Combinatorial Methods and Models: Rudolf Ahlswede?s Lectures on Information Theory 4 (eng)
Language: English
Published by Springer, 2017
Series: Book 6 of 11 - Foundations in Signal Processing, Communications and Networking
- Hardcover
- New
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- Title
- Combinatorial Methods and Models: Rudolf Ahlswede?s Lectures on Information Theory 4 (eng)
- Author
- Ahlswede, Rudolf
- Publisher
- Springer
- Publication year
- 2017
- Condition
- new
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 3319531379
- ISBN 13
- 9783319531373
- Item weight
- 0.82 kilograms
- Series
- Book 6 of 11: Foundations in Signal Processing, Communications and Networking
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.
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About the Author
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 theory of identification, while also advancing the fields of combinatorics and number theory. These efforts culminated in his research program “Development of a General Theory of Information Transfer”. In recognition of his work, Rudolf Ahlswede received several awards for “Best Paper”, as well as the distinguished “Shannon Award”.
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