Codes correcteurs d'erreurSécurité Informatique (STI)

This course is an introduction to information theory and error correction codes. The aim is to understand the fundamental theoretical basis of the correction codes and then apply them by implementing a code with reasonable performance in practice.

1. Information theory (Shannon's entropy, mutual information, channels and capabilities, Shannon's second theorem)
2. Reminders of linear algebra (Groups, body, vector spaces, matrices, polynomials)
3. Coding and correction (parameters, maximum likelihood principle, minimum distance, correction, perfect codes, examples)
4. Linear codes (generator matrix, control matrix, syndrome and decoding, MDS codes, Hamming code)
5. Iterative decoding (LDPC codes, representation and decoding with a Tanner graph)

For FISE:

• A theoretical exam of about 1 hour, accounting for 75% of the grade. Students can consult a course slip that will be distributed to them on the day of the exam, the calculator is authorized.
• A project to be carried out during the last 4 sessions of TD, accounting for 25% of the note, concerning the implementation of LDPC codes.

For FISA:

• 2 30-40 minute controls during TD sessions, each accounting for 25% of the grade. Students can view a course slip that will be distributed to them on the day of the examination, the calculator is authorized.
• A project to be carried out during the last 4 sessions of TD, counting 50% of the note, on the implementation of LDPC codes.

Code theory - Third edition. Compression, encryption, correction (Jean-Guillaume Dumas, Jean-Louis Roch, Sébastien Varrette, Eric Tannier)

Elements of Information Theory, 2nd Edition (Thomas M. Cover, Joy A. Thomas)