Coding Theory (KDT)

How Can Data Remain Error-Free? Learn how information can be transmitted reliably despite interference, develop your own error-correcting codes, and understand how they are used in communication, image processing, and encryption.

Contents

• The lecture provides an introduction to the fundamental concepts and questions of coding theory, which deals with the construction and use of error-tolerant codes. Building on the foundational work of Hamming, Golay, and Shannon, it offers an overview of the significance of coding theory and its diverse applications. These range from communications and storage technology to image processing and pattern recognition, and even cryptography and biology.A central component of the course is the importance of algorithmic methods for the efficient encoding and decoding of information. To this end, the fundamentals of the theory of linear codes are taught, and various important code classes along with their associated decoding algorithms are presented. These include, among others, Hamming, Reed–Solomon, Golay, BCH, Reed–Muller, and Goppa codes. In addition, selected asymptotic bounds on the information rate of codes are covered.A particular connection exists to artificial intelligence and machine learning, since modern AI systems must process, transmit, and store large amounts of data. Error correction and robust data transmission are therefore relevant, for example, to the storage of training data, communication between networked AI systems, and the reliable processing of image, audio, and sensor data. Furthermore, there are connections between coding theory and AI in the efficient representation and compression of information, as well as in methods that enable robust and error-tolerant representations of data. The course thus not only conveys the mathematical and algorithmic foundations of coding theory but also highlights their relevance to modern applications, particularly in the context of large data-driven AI systems.

Competencies

Students are able to

• understand and apply mathematical basics of coding theory
• analyse linear codes and codes in general
• develop codes with prescribed parameters of error detection and error correction
• understand applications of coding theory in computer sciences

Literature

• W. C. Huffman and V. Pless, "Fundamentals of Error-Correcting Codes". Cambridge, U.K.: Cambridge University Press, 2003.
• J. H. van Lint, "Introduction to Coding Theory, 3rd rev. and expanded ed.", Graduate Texts in Mathematics, vol. 86. Berlin, Germany: Springer, 1999.
• W. Lütkebohmert, "Codierungstheorie: Algebraisch-geometrische Grundlagen und Algorithmen", 1. Aufl. Wiesbaden, Germany: Vieweg, 2003.
• F. J. MacWilliams and N. J. A. Sloane, "The Theory of Error-Correcting Codes". Amsterdam, The Netherlands: North-Holland, 1977.
• D. Jungnickel, "Codierungstheorie". Heidelberg, Germany: Spektrum Akademischer Verlag, 1995.
• R.-H. Schulz," Codierungstheorie: Eine Einführung", 2. Aufl. Wiesbaden, Germany: Vieweg, 2003.
• S. Lin and J. Li, "Fundamentals of Classical and Modern Error-Correcting Codes". Cambridge, U.K.: Cambridge University Press, 2022.
• I. F. Blake, "Essays on Coding Theory". Cambridge, U.K.: Cambridge University Press, 2024.
• R. Lidl and H. Niederreiter, "Finite Fields", 2nd ed., Encyclopedia of Mathematics and Its Applications, vol. 20. Cambridge, U.K.: Cambridge University Press, 1997.
• W. C. Huffman and V. Pless, Eds., Handbook of Coding Theory, vols. 1–2. Amsterdam, The Netherlands: Elsevier, 1998.

Lecturer

• Prof. Dr. Lutz Strüngmann

Recommended Previous Knowledge 

• Math for Computer Scientists 2 (MA2)

Module Details

Semester	6/7
Lecture Language	German
Frequency	Not regularly Im Durchschnitt alle 2 Semester
Credit Points (ECTS)	5
Course Coordinator	Prof. Dr. Lutz Strüngmann
Duration	1 Semester
Course Achievement	None
Prerequisite for exam	None
Exam	Continuous Assessment (CA)

Weekly Hours (SWS) 

Lecture	2 SWS
Exercises	2 SWS
Sum	4 SWS

Work Load 

Lecture	45 h
Self Study	60 h
Assignments	15 h
Exam Preparation	30 h
Sum	150 h