Code
IGSF SIC 4251
Niveau
M1
Graduate
Graduate
Semestre
Fall
Domaine
Signal et Communications
Programme
Programme Ingénieur
Langue
Anglais/English
Crédits ECTS
2,5
Coordonnateur(s)
Département
- Communications, Images et Traitement de l'information
Organisation
Cours/TD/TP/projet/examen :Acquis d'apprentissage
• To master the basics of Information Theory, of data compression algorithms and of error correction coding
• To be able to implement some classical lossless compression algorithms (Huffmann, Lempel-Ziv)
• To be able to determine the capacity of some simple noisy communication channels
• To be able to design the minimum distance decoding table of a linear code
Prérequis
Basic knowledge in probability, in linear algebra and in analysis.
Contenu
• Introduction : main topics, some application domains
• Source of information (staionary random process, examples)
• Entropy/entropy rate of a source
• Asymptotic Equipartition Property, typical sequences, First Shannon Theorem
• Introduction to compression : lossless and lossy
• Lossless compression
o Uniquely decodable code, prefix code, Kraft inequality
o Huffmann Algorithm
o Universal Coding
o Lempel-Ziv algorithm
• Noisy communication channel
• Conditional entropy, mutual information
• Conditional Asymptotic Equipartition Property, channel capacity, Second Shannon Theorem
• Fano inequality, reciprocal of the second Shannon theorem
• Linear error correcting codes
Evaluation
Exam (3h)