Large deviations, hypotheses testing, and source coding for finite Markov chains

Let{X_{n}} n geq 1be a finite Markov chain with transition probability matrix of strictly positive entries. A large deviation theorem is proved for the empirical transition count matrix and is used to get asymptotically optimal critical regions for testing simple hypotheses about the transition matrix. As a corollary, the error exponent in the source coding theorem for{X_{n}}is obtained. These results generalize the corresponding results for the independent and identically distributed case.     

On testing simple hypotheses in finite time with Hellman-Cover automata

Asymptoticallyvarepsilon-optimal automata were developed by Hellman and Cover [4] for testing simple hypotheses concerning the parameter of an independent identically distributed sequence of Bernoulli random variables. These automata permit transitions only between adjacent states and employ artificial randomization only at extreme states. In this paper we study the problem of approximating the optimal Hellman-Cover automaton in fixed-sample-size problems. It is shown that the optimal level of the parameter, which regulates the probability of transitions out of an extreme state, tends to zero at the rateln n/nin symmetric testing problems wherenis the sample size. We develop an approximation for the optimal parameter value valid fornsufficiently large.     

Reflector surface deviations in large parabolic antennas

One of the important factors affecting the efficiency of parabolic reflector antennas is the degree to which the surface of the reflector deviates from the true parabolic shape. For a given reflector surface it is also important to locate the focal point of the best-fit paraboloid relative to the existing feed support structure. A simple method is presented for making these measurements, and results are given for a particular 60-ft diameter reflector. Static measurements were made with the antenna axis pointed vertically upwards, and changes were also measured as a function of elevation angle and wind. When the surface errors have a Gaussian distribution relative to the focal point, simple theory indicates that the received power relative to that from a perfect reflecting surface isP/P_{0} = exp -(2pi sigma / lambda)^{2}wheresigmais the standard deviation of the surface errors andlambdais the operating wavelength.     

An introduction to large deviations for communication networks

This paper is an introduction to some large deviations techniques that have been used for analyzing models of communication networks. Starting from the beginning (sequences of i.i.d. random variables), it progresses to some Markov processes in discrete or continuous time. It illustrates the meaning of most theorems by applying them to a common example. Then the AMS model of buffering in ATM is analyzed in a variety of ways. Finally, a few other common models are discussed     

Robust detection of signals: A large deviations approach

Robust detection of a signal is considered for the case of independent and identically distributed observations. Following an asymptotic but nonlocal approach, the exponential rates of decrease of the error probabilities are considered as measure of performance. Under this measure a robust detection structure for the symmetric density case is derived. This detection structure is a generalization of an existing result for the local case and is reduced to it when the signal magnitude tends to zero.     

On universal quantization

The quantization ofn-dimensional vectors inR^{n}with an arbitrary probability measure, under a mean-square error constraint, is discussed. It is demonstrated that a uniform, one-dimensional quantizer followed by a noiseless digital variable-rate encoder ("entropy encoding") can yield a rate that is, for anyn, no more than0.754bit-per-sample higher than the rate associated with the optimaln-dimensionai quantizer, regardless of the probabilistic characterization of the inputn-vector for the allowable mean-square error.     

Optimum testing of multiple hypotheses in quantum detection theory

The problem of specifying the optimum quantum detector in multiple hypotheses testing is considered for application to optical communications. The quantum digital detection problem is formulated as a linear programming problem on an infinite-dimensional space. A necessary and sufficient condition is derived by the application of a general duality theorem specifying the optimum detector in terms of a set of linear operator equations and inequalities. Existence of the optimum quantum detector is also established. The optimality of commuting detection operators is discussed in some examples. The structure and performance of the optimal receiver are derived for the quantum detection of narrow-band coherent orthogonal and simplex signals. It is shown that modal photon counting is asymptotically optimum in the limit of a large signaling alphabet and that the capacity goes to infinity in the absence of a bandwidth limitation.     

