#### INF563 — Introduction to Information Theory

##### Coordinator : Jean-Pierre Tillich (jean-pierre.tillich@inria.fr)

#### Objectives :

Information theory deals with finding the fundamental limits for compressing a signal, storing data or communicating information reliably over a noisy channel for instance. It turns out that all these limits can be expressed in terms of a single quantity which is entropy. The foundations of this domain were laid by Shannon who quantified in a very elegant way these limits.

We will cover during this course his major results and will also give the modern answers to this kind of issue that give very effective schemes for compressing or protecting data against noise. Now this theory has also found applications in many other areas such as cryptography, biology, quantum computing, linguistics, plagiarism detection or pattern recognition. We will cover some of those other applications during the course.

#### Content :

The course is divided into nine lectures and nine exercise or lab sessions. These cover the main algorithmical and mathematical concepts involved in information theory. The topics covered include:

- Entropy, typical sequences
- Memoryless source coding
- Memoryless source coding, Huffman code, Shannon-Fano-Elias code, Shannon code and arithmetic coding
- adaptative Huffman coding, universal coding of a source
- Stationnary source, typical sequences, AEP
- Channel coding, capacity, Shannon theorem
- Linear codes, Hamming and Reed-Solomon codes, decoding, concatenated codes
- Polar codes
Applications of Information Theory to other domains.

###### Suggested readings:

T. Cover, J. Thomas, "Elements of Information Theory". Wiley Series in Telecommunications, 1991.

#### Language :

The course material is in English. Lectures can be taught either in French or in English, at the students' convenience.

#### Evaluation :

The course is validated by an oral examination.

#### Prerequisites :

Some basic background in statistics or probability theory is desirable but not mandatory.

in computer science: some knowledge of algorithms and programming such as INF411 or INF421.