Overview
- Contains Rudolf Ahlswede's Lecture on Identification Theory
- Surveys recent results in Identification Theory
- Gunter Dueck's afterword details his collaboration with Rudolf Ahlswede
Part of the book series: Foundations in Signal Processing, Communications and Networking (SIGNAL, volume 16)
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Table of contents (28 chapters)
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Front Matter
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Identification via Channels
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Front Matter
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A General Theory of Information Transfer
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Front Matter
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Identification, Mystery Numbers, or Common Randomness
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Front Matter
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Keywords
About this book
The sixth volume of Rudolf Ahlswede's lectures on Information Theory is focused on Identification Theory. In contrast to Shannon's classical coding scheme for the transmission of a message over a noisy channel, in the theory of identification the decoder is not really interested in what the received message is, but only in deciding whether a message, which is of special interest to him, has been sent or not. There are also algorithmic problems where it is not necessary to calculate the solution, but only to check whether a certain given answer is correct. Depending on the problem, this answer might be much easier to give than finding the solution. ``Easier'' in this context means using fewer resources like channel usage, computing time or storage space.
Ahlswede and Dueck's main result was that, in contrast to transmission problems, where the possible code sizes grow exponentially fast with block length, the size of identification codes will grow doubly exponentially fast. The theory of identification has now developed into a sophisticated mathematical discipline with many branches and facets, forming part of the Post Shannon theory in which Ahlswede was one of the leading experts. New discoveries in this theory are motivated both by concrete engineering problems and by explorations of the inherent properties of the mathematical structures.
Rudolf Ahlswede wrote:
It seems that the whole body of present day Information Theory will undergo serious revisions and some dramatic expansions. In this book we will open several directions of future research and start the mathematical description of communication models in great generality. For some specific problems we provide solutions or ideas for their solutions.
The lectures presented in this work, which consists of 10 volumes, are suitable for graduate students in Mathematics, and also for those working in Theoretical Computer Science, Physics, and Electrical Engineering with abackground 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.
The book also contains an afterword by Gunter Dueck.
Reviews
“The text is well organized and the book is easy to read and should be suitable for graduate students in mathematics, in theoretical computer science, physics and electrical engineering with basic knowledge in probability theory.” (Jaak Henno, zbMATH 1477.94005, 2022)
Authors, Editors and Affiliations
About the editors
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”.
Bibliographic Information
Book Title: Identification and Other Probabilistic Models
Book Subtitle: Rudolf Ahlswede’s Lectures on Information Theory 6
Authors: Rudolf Ahlswede
Editors: Alexander Ahlswede, Ingo Althöfer, Christian Deppe, Ulrich Tamm
Series Title: Foundations in Signal Processing, Communications and Networking
DOI: https://doi.org/10.1007/978-3-030-65072-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-65070-4Published: 23 June 2021
eBook ISBN: 978-3-030-65072-8Published: 22 June 2021
Series ISSN: 1863-8538
Series E-ISSN: 1863-8546
Edition Number: 1
Number of Pages: XXII, 724
Number of Illustrations: 36 b/w illustrations