Error Control Codes

Garant předmětu:

Pavel Kubalík

Lecturer:

Pavel Kubalík

Tutor:

Pavel Kubalík

Supervisor:

Department of Digital Design

Synopsis:

The course expands the basic knowledge of security codes used in current systems for error detection and correction. It provides the necessary mathematical theory and principles of linear, cyclic codes and codes for the correction of multiple errors, clusters of errors and whole syllables (bytes). Students will also learn how to implement these detections and corrections for different types of transmissions (parallel, serial) when storing data in memory and when transmitting 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. Codes for arithmetic operations.

Syllabus of tutorials:

1. Finite fields and polynomials.

2. Linear codes.

3. Cyclic codes.

4. Test.

5. Burst error correction.

6. BCH codes.

Study Objective:

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.

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 Correcting Codes with an Introduction to Cryptography and Information Theory. Wiley, 1991. ISBN 978-0-471-62187-4.

Note:

Time-table for winter semester 2023/2024:

Time-table is not available yet

Time-table for summer semester 2023/2024:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon	roomTH:A-1242 Kubalík P. 11:00–12:30 (lecture parallel1) Thákurova 7 (budova FSv)
Tue	roomTH:A-1048 Kubalík P. 12:45–14:15 ODD WEEK (lecture parallel1 parallel nr.101) Thákurova 7 (budova FSv) Servitova laborka
Wed
Thu
Fri

The course is a part of the following study plans:

• Master specialization Software Engineering, in English, 2021 (elective course)
• Master specialization Computer Security, in English, 2021 (elective course)
• Master specialization Computer Systems and Networks, in English, 2021 (elective course)
• Master specialization Design and Programming of Embedded Systems, in English, 2021 (PS)
• Master specialization Computer Science, in English, 2021 (VO)