Wave theory of information

Prof. Massimo Franceschetti

Spring 2018 EBU1 2315  TTh 3:30 PM - 4:50 PM

An advanced course on signal analysis and information theory, blending wave propagation with communication. The objective is to have students reflect on the physical meaning of information, and on the limits to information transfer through wave propagation in multiple scattering environments.

Syllabus.

Continuous time signals and information content. Kolmogorov and Shannon entropies and Capacities.  Heisenberg’s uncertainty principle. Slepian’s concentration problem. Spheroidal wave functions. Function spaces. Kolmogorov N-width. Degrees of freedom of bandlimited signals. Hilbert-Schmidt Integral operators. Hilbert-Schmidt decomposition. Elements of EM wave propagation. Green’s function. Space-time-frequency-wavenumber spectra. Elements of multiple scattering theory. Stochastic representations and Karhunen Loeve decomposition.

Information flow. Energy limitations, bandwidth limitations. Multi-user communication. Information theoretic and physical limits.

Grading.

There will be homework exercises and a final report in Latex on a research paper related to the class material. You are also asked to participate in class and to provide feedback on the lecture notes.

Prerequisites.

The course is mostly self contained, however previous knowledge of network information theory, real and complex analysis, functional vector spaces, and wave theory is useful to gain a deeper understanding of the covered topics.

Book

1000. M.Franceschetti. Wave Theory of Information. Cambridge University Press, 2018.
      

Reference books for the eager reader.

A. Pinkus. N-widths in approximation theory.Springer, 1985.

R.Gallager. Information theory and reliable communication. Wiley, 1968.

Classic papers you should definitely read.

C.E. Shannon (1949) Communication in the presence of noise. Proceedings of the IRE, 37, pp. 10-21

D.Slepian (1976). On Bandwidth. Proceedings of the IEEE, 64(3), pp. 292-300
D.Slepian (1983). Some comments on Fourier analysis, uncertainty and modeling. SIAM Review, 25(3), pp. 379-393

There will be additional papers posted in the handouts section.