The fifth volume of Rudolf Ahlswede’s lectures on Information Theory focuses on several problems that were at the heart of a lot of his research. One of the highlights of the entire lecture note series is surely Part I of this volume on arbitrarily varying channels (AVC), a subject in which Ahlswede was probably the world's leading expert. Appended to Part I is a survey by Holger Boche and Ahmed Mansour on recent results concerning AVC and arbitrarily varying wiretap channels (AVWC). After a short Part II on continuous data compression, Part III, the longest part of the book, is devoted to distributed information. This Part includes discussions on a variety of related topics; among them let us emphasize two which are famously associated with Ahlswede: "multiple descriptions", on which he produced some of the best research worldwide, and "network coding", which had Ahlswede among the authors of its pioneering paper. The final Part IV on "Statistical Inference under Communication constraints" is mainly based on Ahlswede’s joint paper with Imre Csiszar, which received the Best Paper Award of the IEEE Information Theory Society.
The lectures presented in this work, which consists of 10 volumes, are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with a background in basic Mathematics. The lectures can be used either as the basis for courses or to supplement them in many ways. Ph.D. students will also find research problems, often with conjectures, that offer potential subjects for a thesis. More advanced researchers may find questions which form the basis of entire research programs.
Rudolf Ahlswede (1938–2010) studied Mathematics in Göttingen, and held postdoc positions in Erlangen, Germany and Ohio, USA. From 1977 on he was full Professor of Applied Mathematics at the University of Bielefeld. His work represents an essential contribution to information theory and networking. He developed and contributed to a number of central areas, including network coding and the theory of identification, while also advancing the fields of combinatorics and number theory. These efforts culminated in his research program on the “Development of a General Theory of Information Transfer”. In recognition of his work, he received several awards for “Best Paper”, as well as the distinguished “Shannon Award”.
This volume is the first to present a self-contained, comprehensive overview of information-theoretic models of complex networks with an emphasis on applications. As such, it marks a first step toward establishing advanced statistical information theory as a unified theoretical basis of complex networks for all scientific disciplines and can serve as a valuable resource for a diverse audience of advanced students and professional scientists. While it is primarily intended as a reference for research, the book could also be a useful supplemental graduate text in courses related to information science, graph theory, machine learning, and computational biology, among others.
In this book, a systematic treatment of this practical design problem is provided for signal processing in the physical layer with multiple antennas. The design of robust signal processing algorithms is based on a description of the errors and the uncertainties in the system's model. It applies principles of modern estimation, optimization, and information theory. Tutorial introductions to relevant literature and mathematical foundations give the necessary background and context to the reader.
The book provides detailed derivations and enlightening insights into the related technical problems covering the following topics in detail: An overview of the principles of training-based multiple-input multiple-output (MIMO) channel estimation. Robust minimax estimation of the wireless communication channel. Robust minimax prediction of the wireless communication channel based on the maximum Doppler frequency. Identification of channel and noise correlations (power delay profile, spatial and temporal correlations, spatial correlations of interference). Interpolation of band-limited autocovariance sequences. Robust linear and nonlinear precoding for the multi-user downlink with multiple antennas which is based on incomplete channel state information or channel correlations (performance measures, duality, robust Tomlinson-Harashima precoding, robust vector precoding, nonlinear beamforming).