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At the end of the course, the students are able to - state and understand the goal of channel coding, - name current areas of applications of channel codes and identify the applied code classes, - to choose a suitable coding scheme, adapt its parameters, evaluate it, and apply decoding algorithms, - for a known given coding scheme and a given application: to evaluate its error-correcting capabilities and limits, also in comparison to other error-correcting codes and to bounds, - to understand coding schemes which were not discussed in the lecture after appropriate literature research.

This course deals with modern coding approaches for coding and storage. No previous knowledge of channel coding is required. - Applications of Channel Coding - Channel Coding Principles: Channel Models, Decoding Principles, Hamming Metric - Finite Fields: Groups, Fields, Prime Fields, Extension Fields, Vector Spaces - Linear Block Codes: Definition, Encoding, Coset Decoding, Bounds (Hamming Bound, Singleton Bound, Gilbert- Varshamov Bound), Hamming Codes, Perfect Codes - Reed-Solomon Codes: MDS Codes, Definition, Key Equation, Unique Decoding, List Decoding - BCH Codes: Minimal Polynomials, Generator and Parity-Check Polynomial, BCH Bound, Efficient Decoding - Convolutional Codes: State Diagram, Shift Register, Viterbi Decoding - Reed-Muller Codes: Definition, Simplex Code, Plotkin Construction - Concatenated Codes: Basic Concepts

- Mathematical basics (linear algebra)

Lecture: The fundamental theoretical contents are presented in the lecture (by a slide presentation and on the black board) and illustrated with examples. Students are encouraged to ask questions and discuss the topics of the lecture. Tutorial: In an accompanying tutorial, the contents of the lecture are applied to examples.

In a final written exam about the content of the lecture, the students should demonstrate their understanding of the considered coding schemes and the respective applications. They have to show, without supporting material (one sheet of handwritten notes is allowed), that they can evaluate and design coding schemes and apply decoding algorithms.

Lecture notes are provided. The following additional literature is recommended: - Justesen, J. and Hoholdt, T.: “A Course in Error-Correcting Codes”, European Mathematical Society, 2004. - Roth, R. M.: “Introduction to Coding Theory”, Cambridge Univ. Press, 2006 - Bossert, M.: “Kanalcodierung”. 3Rd edition, Oldenburg, 2013 (English version: “Channel Coding for Communications”, Wiley, 1999)