Center for Interdisziplinary Research

General Theory of Information Transfer and Combinatorics

Opening Workshop of the ZiF:Research Group "General Theory of Information Transfer and Combinatorics"

Date: November 4 - 9, 2002
Scientific Organizer: Prof. Rudolf Ahlswede (Bielefeld)

At the beginning of the opening conference, the Managing Director of the ZiF, Prof. Dr. Ipke Wachsmuth, welcomed over 70 researchers from 19 different countries.

Reception in Bielefeld's old city hall

A picture taken at mayor Helling's reception in honor of the Research Group in the old town hall of Bielefeld.

From left to right:
Prof. Vladimir Levenshtein (Moscow)
Prof. Rudolf Ahlswede (Research Group organizer)
Dr. Anastassia Vasil'eva (Novosibirsk)
Prof. Ipke Wachsmuth (Managing Director of the ZiF)

Rudolf Ahlswede then outlined the leading ideas of the research program. After giving a compact description of Shannon's celebrated theory of communication he described his creation of the theory of identification in the presence of noise, which was worked out together with Guenter Dueck. It goes considerably beyond Shannon's theory. "Transmission" (classical) concerns the question "How many messages can we transmit over a noisy channel?" One tries to give an answer to the question "What is the actual message from M={1,...,m}?"
On the other hand in "identification" it is asked "How many possible messages can the receiver of a noisy channel identify?" One tries to give an answer to the question "Is the actual message i ?" Here i can be any member of the set of possible messages N={1,2,...,n}.
This theory initiated other research areas on Alarm Systems and Common Randomness, which gave a new impetus to Cryptology. It also led to the discovery of new methods which became fruitful even for the classical theory of transmission, for instance in studies of robustness like arbitrarily varying channels, optimal coding procedures in case of complete feedback, novel approximation problems for output statistics and generation of common randomness, the key issue in Cryptology.
Moreover the work on identification has led to reconsiderations of the basic assumptions of Shannon's theory. It deals with "messages", which are elements of a "prescribed set of objects", known to the communicators. The receiver wants to know the true message. This basic model occurring in all engineering work on communication channels and networks addresses a very special communication situation. More generally they are characterized by
1. The questions of the receivers concerning the given "ensemble", to be answered by the sender(s)
2. The prior knowledge of the receivers
3. The senders' prior knowledge.
It seems that the whole body of present day Information Theory will undergo serious revisions and some dramatic expansions. A general theory of information transfer abbreviated as GTIT, was developed and to some degree analyzed. It extends the frontiers of information theory in several directions.
Another direction of research was initiated by the work of Ahlswede, Cai, Li and Yeung in which first optimal results on information flows in networks were presented. Prior to their work it was not recognized that information flows follow completely different rules as flows of physical commodities.
Other researchers suggested further information problems from fields like, for instance, Bioinformatics, Animal Communication and Quantum Theory.
The main goal of the research project is to explore how the new theory of general information transfer can find applications in other fields both along theoretical and experimental lines. Furthermore it needs to be examined whether the informational phenomena from other areas make it necessary to extend existing or even create new models.
In the present shape of the research group the main directions of research will be in the following fields: Biology - Animal Communication and Language Evolution, Cryptology, General Theory of Information Transfer, Networks - Flows and Learning, Philosophy - Concepts of Information, Quantum Information, Reconstruction of Sequences, Statistics and Probability Theory, Search, Sorting and Ordering.
It should be noted that there are further areas with interesting independent information problems, like Chemistry or Game Theory, but this would go beyond the scope of the already very comprehensive project.
After formulations of mathematical models in the above mentioned areas have been obtained it is to be expected that difficult combinatorial problems arise, which will then be attacked by experts in mathematics.
After the two preparatory meetings in the beginning of 2002, the opening conference also helped attracting further outstanding scientists to join the project as fellows.
Two days of the conference were devoted to the memory of Levon Khachatrian from the Department of Mathematics of the University of Bielefeld. There were talks about each field of research to which he contributed significantly. This included the fields: Combinatorial Number Theory, Cryptography, Combinatorics, Coding Theory and Networks. One lecture had the title "Extremely Strong Results of Levon Khachatrian in Extremal Set Theory".

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