Error Control Codes

Course guarantor:

Pavel Kubalík, Alois Pluháček

Lecturer:

Pavel Kubalík

Tutor:

Pavel Kubalík

Supervisor:

Department of Digital Design

Synopsis:

The goal of the course is to present various ways to detect or correct individual errors and burst errors in data stored into memories or transmitted via channels.

Requirements:

Linear and abstract algebra basics, design of combinational and sequential logic circuits at the gate level.

Syllabus of lectures:

1. Error control codes - basic principles.

2. Linear codes.

3. Codes generated by a polynomial.

4. Cyclic codes, finite fields, and minimal polynomials.

5. Burst error correction codes.

6. Hardware for burst error correction methods.

7. Sums and products of codes and RM codes.

8. BCH codes.

9. Correction codes for byte errors, generalized Hamming codes.

10. RS (Read-Solomon) codes.

11. Convolutional and turbo codes.

12. Codes for arithmetic operations.

Syllabus of tutorials:

1. Finite fields and polynomials.

2. Lineární kódy.

3. Cyclic codes.

4. Test.

5. Burst error correction.

6. BCH codes.

Study Objective:

Errors can be superposed on memory stored data or on data transmitted via channels. Codes to detect or even to correct of errors, theirs burst or group will bepresented, as well as coder and decoder design.

Study materials:

1. Moreira, J. C. - Farrell, P. G. : Essentials of Error-Control Coding. Wiley, 2006. ISBN 047002920X.

2. Lin, S. - Costello, D. J. : Error Control Coding (2nd Edition). Prentice Hall, 2004. ISBN 0130426725.

3. Purser, M. : Introduction to Error Correcting Code. Artech House Publishers, 1994. ISBN 978-0890067840.

4. Adámek, J. : Foundations of Coding: Theory and Applications of Error[U+2010]Correcting Codes with an Introduction to Cryptography and Information Theory. Wiley, 1991. ISBN 978-0-471-62187-4.

Note:

Further information:

https://courses.fit.cvut.cz/MI-BKO/

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Master specialization Computer Science, in Czech, 2018-2019 (elective course)
• Master specialization Computer Security, in Czech, 2020 (elective course)
• Master specialization Design and Programming of Embedded Systems, in Czech, 2020 (PS)
• Master specialization Computer Systems and Networks, in Czech, 202 (elective course)
• Master specialization Management Informatics, in Czech, 2020 (elective course)
• Master specialization Software Engineering, in Czech, 2020 (elective course)
• Master specialization System Programming, in Czech, version from 2020 (elective course)
• Master specialization Web Engineering, in Czech, 2020 (elective course)
• Master specialization Knowledge Engineering, in Czech, 2020 (elective course)
• Master specialization Computer Science, in Czech, 2020 (elective course)
• Mgr. programme, for the phase of study without specialisation, ver. for 2020 and higher (PS, VO)
• Master Specialization Digital Business Engineering, 2023 (VO)
• Master specialization System Programming, in Czech, version from 2023 (elective course)
• Master specialization Computer Science, in Czech, 2023 (elective course)