Probabilistic methods and distributed information. Rudolf Ahlswede's lectures on information theory 5. Edited by Alexander Ahlswede, Ingo Althöfer, Christian Deppe and Ulrich Tamm. With contributions by Vladimir Blinovsky, Holger Boche, Ulrich Krengel and Ahmed Mansour
The book under review is the fifth volume of Rudolf Ahlswede's lectures on Information Theory. It consists of 23 chapters grouped thematically in four parts. All parts address problems to which Ahlswede has significant contributions. Part I titled ``Arbitrarily Varying Channels'' presents an array on which Rudolf Ahlswede was the leading expert worldwide and he carried out a lot of his own research. The name arbitrary varying channels (AVC) itself is used for the first time by Ahlswede and he proved the first significant result for the AVC with average error probability for deterministic code which is that the \(a\)-capacity is either zero or the random code capacity (Theorem 3.1 in Ch. 3). The proof is based on the elimination theory introduced by Rudolf Ahlswede. Next chapters consider variants of AVC. The eighth chapter presents the relation of AVC with two other models in Information theory: channels with localized errors and writing-type memories and OV-channels. The last ninth chapter in this part is a survey of recent results on AVC and arbitrary varying wiretap channels (AVWC). ``Continuous Data Compression'' is the second part in this volume. It present the relation between AVC techniques and the encoding of so called individual sequences. The main result is a generalization of the Slepian-Wolf theorem for correlated source within the framework of individual sequences. The third part titled ``Distributed Information'' consists 10 chapters and it is the largest part of the volume. Most of the chapters discuss various problems of network coding and, of course, the accent is on the random network coding. In chapter 21 it is investigated the theoretical and computational determination of maximum achievable information rate for network switching as a special case of the general network coding, in single -- and multisource multicast networks. It is shown that theory of games can play a central role in both theoretic and algorithmic aspects of network switching. Chapter 15 discusses the problem of distribution of data in a memory devices -- a problem of practical interest. The last fourth part ``Statistical interference under communication constrains'' presents and analyzes results that establish connections between Statistic and Information Theory. Hypothesis testing and estimation under communication constrains are considered. In the introduced models (with side information) Fisher's and Shannon's informations are compatible. Like to the previous volumes of Rudolf Ahlswede's lectures on Information Theory the fifth volume is a valuable text- and reference book for Ph.D. students and researchers. It is a rich source of problems suitable for further investigation. The lectures also give detail information about the history of considered problems supplied with rich references.
scientific article; zbMATH DE number 7024127