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Technical University of Munich

Channel Coding

Lecturer (assistant)
Antonia Wachter-Zeh
Luis Maßny
Frederik Walter
Anisha Banerjee
Jessica Bariffi
Number 0000004399
Type lecture with integrated exercises
Duration 5 SWS
Term Wintersemester 2024/25
Language of instruction English
Position within curricula See TUMonline
Dates See TUMonline

Admission information

See TUMonline

Objectives

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.

Description

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

Prerequisites

- Mathematical basics (linear algebra)

Teaching and learning methods

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.

Examination

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.

Recommended literature

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)

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