### Optimization and Systems Theory Seminar

Friday, April 7, 2000, 11.00-12.00, Room 3721, Lindstedtsv. 25

**Professor Joachim
Rosenthal**

Department of Mathematics

University of Notre Dame

Notre Dame, Indiana

USA

and

Department of Communication Systems

Ecole Polytechnique Fédérale de Lausanne - EPFL

Lausanne

Switzerland

E-mail: Joachim.J.Rosenthal.1@nd.edu

####
Reflections on Shannon's three challenges

In 1948/1949 Claude Shannon wrote two papers [Sha48,Sha49]
which became the foundation of modern information theory. The
papers showed that information can be compressed up to the
`entropy', that data can be transmitted error free at a rate
below the capacity and that there exist provable secure
cryptographic systems. These were all fundamental theoretical
result. The challenge remained to build practical systems which
came close to the theoretical optimal systems predicted by
Shannon.
In this overview talk we will explain how the first two
challenges concerning coding theory have resulted in practical
solutions which are very close to optimal. Then we explain why
the gap between the practical implementation of cryptographic
protocols with the theoretical result of Shannon is
largest.

[Sha48] C. E. Shannon, *A mathematical theory
of communication*, Bell System Tech. J. 27 (1948),
379-423 and 623-656.

[Sha49] C. E. Shannon, *Communication theory
of secrecy systems*, Bell System Tech. J. 28 (1949),
656-715.

Calendar of seminars

*Last update: March 28, 2000 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*