Informationstheorie (IT)5 ECTS
(englische Bezeichnung: Information Theory and Coding)
(Prüfungsordnungsmodul: Information Technology - DT)

Lehrveranstaltungen:

• • Information Theory
    (Vorlesung, 3 SWS, Ralf Müller, Mi, 14:15 - 15:45, H6; Di, 12:15 - 13:45, H6)
  • Tutorial for Information Theory
    (Übung, 1 SWS, Christoph Rachinger, Zeit und Raum n.V.)

Inhalt:

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

Lernziele und Kompetenzen:

The students apply Bayesian inference to problems in both communications and everyday's life. The students explain the concept of digital communications by means of source compression and forward-error correction coding. For the design of communication systems, they use the concepts of entropy and channel capacity. They calculate these quanities for memoryless sources and channels. The students proof both the source coding and the channel coding theorem.
The students compare various methods of source coding with respect to compression rate and complexity. The students apply source compression methods to measure mutual information.
The students factorize multivariate functions, represent them by graphs, and marginalize them with respect to various variables.
The students explain the design of error-correcting codes and the role of minimum distance. They decode error-correcting codes by means of maximum-likelihood decoding and message passing. The students apply distributed algorithms to problems in both communications and everyday’s life.
The students improve the properties of low-density parity-check codes by widening the girth and/or irregularity in the degree distribution.
The students transform source images into the frequency domain to improve lossy compression.

Literatur:

• MacKay, D.: Information Theory, Inference, and Learning Algorithms, Cambridge University Press, Cambridge, 2003.

Weitere Informationen:

Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:

1. Computational Engineering (Rechnergestütztes Ingenieurwesen) (Master of Science)
   (Po-Vers. 2013 | TechFak | Computational Engineering (Rechnergestütztes Ingenieurwesen) (Master of Science) | Wahlpflichtbereich Technisches Anwendungsfach | Information Technology - DT)

Studien-/Prüfungsleistungen:

Vorlesung und Übung Informationstheorie (Prüfungsnummer: 36001)

(englischer Titel: Lecture/Tutorial: Information Theory)

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

Anteil an der Berechnung der Modulnote: 100.0 %

Prüfungssprache: Deutsch oder Englisch

Erstablegung: WS 2016/2017, 1. Wdh.: SS 2017, 2. Wdh.: keine Wiederholung

1. Prüfer:

Ralf Müller