Information Theory and Coding
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| B2M01TIK | Z,ZK | 6 | 3P+1C | Czech |
- Garant předmětu:
- Jan Hamhalter
- Lecturer:
- Alena Gollová, Jan Hamhalter
- Tutor:
- Alena Gollová
- 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 in error detection and correction. Countimg modulo n.
2) Linear algebra over field Zp.
3) Linear codes - generating and controling matrix.
4) Error correction, Hamming codes.
5) Polynomials over Zp and quotient rings of polynomials.
6) Cyclic codes - generating and controling polynomial.
7) Galois fields, primitive element.
8) Generating roots of cyclic codes in a field.
9) BCH codes.
10) Information theory - probability and entropy.
11) Entropy, divergence, mutual information.
12) Data compression and source coding.
13) Universal source coding (Lempel - Ziv).
14) Information channel. Shannon theorem about capacity of channel.
- Syllabus of tutorials:
-
1) Algebraic structures in error detection and correction. Countimg modulo n.
2) Linear algebra over field Zp.
3) Linear codes - generating and controling matrix.
4) Error correction, Hamming codes.
5) Polynomials over Zp and quotient rings of polynomials.
6) Cyclic codes - generating and controling polynomial.
7) Galois fields, primitive element.
8) Generating roots of cyclic codes in a field.
9) BCH codes.
10) Information theory - probability and entropy.
11) Entropy, divergence, mutual information.
12) Data compression and source coding.
13) Universal source coding (Lempel - Ziv).
14) Information channel. Shannon theorem about capacity of channel.
- Study Objective:
-
Understanding of mathematical models used in coding and transmission of digital information.
- 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.
[3] Adámek, J.: Kódování. SNTL, Praha, 1989.
[4] Vajda, I.: Teorie informace. Vydavatelství ČVUT, 2004.
- Note:
- Further information:
- https://math.fel.cvut.cz/en/people/gollova/tik.html
- Time-table for winter semester 2022/2023:
- Time-table is not available yet
- Time-table for summer semester 2022/2023:
-
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 Tue Wed Thu Fri - The course is a part of the following study plans:
-
- Electronics and Communications (compulsory elective course)