Combinatorial Methods and Models: Rudolf Ahlswede s Lectures on Information Theory - Couverture rigide

Ahlswede, Rudolf

9783319531373: Combinatorial Methods and Models: Rudolf Ahlswede s Lectures on Information Theory

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ISBN 10 : 3319531379 ISBN 13 : 9783319531373

Editeur : Springer International Publishing AG, 2017

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�diteurSpringer International Publishing AG
Date d'�dition2017
ISBN 10 3319531379
ISBN 13 9783319531373
ReliureReli�
Langueanglais
Num�ro d'�dition1
Nombre de pages385
�diteurAhlswede Alexander, Alth�fer Ingo, Deppe Christian, Tamm Ulrich

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9783319850733: Combinatorial Methods and Models: Rudolf Ahlswede’s Lectures on Information Theory 4

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Combinatorial Methods and Models 4

Rudolf Ahlswede

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ISBN 10 : 3319531379 ISBN 13 : 9783319531373

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Gebunden. Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Written by a well-known authorUseful as a self-study guide&nbspIncludes comments from an invited well-known expertRudolf Ahlswede (1938 - 2010) studied Mathematics in Goettingen, and held postdo. N� de r�f. du vendeur 135642187

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Combinatorial Methods and Models : Rudolf Ahlswede�s Lectures on Information Theory 4

Rudolf Ahlswede

Edit� par Springer International Publishing, 2017

ISBN 10 : 3319531379 ISBN 13 : 9783319531373

Neuf Couverture rigide

Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne

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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 concentrateson 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 presentedin 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. N� de r�f. du vendeur 9783319531373

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Combinatorial Methods and Models

Rudolf Ahlswede

Edit� par Springer International Publishing Jul 2017, 2017

ISBN 10 : 3319531379 ISBN 13 : 9783319531373

Neuf Couverture rigide

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Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne

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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 404 pp. Englisch. N� de r�f. du vendeur 9783319531373

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