Error Control Coding

Course guarantor:

Lecturer:

Tutor:

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Department of Digital Design

Synopsis:

The course extends the basic knowledge of error-control codes used in modern systems for error detection and correction. It presents the necessary mathematical theory and the principles of linear and cyclic codes, as well as codes for correcting multiple errors, burst errors, and whole symbols (bytes). Students will also learn how to implement these detection and correction techniques for different types of transmission (parallel and serial), when storing data in memories and when transmitting it over telecommunication 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. (2) Codes for arithmetic operations. Summary.

Syllabus of tutorials:

Study Objective:

The course extends the basic knowledge of error-control codes used in modern systems for error detection and correction. It presents the necessary mathematical theory and the principles of linear and cyclic codes, as well as codes for correcting multiple errors, burst errors, and whole symbols (bytes). Students will also learn how to implement these detection and correction techniques for different types of transmission (parallel and serial), when storing data in memories and when transmitting it over telecommunication channels.

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 ErrorCorrecting 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/

No time-table has been prepared for this course

The course is a part of the following study plans: