Advanced Information Theory (IT-A)5 ECTS
(englische Bezeichnung: Advanced Information Theory)
(Prüfungsordnungsmodul: Advanced Topics in Information Theory)

Lehrveranstaltungen:

• • Advanced Information Theory
    (Vorlesung, 3 SWS, Ralf Müller, Di, 08:15 - 09:45, 0.151-115; Mi, 12:15 - 13:45, 0.151-115)
  • Tutorial for Advanced Information Theory
    (Übung, 1 SWS, Ralf Müller et al., Zeit und Raum n.V.)

Inhalt:

Rate region, multiuser source coding, time sharing, multiuser channel codes, multiple-access channel (MAC), capacity region, mutual information versus minimum-mean squared error, Gaussian MAC , power region, Gaussian vector MAC, source coding with side information, degraded broadcast channel, Gaussian broadcast-MAC duality, Gaussian vector broadcast channel, dirty-paper coding, physically degraded relay channel, scalar Gaussian relay channel, Gaussian interference channel, cut-set bound, fading channels, multiuser water filling, block fading, diversity, user diversity, capacity versus outage, near-far gain, dual antenna arrays, Wishart distribution, factor iid model, Kronecker model, convergence of random variables, semi-circle law, quarter circle law, full circle law, Haar distribution, Marchenko-Pastur distribution, Stieltjes transform, Girko’s law, unitary invariance, freeness, free convolution, R-transform, free central limit theorem, free Poisson limit theorem, subordination, S-transform, R-diagonal random matrices, R-diagonal free convolution, Haagerup-Larsen law, operator-valued freeness, linearization of noncommutative polynomials, free Fourier transform.

Lernziele und Kompetenzen:

The students explain various types of multiuser channels and their limits to transport information.
The students explain the limits of distributed source coding algorithms.
The students find the limiting eigenvalue distributions of various types of random matrices.
The students explain Stieltjes, R- and S-transforms.
The students explain the limits of various types of fading channels.
The students design coding and decoding methods for a given type of multiuser channel.
The students perform additive and multiplicative free convolution.
The students calculate the asymptotic eigenvalues distributions of given random matrix ensembles.
The students construct random matrix ensembles with a given eigenvalue distribution.
The students linearize matrix polynomials.
The students collaborate on solving exercise problems.

Literatur:

Cover, T., Thomas, J.: Elements of Information Theory, 2nd ed., Wiley, Hoboken, 2006. Couillet, R., Debbah, M.: Random Matrix Methods for Wireless Communications, Cambridge Univ. Press, Cambridge, 2011.

Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:

1. Elektrotechnik, Elektronik und Informationstechnik (Master of Science)
   (Po-Vers. 2015s | TechFak | Elektrotechnik, Elektronik und Informationstechnik (Master of Science) | Masterprüfung | Studienrichtung Informationstechnik | Vertiefungsmodule Informationstechnik | Advanced Topics in Information Theory)

Studien-/Prüfungsleistungen:

Advanced Topics in Information Theory (Prüfungsnummer: 35821)

(englischer Titel: Advanced Topics in Information Theory)

Prüfungsleistung, Klausur, Dauer (in Minuten): 90, benotet, 5 ECTS

Anteil an der Berechnung der Modulnote: 100.0 %

Erstablegung: WS 2017/2018, 1. Wdh.: SS 2018

1. Prüfer:

Ralf Müller