CTU FEE Moodle
Information Theory and Coding
B232 - Summer 23/24
Information Theory and Coding - B2M01TIK
| Credits | 6 |
| Semesters | Summer |
| Completion | Assessment + Examination |
| Language of teaching | Czech |
| Extent of teaching | 3P+1C |
Annotation
Fundamentals of information theory with a view towards efficient data compression and reliable transmission of information using selfcorrecting codes.
Study targets
Understanding of mathematical models used in coding and transmission of digital information.
Course outlines
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.
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.
Exercises outlines
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.
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.
Literature
[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.
[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.
Requirements
Probability and statistics
Discrete mathematics
Discrete mathematics