The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

Unsupervised texture segmentation using Gabor filters

In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.

/pdf/fading-channels-information-theoretic-and-communications-2ipqbail97.pdf

Fading channels: information-theoretic and communications aspects

Digital processing of speech signals

This paper considers a multi-cell multiple antenna system with precoding used at the base stations for downlink transmission. Channel state information (CSI) is essential for precoding at the base stations. An effective technique for obtaining this CSI is time-division duplex (TDD) operation where uplink training in conjunction with reciprocity simultaneously provides the base stations with downlink as well as uplink channel estimates. This paper mathematically characterizes the impact that uplink training has on the performance of such multi-cell multiple antenna systems. When non-orthogonal training sequences are used for uplink training, the paper shows that the precoding matrix used by the base station in one cell becomes corrupted by the channel between that base station and the users in other cells in an undesirable manner. This paper analyzes this fundamental problem of pilot contamination in multi-cell systems. Furthermore, it develops a new multi-cell MMSE-based precoding method that mitigates this problem. In addition to being linear, this precoding method has a simple closed-form expression that results from an intuitive optimization. Numerical results show significant performance gains compared to certain popular single-cell precoding methods.

/pdf/pilot-contamination-and-precoding-in-multi-cell-tdd-systems-326zvjyo0u.pdf

Pilot Contamination and Precoding in Multi-Cell TDD Systems

A scalable and adaptive temporal segmentation algorithm for video coding

The segmentation of an image is critical to the eventual success or failure of image analysis. Most commonly, the similarity or/and discontinuity between pixels in the image is used to group pixels into regions or to produce region contours. The principal difficulty shared by existing segmentation algorithms is that the segmented regions usually do not reflect the objects as perceived by a human being. Unexpected regions are often generated before desired ones are defined. The proposed perceptual segmentation algorithm remedies this aspect based on a novel combination of the homogeneity of regions and the saliency of their contours. Homogeneous regions are defined using the recursive shortest spanning tree algorithm. The saliency of region contours are detected by investigating the intensity gradient and geometric characters of the contour pixels, so as to generate a saliency map of the region contours. By combining the homogeneity from the original image and the saliency from the saliency map, the proposed approach is able to subdivide an image into regions in an order closer to the sequence determined by their perceptual significance.

Perceptual saliency weighted segmentation algorithm

A simple alternative approach to the conventional method for the synthesis of digital Chebychev filters is outlined. Conventionally, digital filters are obtained by transforming Continuous filters. It is shown that synthesis of Cheby?chev digital filters may be performed in the zplane, without referring to continuous filters.

Synthesis of Chebychev digital filters

This paper presents an efficient mode decision algorithm for H.263 to H.264 interframe transcoding. The proposed scheme uses a support vector machines (SVMs) approach to investigate the relationship between data extracted from H.263 decoding stage and the optimal coding mode in H.264 re-encoding process. Based on the SVM classifier, the transcoder only enables a subset of candidate modes for each macroblock in the rate-distortion-optimized mode decision in H.264. The objective is to eliminate unlikely modes in earlier stages in order to achieve computation saving. Simulation results show that the proposed method can reduce the computational complexity of interframe transcoding by up to 77% while maintaining similar rate-distortion performance.

https://www.eie.polyu.edu.hk/~wcsiu/paper_store/Conference/2009_Conf/2009_C5_ISCAS_JingSiuChauConstantinides.pdf

Efficient inter mode decision for H.263 to H.264 video transcoding using support vector machines

In a multi-user direct sequence code division multiple access (DS-CDMA) system, retrieval of the transmitted signals with a conventional receiver is difficult when there is chip asynchronism, multi path propagation and the associated near-far problem. The results show that despite these problems an adaptive linear receiver based on a mixed cross correlation and constant modulus algorithm (CC-CMA) has the potential to retrieve all users simultaneously. In this paper, we propose several algorithms based on Quasi-Newton type algorithms. Compared with the conventional CC-CMA algorithm, the proposed algorithms achieve faster convergence at low computational cost. Simulations support the improved convergence properties of the algorithm.

/pdf/fast-convergent-multiuser-constant-modulus-algorithm-for-use-52k9k78c8q.pdf

Anthony G. Constantinides

Papers

A scalable and adaptive temporal segmentation algorithm for video coding

Perceptual saliency weighted segmentation algorithm

Synthesis of Chebychev digital filters

Efficient inter mode decision for H.263 to H.264 video transcoding using support vector machines

Fast convergent multiuser constant modulus algorithm for use in multiuser DS-CDMA environment