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Informatique et Mathématiques appliquées
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> Formation > Cursus ingénieur

Information theory - 3MMTINF

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  • Number of hours

    • Lectures : 16.5
    • Tutorials : 16.5
    ECTS : 3.0

Goals

Provide the theoretical fundamentals for the quantitative measurement of information (what is a bit of information?), Representation, storage, transmission, protection and information hiding. Application to lossless compression, error correcting codes, transmission security and content security (steganography).

Contact Jean-Marc BROSSIER

Content

  • Uncertainty and information. Entropies . The Shannon entropy and its properties. Entropy and information transfer.
  • Structure of a communication chain. Information and compression. Channel capacity and channel coding.
  • Coding of discrete sources. Asymptotic equipartition. Theoretical optimal codes . Construction of optimal codes.
  • Transmit and store information. Discrete channel (binary symmetric channel). Channel coding and second Shannon theorem.
  • Error correcting codes. Repetition and second Shannon theorem. Error detection codes. Error correcting codes. Linear block codes. Hamming distance and Euclidean distance. Maximum likelihood decoding.
  • Some applications: steganography, information leakage and security.


Prerequisites

Probability

Tests



N1 = E1
N2= E2

Bibliography

C. Shannon, W. Weaver, La théorie mathématique de la communication, Cassini, avril 2018.

Théorie de l'information et du codage. O. Rioul. Hermès, 2007.

Elements of Information Theory. T.M. Cover, Joy A. Thomas. John Wiley & Sons Inc, 2006.

David J.C. MacKay “Information Theory, Inference, and Learning Algorithm”, Cambridge Univ. Press, 2003. http://www.cs.toronto.edu/~mackay/itila/book.html

R.G. Gallager, « Information Theory and reliable communication », Wiley, 1968

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Date of update January 15, 2017

Grenoble INP Institut d'ingénierie Univ. Grenoble Alpes