Error-Identification and Error-Correcting Codes
PIB-FFKC
P221-0109
pi2
2
V
3
5
no
German
Written exam 90 min.
DFBI-346
Computer Science and Web Engineering
5
optional course
KI656
Computer Science and Communication Systems
5
optional course
KIB-FFKC
Computer Science and Communication Systems
5
optional course
KIB-FFKC
Computer Science and Communication Systems
5
optional course
MST.FKC
Mechatronics and Sensor Technology
5
optional course
MST.FKC
Mechatronics and Sensor Technology
5
optional course
MST.FKC
Mechatronics and Sensor Technology
5
optional course
PIBWI56
Applied Informatics
5
optional course
PIB-FFKC
Applied Informatics
5
optional course
MST.FKC
Mechatronics and Sensor Technology
5
optional course
30 class hours (= 22.5 clock hours) over a 15-week period.The total student study time is 90 hours (equivalent to 3 ECTS credits).There are therefore 67.5 hours available for class preparation and follow-up work and exam preparation.
Dipl.-Math. Wolfgang Braun
wb
Dipl.-Math. Wolfgang Braun
wb
After successfully completing this module, students will have a basic understanding of the importance and problems of error identification and correction. In addition, they will:
- be able to explain basic terms (redundancy, code rate, generator matrix, check matrix, Hamming distance,
Hamming limit, _)
- have mastered arithmetics in finite fields of the type GF (p)
- Coding and decoding of linear binary block codes: have an understanding of the theoretical interrelationships
and have mastered execution by means of matrix calculation
- be able to construct Hamming codes
- be able to classify binary block codes according to their performance capability
- Coding and decoding of cyclic codes via GF (2): have an understanding of the theoretical interrelationships
and have mastered execution by means of polynomial operations
- have knowledge of coding theory applications in various fields
- be able to implement basic algorithms from the lecture in a common programming language
- have gained insights into how the coding theory can be developed further
- have learned how mathematical theories can be translated into practice-relevant algorithms in computer science
- Principle of coding a message for error identification and error correction
- Simple error identification and correction procedures (ISBN No., EAN code, repeat code, 2-dimensional
parity, _.)
- The ring of integers, residue classes
- Computations in finite fields GF (p)
- n-dimensional vector spaces over GF (p)
- Linear block codes over GF (2)
- Hamming codes
- Cyclic codes over GF (2)
- Applications and perspectives (ECC-RAM, CRC-32, CIRC, digital TV,
matrix codes, extension of coding theory by GF (2^n), convolutional codes, _.)
The lecture will concentrate on the algebraic methods. A statistical treatment of the transmission channel (e.g. _Entropy_, _Markov sources_), as well as an implementation of the algorithms by means of hardware are not part of this lecture.
Lecture with integrated exercises using a script, demonstration of basic algorithms using Maple.
Lecture script with exercises
Werner, M.: Information und Codierung, vieweg, Braunschweig/Wiesbaden 2002
Klimant, H. u.a. : Informations- und Kodierungstheorie, Teubner, Wiesbaden 2006
Schulz, R.-H. : Codierungstheorie, vieweg, Wiesbaden 2003
SS 2022
SS 2021
SS 2020
Fri Sep 13 15:01:53 CEST 2024, CKEY=fkcodes, BKEY=pi2, CID=[?], LANGUAGE=en, DATE=13.09.2024