EN2500 Information Theory and Source Coding 7.5 credits

Information theory of discrete and continuous variables: entropy, Kraft inequality, relative entropy, entropy rate, redundancy rate, mutual information, asymptotic equipartition. Estimation of probability density and probability mass functions. Expectation-Maximization algorithm. Maximum entropy principle.

Lossless coding: nonadaptive codes: Shannon, Huffmann, arithmetic codes. Universal and adaptive codes. Ziv-Lempel codes.

Rate-distortion theory: the rate-distortion function, Shannon lower bound, rate distribution over independent variables, reverse waterfilling, Blahut algorithm.

High-rate quantization: constrained-resolution and constrained-entropy quantization. Vector versus scalar quantization. Practical high-rate-theory-based quantizers: mixture and lattice quantizers, companding.

Low-rate quantization: Lloyd training algorithm for constrained-resolution and constrained-entropy cases. Structured vector quantization (tree-structured, multi-stage, gain-shape, lattice). Fast search methods.

Transforms and filter banks: bases and frames. Transforms and filter banks. Fixed transforms: DFT, DCT, MLT, Gabor frames, Balian-Low theorem. A-priori adaptation: Karhunen-Loeve, a-priori energy concentration. A-posteriori adaptation: a-posteriori energy concentration, best-basis search, matching pursuit.

Linear prediction: closed-loop prediction, noise-shaping, analysis-by-synthesis, spectral flatness, Kolmogorov's Formula, spectral flatness, redundancy, forward and backward prediction.

To obtain an understanding of the theoretical principles of source coding.

For single course students: 120 credits and documented proficiency in English B or equivalent

EQ1220 Signal Theory or equivalent.

W.B. Kleijn, A basis for source coding, KTH-S3 (2004).

If the course is discontinued, students may request to be examined during the following two academic years.

• HEM1 - Assignment, 1.5 credits, grading scale: P, F
• TEN1 - Examination, 6.0 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Written examination.
Homework.

Markus Flierl

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.