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Web page:
http://math.feld.cvut.cz/gollova/tik.html
Anotation:
Fundamentals of information theory with a view towards efficient data compression and reliable transmission of information.
Study targets:
Understanding of mathematical models used in coding and transmission of digital information.
Course outlines:
| 1) | | Entropy, divergence, mutual information. Conditional entropy and conditional information. |
| 2) | | Entropy rate of stationary and ergodic sources. |
| 3) | | Universal source coding. Lempel-Ziv coding. |
| 4) | | Information channel. Basic types. |
| 5) | | Channel capacity. Blahut-Arimoto algorithm. |
| 6) | | Shannon theorem. |
| 7) | | Introduction to secret sharing schemes. |
| 8) | | Algebraic structures in error detection and correction. Groups and finite fields. |
| 9) | | Linear codes. Hamming codes. |
| 10) | | Polynomials over Z_p and quotient rings. |
| 11) | | Cyclic codes. |
| 12) | | Galois fields, primitive elements and field characteristics. |
| 13) | | BCH codes. |
| 14) | | Reserve. |
Exercises outline:
| 1) | | Entropy, divergence, mutual information. Conditional entropy and conditional information. |
| 2) | | Entropy rate of stationary and ergodic sources. |
| 3) | | Universal source coding. Lempel-Ziv coding. |
| 4) | | Information channel. Basic types. |
| 5) | | Channel capacity. Blahut-Arimoto algorithm. |
| 6) | | Shannon theorem. |
| 7) | | Introduction to secret sharing schemes. |
| 8) | | Algebraic structures in error detection and correction. Groups and finite fields. |
| 9) | | Linear codes. Hamming codes. |
| 10) | | Polynomials over Z_p and quotient rings. |
| 11) | | Cyclic codes. |
| 12) | | Galois fields, primitive elements and field characteristics. |
| 13) | | BCH codes. |
| 14) | | Reserve. |
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. |
Requirements:
Probability, statistics, and information theory (A0B01PSI),
Discrete mathematics (A4B01DMA)
For more information see
http://math.feld.cvut.cz/gollova/tik.html
Keywords:
entropy, information, channel capacity, secret sharing scheme, linear codes, Hamming codes, cyclic codes and BCH codes
Subject is included into these academic programs:
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Proposal and Realization: I. Halaška (K336), J. Novák (K336) |