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Information theory. --- Combinatorial analysis. --- Théorie de l'information --- Analyse combinatoire --- Ahlswede, Rudolf, --- Combinatorial analysis --- Information theory --- Computer Science --- Algebra --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Communication theory --- Combinatorics --- Computer science. --- Computer communication systems. --- Data structures (Computer science). --- Algorithms. --- Numerical analysis. --- Computer science --- Computer Science. --- Computer Communication Networks. --- Algorithm Analysis and Problem Complexity. --- Discrete Mathematics in Computer Science. --- Numeric Computing. --- Data Structures, Cryptology and Information Theory. --- Mathematics. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematical analysis --- Algorism --- Arithmetic --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- File organization (Computer science) --- Abstract data types (Computer science) --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Network computers --- Informatics --- Science --- Foundations --- Distributed processing --- Communication --- Cybernetics --- Computer software. --- Computational complexity. --- Electronic data processing. --- Data structures (Computer scienc. --- Data Structures and Information Theory. --- Complexity, Computational --- Machine theory --- Software, Computer --- Computer systems --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Automation --- Computer science—Mathematics. --- Computer networks. --- Discrete mathematics. --- Numerical Analysis. --- Discrete mathematical structures --- Mathematical structures, Discrete --- Structures, Discrete mathematical --- Numerical analysis

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The calculation of channel capacities was one of Rudolf Ahlswede's specialties and is the main topic of this second volume of his Lectures on Information Theory. Here we find a detailed account of some very classical material from the early days of Information Theory, including developments from the USA, Russia, Hungary and which Ahlswede was probably in a unique position to describe the German school centered around his supervisor Konrad Jacobs. These lectures made an approach to a rigorous justification of the foundations of Information Theory. This is the second of several volumes documenting Rudolf Ahlswede's lectures on Information Theory. Each volume includes comments from an invited well-known expert. In the supplement to the present volume, Gerhard Kramer contributes his insights. Classical information processing concerns the main tasks of gaining knowledge and the storage, transmission and hiding of data. The first task is the prime goal of Statistics. For transmission and hiding of data, Shannon developed an impressive mathematical theory called Information Theory, which he based on probabilistic models. The theory largely involves the concept of codes with small error probabilities in spite of noise in the transmission, which is modeled by channels. The lectures presented in this work 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 as the basis for courses or to supplement courses 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.

Mathematics. --- Information and Communication, Circuits. --- Mathématiques --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Computer Science --- Mathematical Theory --- Information theory. --- Artificial intelligence. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Communication theory --- Communication --- Cybernetics --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Math --- Science

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The fourth volume of Rudolf Ahlswede’s lectures on Information Theory is focused on Combinatorics. Ahlswede was originally motivated to study combinatorial aspects of Information Theory via zero-error codes: in this case the structure of the coding problems usually drastically changes from probabilistic to combinatorial. The best example is Shannon’s zero error capacity, where independent sets in graphs have to be examined. The extension to multiple access channels leads to the Zarankiewicz problem. A code can be regarded combinatorially as a hypergraph; and many coding theorems can be obtained by appropriate colourings or coverings of the underlying hypergraphs. Several such colouring and covering techniques and their applications are introduced in this book. Furthermore, codes produced by permutations and one of Ahlswede’s favourite research fields -- extremal problems in Combinatorics -- are presented. Whereas the first part of the book concentrates on combinatorial methods in order to analyse classical codes as prefix codes or codes in the Hamming metric, the second is devoted to combinatorial models in Information Theory. Here the code concept already relies on a rather combinatorial structure, as in several concrete models of multiple access channels or more refined distortions. An analytical tool coming into play, especially during the analysis of perfect codes, is the use of orthogonal polynomials. Classical information processing concerns the main tasks of gaining knowledge and the storage, transmission and hiding of data. The first task is the prime goal of Statistics. For transmission and hiding data, Shannon developed an impressive mathematical theory called Information Theory, which he based on probabilistic models. The theory largely involves the concept of codes with small error probabilities in spite of noise in the transmission, which is modeled by channels. The lectures presented in this work 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 as the basis for courses or to supplement courses 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.

Combinatorial optimization --- Data processing. --- Optimization, Combinatorial --- Mathematics. --- Information theory. --- Combinatorics. --- Information and Communication, Circuits. --- Combinatorial analysis --- Mathematical optimization --- Math --- Science --- Combinatorics --- Algebra --- Mathematical analysis --- Communication theory --- Communication --- Cybernetics

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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.

Information theory. --- Mathematics. --- Telecommunication. --- Coding theory. --- Information and Communication, Circuits. --- Communications Engineering, Networks. --- Coding and Information Theory. --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Electric communication --- Mass communication --- Telecom --- Telecommunication industry --- Telecommunications --- Communication --- Telecommuting --- Math --- Science --- Electrical engineering. --- Electric engineering --- Engineering --- Communication theory --- Cybernetics