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Codes correcteurs d'erreur

3EAH10 Codes correcteurs d'erreur Electronique et Physique appliquee S9
Cours : 6 h TD : 0 h TP : 6 h Projet : 0 h Total : 12 h
Responsable : Stephane Flament
Pré-requis
Linear Algebra, Vector space, Probability
Objectifs de l'enseignement
First objective is to show how the whole coding-decoding process allows reduction of the Bit Error Rate even if the coding process itself leads to a significant increase of the Bit Error Rate.
Second objective is to show how it is possible to design an error correcting code for specific applications
Programme détaillé
Introduction : Compression, cryptography, error correctiion coding
Proof of Bit Error Rate improvement provided by intoduction of error - correcting codes.
Different kinds of errors : case of uniform bit error property and case of burst errors
Matricial and polynomial representation of Block error correcting codes
Polynomial Cyclic codes
Applications (TD ou TP)
Exemple of implementation of perfect codes like Hamming and Golay codes and burst error error correcting codes like Fire codes.
Compétences acquises
Selection and implementation of block error - correcting code
Understanding of polynomial cyclic codes selection
Bibliographie
1. Codes correcteurs, J. Badrikian, Ed. Ellipses (2002)
2. Théorie des codes, J.-G. Dumas, J-L. Roch, E. Tannier, S. Varrette, 2nd Edition, Ed. Dunod (2013)
3. Fundamentals in Information Theory and coding, M. Borda, Ed. Springer 2011

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