Foundations in Signal Processing, Communications and Networking

Combinatorial Methods and Models

Rudolf Ahlswede’s Lectures on Information Theory 4

Authors: Ahlswede, Rudolf

Editors: Ahlswede, A., Althöfer, I., Deppe, C., Tamm, U. (Eds.)

  • Written by a well-known author
  • Useful as a self-study guide 
  • Includes comments from an invited well-known expert
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About this book

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.



About the authors

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”.

Table of contents (6 chapters)

  • Covering, Coloring, and Packing Hypergraphs

    Ahlswede, Rudolf

    Pages 3-55

  • Codes Produced by Permutations: The Link Between Source and Channel Coding

    Ahlswede, Rudolf

    Pages 57-88

  • Results for Classical Extremal Problems

    Ahlswede, Rudolf

    Pages 89-109

  • Coding for the Multiple-Access Channel: The Combinatorial Model

    Ahlswede, Rudolf

    Pages 113-232

  • Packing: Combinatorial Models for Various Types of Errors

    Ahlswede, Rudolf

    Pages 233-305

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-319-53139-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-319-53137-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Combinatorial Methods and Models
Book Subtitle
Rudolf Ahlswede’s Lectures on Information Theory 4
Authors
Editors
  • Alexander Ahlswede
  • Ingo Althöfer
  • Christian Deppe
  • Ulrich Tamm
Series Title
Foundations in Signal Processing, Communications and Networking
Series Volume
13
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-53139-7
DOI
10.1007/978-3-319-53139-7
Hardcover ISBN
978-3-319-53137-3
Series ISSN
1863-8538
Edition Number
1
Number of Pages
XVIII, 385
Number of Illustrations and Tables
11 b/w illustrations
Topics