## Information Theory and Coding

### Details

#### Zeit/Ort n.V.:

• Mo 14:15-15:45, Raum H6
• Alle zwei Wochen Mi 10:15-11:45, Raum H6

#### Studienfächer / Studienrichtungen

• WF EEI-BA ab Sem. 5
• PF EEI-MA-INT ab Sem. 1
• PF CE-BA-TA-IT ab Sem. 5
• WF CE-MA-TA-IT ab Sem. 1
• PF EEI-BA-INT ab Sem. 5
• WF IuK-BA ab Sem. 5
• WPF WING-BA-IKS-ING-MG1 ab Sem. 5
• WPF WING-MA ab Sem. 1
• WPF WING-MA-ET-IT ab Sem. 1
• WPF WING-BA-ET-IT ab Sem. 5
• PF CME-MA ab Sem. 1
• PF ASC-MA ab Sem. 1
• WPF INF-NF-EEI ab Sem. 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)

#### Zusätzliche Informationen

Erwartete Teilnehmerzahl: 91