| Module name (EN): Error-Identification and Error-Correcting Codes |
| Degree programme: Computer Science and Communication Systems, Bachelor, ASPO 01.10.2017 |
| Module code: KIB-FFKC |
| SAP-Submodule-No.: P222-0115 |
| Hours per semester week / Teaching method: 2V (2 hours per week) |
| ECTS credits: 3 |
| Semester: 5 |
| Mandatory course: no |
| Language of instruction: German |
| Assessment: Written exam 90 min. [updated 05.10.2020] |
| Applicability / Curricular relevance: DFBI-346 (P610-0203) 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 (P222-0115) Computer Science and Communication Systems, Bachelor, ASPO 01.10.2017, semester 5, optional course, technical MST.FKC (P231-0131) Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2012, optional course, technical MST.FKC (P231-0131) Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2019, optional course, technical MST.FKC (P231-0131) Mechatronics and Sensor Technology, Bachelor, ASPO 01.10.2020, optional course, technical PIBWI56 (P221-0109) Applied Informatics, Bachelor, ASPO 01.10.2011, semester 5, optional course, informatics specific PIB-FFKC (P221-0109) Applied Informatics, Bachelor, ASPO 01.10.2017, semester 5, optional course, informatics specific MST.FKC (P231-0131) 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 01.10.2006] |
| 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] |
| Module offered in: SS 2022, SS 2021, SS 2020 |
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