Description:

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.

Contents:

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.

Seminar contents:

1. Finite fields and polynomials.
2. Linear codes.
3. Cyclic codes.
4. Test.
5. Burst error correction.
6. BCH codes.

Recommended literature:

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.

Keywords:

error control code, error correcting, linear code, cyclic code, parity, Hamming code, code product , RM code, BCH code, RS code, Fire code, code interleaving, convolutional code, turbo code, product code, residue code

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar