Teaching

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The first part of this course provides an overview on the mathematical measures of information and their connection to practical problems in communication, compression, and inference (within entropy, mutual information, lossless data compression, channel capacity, Gaussian channels, rate distortion theory, Fisher information). This could turn out to be useful for PhD students in mathematics, signal processing, machine learning, statistics, and neuroscience.

The second part will be devoted to developing geometric and algebraic techniques to be applied in communication channels, which will regard linear algebra over finite fields, representation theory, Galois geometries and incidence structures.

Moreover, the last two lectures will be dedicated to some algebra software, such as MAGMA, GAP or SageMath, and the students will elaborate projects on some aspects of the developed theory supported by the use of such softwares.

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References

• Introduction to coding theory, A. Couvreur; 

• Elements of Information Theory, T.M. Cover and J.A. Thomas, John Wiley & Sons 1999;

• Essential Coding Theory, V. Guruswami, A. Rudra and M. Sudan;

• Codes, Cryptology and Curves with Computer Algebra, R. Pellikaan, X.-W. Wu, S. Bulygin and R. Jurrius, Cambridge University Press 2018;

• Coding Theory, A. Ravagnani.

For an algebraic recap see Rings and fields - Lectures by Alexei Skorobogatov, Mathematics Imperial College London 

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For more details about my teaching duties, programs and materials see this link.