## Three challenges of Claude Shannon

- Date: 10/10/2006

Joachim Rosenthal (University of Zurich)

University of British Columbia

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.

The talk will be tutorial in nature and should be accessible to advanced undergraduate students.

Discrete Math Seminar 2006