Error Control Codes

Garant předmětu:

Pavel Kubalík

Přednášející:

Pavel Kubalík

Cvičící:

Pavel Kubalík

Předmět zajišťuje:

katedra číslicového návrhu

Anotace:

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.

Požadavky:

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

Osnova přednášek:

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.

Osnova cvičení:

1. Finite fields and polynomials.

2. Linear codes.

3. Cyclic codes.

4. Test.

5. Burst error correction.

6. BCH codes.

Cíle studia:

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.

Studijní materiály:

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.

Poznámka:

Students who are repeatedly admitted and have successfully completed the AAK course in their previous studies may apply for a differential exam and then the MI-BKO.16 course will be recognized. However, this only applies to the field of Design and Programming of Embedded Systems, while for the field of Computer Security, the subject AAK may be recognized only as an optional subject. For latecomers: A student who lacks AAK will enroll in a BKO and undergo a differential exam. After passing the BKO.16 and the differential exam, the student will be recognized in the compulsory subject AAK. // https://courses.fit.cvut.cz/MIE-BKO/

Rozvrh na zimní semestr 2024/2025:

Rozvrh není připraven

Rozvrh na letní semestr 2024/2025:

Rozvrh není připraven

Předmět je součástí následujících studijních plánů:

• Master specialization Software Engineering, in English, 2021 (volitelný předmět)
• Master specialization Computer Security, in English, 2021 (volitelný předmět)
• Master specialization Computer Systems and Networks, in English, 2021 (volitelný předmět)
• Master specialization Design and Programming of Embedded Systems, in English, 2021 (PS)
• Master specialization Computer Science, in English, 2021 (VO)
• Master specialization Computer Science, in English, 2024 (VO)