## Book Series

Hoger Boche (TU München), together with Wolfgang Utschick (TU München) and Rudolf Mathar (RWTH Aachen), is editor of the book series, "Foundations in Signal Processing, Communications and Networking".

Published titles in this series

This book series presents monographs about fundamental topics and trends in signal processing, communications and networking in the field of information technology. The main focus of the series is to contribute on mathematical foundations and methodologies for the understanding, modeling and optimization of technical systems driven by information technology. Besides classical topics of signal processing, communications and networking the scope of this series includes many topics which are comparably related to information technology, network theory, and control. All monographs will share a rigorous mathematical approach to the addressed topics and an information technology related context.

## Combinatorial Methods and Models (The 4th Volume of the Ahlswede lectures on information theory)

**Volume 13**

Authors: Ahlswede, Rudolf

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

**Rudolf Ahlswede's Lectures on Information Theory 4**

## Combinatorial Methods and Models

July 17, 2017, Hardcover-ISBN 978-3-319-53137-3 (eBook ISBN 978-3-319-53139-7)

On July 17, 2017, the fourth volume of the Ahlswede lectures on the information theory "Combinatorial Methods and Models" from the book series "Foundations in Signal Processing, Communications and Networking" (Eds: Holger Boche, Rudolf Mathar, Wolfgang Utschick) was published.

While the first part of the book focuses on combinatorial methods to analyze classical codes or codes in the Hamming metric, the second part is devoted to combinatorial models in information theory.

This fourth volume contains commentary by Alon Orlitsky and a tribute by Konrad Jakob.

## more Informationen ...

**Volume 13**

Authors: Ahlswede, Rudolf

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

**Rudolf Ahlswede's Lectures on Information Theory 4**

## Combinatorial Methods and Models

June 29, 2017, ISBN 978-3-319-53137-3

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.

**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".

## Published volumes in this series include:

**Volume 12**

Edited by Ahlswede, A., Althöfer, I., Deppe, C., Tamm, U. (Eds.)

**Rudolf Ahlswede's Lectures on Information Theory 3**

## Hiding Data - Selected Topics

1st Edition, 2016, ISBN 978-3-319-31513-3

**Volume 11**

Edited by Ahlswede, Alexander; Alther, Ingo; Deppe, Christian; Tamm, Ulrich (Eds.

**Rudolf Ahlswede's Lectures on Information Theory 2**

## Transmitting and Gaining Data

1st Edition, 2015, ISBN: 978-3-319-12522-0

**Volume 10**

Edited by Ahlswede, A., Althöfer, I., Deppe, C., Tamm, U. (Eds.)

**Rudolf Ahlswede’s Lectures on Information Theory 1**

## Storing and Transmitting Data

1st Edition, 2014, ISBN: 978-3-319-05479-7

**Volume 8**

Edited by Hunger, Raphael

## Analysis and Transceiver Design for the MIMO Broadcast Channel

1st Edition, 2013, ISBN 978-3-642-31692-0

**Volume 7**

Authors: Schubert, Martin, Boche, Holger

## Interference Calculus

2012, eBook ISBN 978-3-642-24621-0;

Hardcover ISBN 978-3-642-24620-3; Softcover ISBN 978-3-642-43393-1

**Volume 4**

Authors: Pohl, Volker, Boche, Holger

## Advanced Topics in System and Signal Theory

**A Mathematical Approach**

2010, eBook ISBN 978-3-642-03639-2;

Hardcover ISBN 978-3-642-03638-5; Softcover ISBN 978-3-642-26096-4

**Volume 3**

Authors: Stanczak, Slawomir, Wiczanowski, Marcin, Boche, Holger

## Fundamentals of Resource Allocation in Wireless Networks

**Theory and Algorithms**

2008, eBook ISBN 978-3-540-79386-1;

Hardcover ISBN 978-3-540-79385-4 Softcover ISBN 978-3-642-24260-1