Source coding, large deviations, and approximate pattern matching

We present a development of parts of rate-distortion theory and pattern-matching algorithms for lossy data compression, centered around a lossy version of the asymptotic equipartition property (AEP). This treatment closely parallels the corresponding development in lossless compression, a point of view that was advanced in an important paper of Wyner and Ziv in 1989. In the lossless case, we review how the AEP underlies the analysis of the Lempel-Ziv algorithm by viewing it as a random code and reducing it to the idealized Shannon code. This also provides information about the redundancy of the Lempel-Ziv algorithm and about the asymptotic behavior of several relevant quantities. In the lossy case, we give various versions of the statement of the generalized AEP and we outline the general methodology of its proof via large deviations. Its relationship with Barron (1985) and Orey's (1985, 1986) generalized AEP is also discussed. The lossy AEP is applied to (i) prove strengthened versions, of Shannon's(1948, 1974) direct source-coding theorem and universal coding theorems; (ii) characterize the performance of "mismatched" codebooks in lossy data compression; ( iii) analyze the performance of pattern-matching algorithms for lossy compression (including Lempel-Ziv schemes); and (iv) determine the first-order asymptotic of waiting times between stationary processes. A refinement to the lossy AEP is then presented, and it is used to (i) prove second-order (direct and converse) lossy source-coding theorems, including universal coding theorems; (ii) characterize which sources are quantitatively easier to compress; (iii) determine the second-order asymptotic of waiting times between stationary processes; and (iv) determine the precise asymptotic behavior of longest match-lengths between stationary processes. Finally, we discuss extensions of the above framework and results to random fields     

通用光伏系统测试平台的设计

为了统一光伏系统测试方案,避免项目管理混乱和不必要的重复设计等问题,提出了一种通用光伏系统测试平台,制定了光伏系统与PC软件端数据交互协议,实现了用来获取常用光伏系统测试参数及具有良好扩张性的通用用户监控界面。测试结果表明,该测试平台很好地解决了上述问题,从而缩短了系统设计周期。     

Beam deviations of large linear arrays due to wavy phase errors

Beam deviations occurring when wavy phase errors are introduced into the aperture of an antenna are treated. As the antenna becomes large, the probability of introduction of such types of phase error increases and beam deviations become a problem. A basic formula that permits the evaluation of beam deviations due to small phase errors is presented and applied to derive, in a general form, expressions for beam deviations which would occur when sinusoidal or rⁿ type phase error arises along a line source where r is a normalized distance and n is zero or a positive integer. Numerical examples show that sinusoidal phase errors often cause comparatively large beam deviations (relative to linear phase gradients), even for tapered illuminations     

A competitive Neyman-Pearson approach to universal hypothesis testing with applications

The problem of hypothesis testing for parametric information sources whose parameters are not explicitly known is considered. A new, modified version of the Neyman-Pearson criterion of optimality, where the uniform constraint on exponential rate of the false-alarm probability is replaced by one that depends on unknown values of the parameters, is proposed. An optimal universal decision rule, based on Kullback-Leibler divergence, is developed and shown to be efficient in the sense of achieving exponential decay of both misdetection and false-alarm probabilities for all values of unknown parameters, whenever such an efficient decision rule exists at all. Furthermore, necessary and sufficient conditions for the existence of such efficient universal tests are established and the best universally achievable error exponents are presented. Finally, the proposed approach is applied to several important problems in signal processing and communications and compared to the generalized likelihood ratio test (LRT).     

Direct-sequence spread-spectrum multiple-access communications with random signature sequences: a large deviations analysis

A direct-sequence spread-spectrum multiple-access bit-error probability analysis is developed using large-deviations theory. Let m denote the number of interfering spread-spectrum signals and let n denote the signature sequence length. Then the large deviations limit is as n to infinity with m fixed. A tight asymptotic expression for the bit-error probability is proven, and in addition, recent large-deviations results with the importance sampling Monte Carlo estimation technique are applied to obtain accurate and computationally efficient estimates of the bit-error probability for finite values of m and n. The large-deviations point of view is compared also to the conventional asymptotics of central limit theory and the associated Gaussian approximation. The Gaussian approximation is accurate and the ratio m/n is moderately large and all signals have roughly equal power. In the near/far situation, however, the Gaussian approximation is quite poor. In contrast, large-deviations techniques are more accurate in the near/far situation, and it is here that these methods provide some important practical insight.<>     

New framework for unsupervised universal steganalysis via SRISP-aided outlier detection

Formulating steganalysis as a binary classification problem has been highly successful. However, the existing detection algorithms are difficult to obtain high detection accuracy when applied in real-world circumstances. Because so-called model mismatch problem often occurs owing to unknown cover source and embedding parameters. To avoid the mess of model mismatch, we propose a new unsupervised universal steganalysis framework to detect individual stego images. First, cover images with statistical properties similar to those of the given test image are searched from a retrieval cover database to establish an aided cover sample set. Second, unsupervised outlier detection is performed on a test set composed of the given test image and its aided cover sample set to determine the type (cover or stego) of the given test image. Our proposed framework, called Similarity Retrieval of Image Statistical Properties (SRISP)-aided unsupervised outlier detection, requires no training, and thus it does not suffer from model mismatch. The framework employs standard steganalysis features and detects each test image individually. Experimental results illustrate that the framework substantially outperforms one-class support vector machine and the traditional unsupervised outlier detectors without considering SRISP; its detection performance is independent of the proportion of stego images in the test samples.     

