Combinatorial methods and models Rudolf Ahlswede's lectures on information theory 4 / edited by Alexander Ahlswede, Ingo Althöfer, Christian Deppe, Ulrich Tamm.
Ahlswede, Rudolf, 1938-; Ahlswede, Alexander.
2018
Q360
Available Online

Linked e-resources

Linked Resource Online Access
Concurrent users Unlimited
Authorized users Authorized users
Document Delivery Supplied Can lend chapters, not whole ebooks

Details

Title Combinatorial methods and models Rudolf Ahlswede's lectures on information theory 4 / edited by Alexander Ahlswede, Ingo Althöfer, Christian Deppe, Ulrich Tamm.
Author Ahlswede, Rudolf, 1938-
ISBN 9783319531397 (electronic book)
3319531395 (electronic book)
9783319531373
3319531379
DOI https://doi.org/10.1007/978-3-319-53139-7
Published Cham : Springer, c2018.
Language English
Description 1 online resource.
Item Number 10.1007/978-3-319-53139-7 doi
Call Number Q360
Dewey Decimal Classification 003/.54
Summary 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.
Bibliography, etc. Note Includes bibliographical references and indexes.
Access Note Access limited to authorized users.
Digital File Characteristics text file PDF
Source of Description Description based on print version record.
Added Author Ahlswede, Alexander.
Series Foundations in signal processing, communications and networking ; v. 13.
Available in Other Form Print version: 9783319531373
Linked Resources Online Access
Record Appears in Online Resources > Ebooks
All Resources
Preface
I Combinatorial Methods for Information Theory.
II Combinatorial Models in Information Theory.
III Supplement
Gedenkworte für Rudolf Ahlswede
Commemorating Rudolf Ahlswede
Comments by Alon Orlitzky
Index.

Browse Subjects

Show more subjects...

Statistics

from
to
Export