Informationstheorie und Codierung (ITC)


Dozent:
Prof. Dr.-Ing. Ralf Müller

Angaben:
Vorlesung, 3 SWS, ECTS-Studium, ECTS-Credits: 5
nur Fachstudium, für Gasthörer zugelassen, Sprache Deutsch
Zeit und Ort: Di 12:15 - 13:45, H6; jede 2. Woche Mi 14:15 - 15:45, R4.15

Studienfächer / Studienrichtungen:
WF EEI-BA 5-6
PF EEI-MA-INT 1-4
PF CE-BA-TA-IT 5
WF CE-MA-TA-IT 1
PF EEI-BA-INT 5-6
WPF IuK-BA 5-6
PF IuK-MA-ÜTMK-EEI 1-4
WPF IuK-MA-ES-EEI 1-4
WPF IuK-MA-KN-EEI 1-4
WPF IuK-MA-MMS-EEI 1-4
WPF IuK-MA-REA-EEI 1-4
WPF IuK-MA-ES 1-4
PF IuK-MA-KOMÜ 1-4
WPF IuK-MA-MMS 1-4
WPF WING-BA-IKS-ING-MG1 5-6
WPF WING-MA 1-4
PF CME-MA 1
PF ASC-MA 1
WPF MT-MA-BDV ab 1

Inhalt:
Introduction to coding and information theory (binomial distribution, (7,4)-Hamming code, parity-check matrix, generator matrix); Probability, entropy, and inference (entropy, conditional probability, Bayes’ law, likelihood, Jensen’s inequality); Inference (inverse probability, statistical inference); Source coding theorem (information content, typical sequences, Chebychev inequality, law of large numbers); Symbol codes (unique decidability, expected codeword length, prefix-free codes, Kraft inequality, Huffman coding); Stream codes (arithmetic coding, Lempel-Ziv coding, Burrows-Wheeler transform); Dependent random variables (mutual information, data processing lemma); Communication over a noisy channel (discrete memory-less channel, channel coding theorem, channel capacity); Noisy-channel coding theorem (jointly-typical sequences, proof of the channel coding theorem, proof of converse, symmetric channels); Gaussian channel (AWGN channel, multivariate Gaussian pdf, capacity of AWGN channel); Binary codes (minimum distance, perfect codes, why perfect codes are bad, why distance isn’t everything); Message passing (distributed counting, path counting, low-cost path, min-sum (=Viterbi) algorithm); Marginalization in graphs (factor graphs, sum-product algorithm); Low-density parity-check codes (density evolution, check node degree, regular vs. irregular codes, girth); Lossy source coding (transform coding and JPEG compression)

ECTS-Informationen:
Credits: 5

Zusätzliche Informationen:
Erwartete Teilnehmerzahl: 55

Zugeordnete Lehrveranstaltungen:
UE: Übungen zu Informationstheorie und Codierung
Dozent: Florian Gruber, M. Sc.
Zeit und Ort: jede 2. Woche Mi 14:15 - 15:45, R4.15