大口径非球面计算全息图检测系统

为了精确地检测大口径非球面面形质量,将曲面圆形计算全息图与补偿镜相结合,应用于非球面折射式检测光学系统中.分析了曲面计算全息图的衍射特性,同时分别阐述了利用曲面计算全息图的这种衍射特性来检测凹非球面及凸非球面的基本原理和方法,给出了具体的设计实例.与传统的非球面检测光学系统相比较,该系统不仅简化了传统光学系统的装调过程,还可以大大降低计算全息图（CGH）与补偿镜的制作精度,减少制作成本.尤其是在凸非球面检测过程中,首次在实验技术方面提出了两步全孔径检测法和调整误差的旋转相减消除法,实验验证了该方法的有效性.     

面向大型地震仪系统的自动化测试框架

由于自动化测试可以使用较少的人工干预实现自动执行大量测试工作从而可以大大提高测试效率,一直受到软件工程师的关注.自动化测试引入大型地震仪系统的测试中,提出了基于混合模型的大型地震仪系统自动化测试框架,并应用于大型地震仪系统的回归测试和稳定性测试中.测试效果分析显示,基于混合模型的大型地震仪系统自动化测试框架具有较高的脚本维护性,可有效缩短脚本维护时间,提高自动化测试效率.     

Landmark matching via large deformation diffeomorphisms

This paper describes the generation of large deformation diffeomorphisms phi:Omega=[0,1](3)right harpoon over left harpoonOmega for landmark matching generated as solutions to the transport equation dphi(x,t)/dt=nu(phi(x,t),t),tin[0,1] and phi(x,0)=x, with the image map defined as phi(.,1) and therefore controlled via the velocity field nu(.,t),tin[0,1]. Imagery are assumed characterized via sets of landmarks {x(n), y(n), n=1, 2, ..., N}. The optimal diffeomorphic match is constructed to minimize a running smoothness cost parallelLnu parallel(2) associated with a linear differential operator L on the velocity field generating the diffeomorphism while simultaneously minimizing the matching end point condition of the landmarks. Both inexact and exact landmark matching is studied here. Given noisy landmarks x(n) matched to y(n ) measured with error covariances Sigma(n), then the matching problem is solved generating the optimal diffeomorphism phi;(x,1)=integral(0)(1 )nu;(phi;(x,t),t)dt+x where nu;(.)argmin(nu(.))integral(1) (1)integral(Omega) parallelLnu(x,t) parallel(2)dxdt +Sigma(n=1)(N)[y(n)-phi(x(n),1)] (T)Sigma(n)(-1)[y(n)-phi(x(n ),1)]. Conditions for the existence of solutions in the space of diffeomorphisms are established, with a gradient algorithm provided for generating the optimal flow solving the minimum problem. Results on matching two-dimensional (2-D) and three-dimensional (3-D) imagery are presented in the macaque monkey.     

高密度散热孔可靠性测试方法研究

随着电子产品向高密度发展,PCB的热问题引起了越来越多的关注,散热孔是解决散热问题的重要方向之一。文章采用TMA、TGA等手段分析不同孔径、间距散热孔的耐热性能,通过对比热应力及无铅回流焊测试结果,探讨衡量散热孔耐热性能的研究手段。     

子孔径拼接干涉测量一大口径双曲面

为了无需辅助元件就能够实现对大口径非球面的检测,将子孔径拼接技术与干涉技术相结合,提出了一种利用子孔径拼接干涉检测非球面的新方法.分析了该技术的基本原理,并基于齐次坐标变换、最小二乘拟合建立了一种综合优化的拼接模型,在此基础上初步设计和搭建了子孔径拼接干涉检测装备.利用该方法对一口径为350 mm的双曲面进行了5个子孔径的拼接检测,得到拼接后的全口径面形误差的PV值为0.319λ,RMS值为0.044λ(=632.8 nm).为了对比和验证,对该非球面进行了零位补偿检测,两种方法测量所得的全口径面形分布是一致的,其PV值和RMS值的偏差分别为0.032λ和0.004λ.实验结果表明:该数学模型和拼接算法是准确可行的,从而提供了一种非零补偿测试大口径非球面的手段.