Sergio Verdú

Entropy, mutual information and divergence measure the randomness, dependence and dissimilarity, respectively, of random objects. In addition to their prominent role in information theory, they have found numerous applications, among others, in probability theory statistics, physics, chemistry, molecular biology, ecology, bioinformatics, neuroscience, machine learning, linguistics, and finance. Many of these applications require a universal estimate of information measures which does not assume knowledge of the statistical properties of the observed data. Over the past few decades, several nonparametric algorithms have been proposed to estimate information measures.Universal Estimation of Information Measures for Analog Sources presents a comprehensive survey of universal estimation of information measures for memoryless analog (real-valued or real vector-valued) sources with an emphasis on the estimation of mutual information and divergence and their applications. The book reviews the consistency of the universal algorithms and the corresponding sufficient conditions as well as their speed of convergence.Universal Estimation of Information Measures for Analog Sources provides a comprehensive review of an increasingly important topic in Information Theory. It will be of interest to students, practitioners and researchers working in Information Theory.

If information theory and estimation theory are thought of as two scientific languages, then their key vocabularies are information measures and estimation measures, respectively. The basic information measures are entropy, mutual information and relative entropy. Among the most important estimation measures are mean square error (MSE) and Fisher information. Playing a paramount role in information theory and estimation theory, those measures are akin to mass, force and velocity in classical mechanics, or energy, entropy and temperature in thermodynamics.The Interplay Between Information and Estimation Measures is intended as handbook of known formulas which directly relate to information measures and estimation measures. It provides intuition and draws connections between these formulas, highlights some important applications, and motivates further explorations. The main focus is on such formulas in the context of the additive Gaussian noise model, with lesser treatment of others such as the Poisson point process channel.Also included are a number of new results which are published here for the first time. Proofs of some basic results are provided, whereas many more technical proofs already available in the literature are omitted. In 2004, the authors of this monograph found a general differential relationship commonly referred to as the I-MMSE formula.In this book a new, complete proof for the I-MMSE formula is developed, which includes some technical details omitted in the original papers relating to this. It concludes by highlighting the impact of the information-estimation relationships on a variety of information-theoretic problems of current interest, and provide some further perspective on their applications.

Originally published in 1998, Multiuser Detection provides a comprehensive treatment of the subject of multiuser digital communications. Multiuser detection is one of the most important areas in modern communications technology, and this self-contained book covers the whole field, starting with simple examples and progressing to complex applications. The author begins with a review of multiaccess communications, dealing in particular with code division multiple access (CDMA) channels. He then discusses simple and optimum approaches for demodulating CDMA channels, and deals with decorrelating and non-decorrelating linear multiuser detection schemes. He also covers in detail more advanced topics such as decision-driven multiuser detection, noncoherent multiuser detection, and array processing. The only prerequisites assumed are undergraduate-level probability, linear algebra, and digital communications. The book contains over 240 exercises.

Random matrix theory has found many applications in physics, statistics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, condensed matter physics, statistical physics, chaotic systems, numerical linear algebra, neural networks, multivariate statistics, information theory, signal processing and small-world networks.This is the first tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained. Furthermore, the application of random matrix theory to the fundamental limits of wireless communication channels is described in depth. The authors have created a uniquely comprehensive work that provides the reader with a full understanding of the foundations of random matrix theory and demonstrates the trends of their applications, particularly in wireless communications.Random Matrix Theory and Wireless Communications is a valuable resource for all students and researchers working on the cutting edge of wireless communications.

Multiuser Detection provides the first comprehensive treatment of the subject of multiuser digital communications. Multiuser detection is one of the most important areas in modern communications technology, and this self-contained book covers the whole field, starting with simple examples and progressing to state-of-the-art applications. The author begins with a review of multiaccess communications, dealing in particular with code division multiple access (CDMA) channels. He then discusses simple and optimum approaches for demodulating CDMA channels, and deals with decorrelating and non-decorrelating linear multiuser detection schemes. He also covers in detail more advanced topics such as decision-driven multiuser detection, noncoherent multiuser detection, and array processing. The only prerequisites assumed are undergraduate-level probability, linear algebra, and digital communications. The book contains over 240 exercises and will be a suitable textbook for electrical engineering students. It will also be an ideal self-study guide for practising engineers, as well as a valuable reference volume for researchers in communications, information theory, and signal processing.