codes).

New solutions for the elliptic Darboux equation are obtained as particular cases of solutions constructed for Heun's general equation. We consider two groups of power series expansions and two new groups of expansions in series of Gauss hypergeometric functions. The convergence of one group in power series is determined by means of ratio tests for infinite series, while the other groups are designed to solve problems which admit finite‐series solutions. Actually, we envisage periodic quasi‐exactly solvable potentials for which the stationary one‐dimensional Schrödinger equation is reduced to the Darboux equation. In general, finite‐ and infinite‐series solutions are obtained from power series expansions for Heun's equation. However, we show that the Schrödinger equation admits additional finite‐series expansions in terms of hypergeometric functions for a family of associated Lamé potentials used in band theory of solids.For each finite‐series solution, we find as well four infinite‐series expansions which are bounded and convergent for all values of the independent variable.

A new dynamic model of light-weight spur gear transmission system considering the elasticity of the shaft and gear body

A system dynamics model of fire-tube shell boiler was developed. The derivation of the dynamics model started with a nonlinear time-variant dynamic modeling based on the transport phenomena in the fire-tube boiler. A linear time-invariant perturbed model around steady-state operating points was then derived. The identifiable parameters τmw, τwa, K, β, and τd were identified by using field test data and least-squares estimation method; the coefficients C’s were, meanwhile, directly predicted by using the small-perturbation relations. Empirical correlations of the identifiable parameters were further derived to account for the variation of parameters with operating conditions. The present perturbed model is thus semi-empirical and can describe the dynamic behaviour of fire-tube boilers over a wide range of operating conditions. The predictions of dynamic responses using the present model were shown to agree very well with the test results.

This paper focuses on the blind recognition of convolutional codes, a significant research problem in cognitive radios and signal interception. The existing methods based on deep learning (DL) usually directly take the received sequence as the input of a network, of which the recognition accuracy for high-rate convolutional codes is often poor. An identification framework called MT-CNN, combining matrix transformation with convolutional neural networks (CNN), is proposed in this paper. We offer a novel matrix transformation algorithm of which the result can highlight the differences between different encoders. Our proposed MT-CNN method adopts a feature fusion strategy, employing the codeword matrix and its feature map obtained through matrix transformation as the network's input. Simulations show that the proposed approach could provide significant improvements compared to existing methods, especially for the convolutional codes with a high rate.

In this article, we study the analyticity of (directed) areas of ε-neighbourhoods of orbits of parabolic germs. The article is motivated by the question of analytic classification using ε-neighbourhoods of orbits in the simplest formal class.We show that the coefficient in front of the ε2 term in the asymptotic expansion in ε, which we call the principal part of the area, is a sectorially analytic function in the initial point of the orbit. It satisfies a cohomological equation similar to the standard trivialization equation for parabolic diffeomorphisms.We give necessary and sufficient conditions on a diffeomorphism f for the existence of a globally analytic solution of this equation. Furthermore, we introduce a new classification type for diffeomorphisms implied by this new equation and investigate the relative position of its classes with respect to the analytic classes.

A Non-Uniform Estimate for the Convergence Speed in the Multi-Dimensional Central Theorem

The paper studies a model of K-distributed clutter in a radar detection problem. The clutter is modelled with a multidimensional Gaussian probability density function where the variance values are represented by a set of independent random variables distributed with a function. The detection of an a prior known target against the considered K-clutter is studied using the likelihood ratio test. To evaluate the probabilities of false alarm (Pfa) and detection (Pd), we propose, as an alternative to the usual Monte Carlo simulation, a procedure that, resorting to analytical and numerical methods, approximates Pfa and Pd by a power series expansion in terms of a suitable parameter of the model. The numerical work is greatly reduced in the region where the expansion holds. In fact, the high-dimensional integrals involved in the power series expansion are reduced to products of low-dimensional ones. A numerical comparison with the standard Monte Carlo computation has been performed on a test case. The approach used here can be adapted to K-models with correlated Gamma variables.

This paper proposes a new iterative framework for the correction of frequency response mismatch in time-interleaved analog-to-digital converters. Based on a general time-varying linear system model for the mismatch, we treat the reconstruction problem as a linear inverse problem and establish a flexible iterative framework for practical implementation. It encumbrances a number of efficient iterative correction algorithms and simplifies their design, implementation, and performance analysis. In particular, an efficient Gauss-Seidel iteration is studied in detail to illustrate how the correction problem can be solved iteratively and how the proposed structure can be efficiently implemented using Farrow-based variable digital filters with few general-purpose multipliers. We also study important issues, such as the sufficient convergence condition and reconstructed signal spectrum, derive new lower bound of signal-to-distortion-and-noise ratio in order to ensure stable operation, and predict the performance of the proposed structure. Furthermore, we propose an extended iterative structure, which is able to cope with systems involving more than one type of mismatches. Finally, the theoretical results and the effectiveness of the proposed approach are validated by means of computer simulations.

In our recent work (Wang, Burgei, and Zhou, 2018) we studied the hearing loss injury among subjects in a crowd with a wide spectrum of heterogeneous individual injury susceptibility due to biovariability. The injury risk of a crowd is defined as the average fraction of injured. We examined mathematically the injury risk of a crowd vs the number of acoustic impulses the crowd is exposed to, under the assumption that all impulses act independently in causing injury regardless of whether one is preceded by another. We concluded that the observed dose-response relation can be explained solely on the basis of biovariability in the form of heterogeneous susceptibility. We derived an analytical solution for the distribution density of injury susceptibility, as a power series expansion in terms of scaled log individual non-injury probability. While theoretically the power series converges for all argument values, in practical computations with IEEE double precision, at large argument values, the numerical accuracy of the power series summation is completely wiped out by the accumulation of round-off errors. In this study, we derive a general asymptotic approximation at large argument values, for the distribution density. The combination of the power series and the asymptotics provides a practical numerical tool for computing the distribution density. We then use this tool to verify numerically that the distribution obtained in our previous theoretical study is indeed a proper density. In addition, we will also develop a very efficient and accurate Pade approximation for the distribution density.