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Error-Identification and Error-Correcting Codes

Module name (EN): Error-Identification and Error-Correcting Codes
Degree programme: Computer Science and Web Engineering, Bachelor, ASPO 01.10.2018
Module code: DFBI-346
Hours per semester week / Teaching method: 2V (2 hours per week)
ECTS credits: 3
Semester: 6
Mandatory course: no
Language of instruction:
German
Assessment:
Curricular relevance:
DFBI-346 Computer Science and Web Engineering, Bachelor, ASPO 01.10.2018, semester 6, optional course, informatics specific
KI656 Computer Science and Communication Systems, Bachelor, ASPO 01.10.2014, semester 5, optional course, technical
KIB-FFKC Computer Science and Communication Systems, Bachelor, ASPO 01.10.2017, semester 5, optional course, technical
MST.FKC Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2012, optional course, technical
MST.FKC Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2019, optional course, technical
PIBWI56 Applied Informatics, Bachelor, ASPO 01.10.2011, semester 5, optional course, informatics specific
PIB-FFKC Applied Informatics, Bachelor, ASPO 01.10.2017, semester 5, optional course, informatics specific
MST.FKC Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2011, optional course, technical
Workload:
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.
Recommended prerequisites (modules):
None.
Recommended as prerequisite for:
Module coordinator:
Dipl.-Math. Wolfgang Braun
Lecturer: Dipl.-Math. Wolfgang Braun

[updated 06.03.2017]
Learning outcomes:
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
 


[updated 06.09.2018]
Module content:
- 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.


[updated 19.02.2018]
Teaching methods/Media:
Lecture with integrated exercises using a script, demonstration of basic algorithms using Maple.

[updated 19.02.2018]
Recommended or required reading:
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

[updated 19.02.2018]
[Fri Aug 14 01:53:22 CEST 2020, CKEY=fkcodes, BKEY=dfi2, CID=DFBI-346, LANGUAGE=en, DATE=14.08.2020]