Aims

- To explain the notions, methods and results that are used in the analysis and design of information representation, protection and correction systems.

- To present not only general results that determine the possibilities offered by information theory, but also effective compression, security and correction methods.

- To provide some design tools for multimedia (image, sound, data) information coding.

Main themes

- Information representation: decorrelation coding and entropic coding.
- Information security: cryptographic coding.
- Information correction: channel coding theory and error-correcting codes.

Content and teaching methods

- Basic notions in information theory; mutual information and entropy.
- Discrete source coding by fixed length-codes and variable-length codes.
- Decorrelation coding and coding gain notions.
- Basic notions in cryptology; secret-key and public-key cryptographic coding systems.
- Discrete memoryless channel; capacity notion; noisy channel coding theorem.
- General block coding theory; role of the minimum distance.
- Linear codes: generator matrix and parity-check matrix; syndrome decoding.
- Study of certain classes of linear block codes: cyclic codes and Reed--Solomon codes.
- Introduction to convolution codes.

Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)

- Prerequisite:
(1) FSAB 1101, FSAB 1102, FSAB 1103: Mathematics (linear algebra).
(2) FSAB 1104: Probability and statistics (basic probability notions).

- References:
(1) R.G. Gallager, Information Theory and Reliable Communication', Wiley, 1968.
(2) F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland, 1977.

- Assessment
Written examination (no document allowed)

Miscellaneous

Basic notions in information theory; mutual information and entropy.
<br>Discrete source coding by fixed length-codes and variable-length codes.
<br>Decorrelation coding and coding gain notions.
<br>Basic notions in cryptology; secret-key and public-key
cryptographic coding systems.
<br>Discrete memoryless channel; capacity notion; noisy channel coding
theorem.
<br>General block coding theory; role of the minimum distance.
<br>Linear codes: generator matrix and parity-check matrix;
syndrome decoding.
<br>Study of certain classes of linear block codes: cyclic codes
and Reed--Solomon codes.
<br>Introduction to convolution codes.

Programmes in which this activity is taught

Other credits in programs