Information Theory and Coding

Course guarantor:

Alena Gollová

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Fundamentals of information theory with a view towards efficient data compression and reliable transmission of information using selfcorrecting codes.

Requirements:

Probability and statistics

Discrete mathematics

Syllabus of lectures:

1. Algebraic structures used in error detection and correction.

2. Linear spaces over the field Zp.

3. Linear codes - generating and control matrices.

4. Error correction, Hamming codes.

5. Polynomials over Zp and factor circuits of polynomials.

6. Cyclic codes - generating and control polynomial.

7. Galois fields, primitive element.

8. Roots of cyclic codes in the field.

9. BCH codes.

10. Information theory - probability and entropy.

11. Entropy, information divergence, mutual information.

12. Data compression and source coding.

13. Universal compression (Lempel - Ziv).

14. Information channel, Shannon's channel capacity theorem.

Syllabus of tutorials:

1. Algebraic structures used in error detection and correction.

2. Linear spaces over the field Zp.

3. Linear codes - generating and control matrices.

4. Error correction, Hamming codes.

5. Polynomials over Zp and factor circuits of polynomials.

6. Cyclic codes - generating and control polynomial.

7. Galois fields, primitive element.

8. Roots of cyclic codes in the field.

9. BCH codes.

10. Information theory - probability and entropy.

11. Entropy, information divergence, mutual information.

12. Data compression and source coding.

13. Universal compression (Lempel - Ziv).

14. Information channel, Shannon's channel capacity theorem.

Study Objective:

The course introduces students to the mathematical foundations of digital information processing, effective data compression and data transmission using self-correcting codes.

Study materials:

[1] Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, 2006.

[2] Yeung, R.W.: Information Theory and Network Coding. Springer, 2008.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: