Subject description - B2M01TIK
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Explanatory Notes
Instructions
| B2M01TIK | Information Theory and Coding | ||
|---|---|---|---|
| Roles: | PV | Extent of teaching: | 3P+1C |
| Department: | 13101 | Language of teaching: | CS |
| Guarantors: | Hamhalter J. | Completion: | Z,ZK |
| Lecturers: | Gollová A., Hamhalter J. | Credits: | 6 |
| Tutors: | Gollová A. | Semester: | L |
Web page:
https://math.fel.cvut.cz/en/people/gollova/tik.htmlAnotation:
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. |
Exercises outline:
| 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. |
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 and statistics Discrete mathematicsKeywords:
entropy, information, channel capacity, linear codes, Hamming codes, cyclic codes and BCH codes Subject is included into these academic programs:| Program | Branch | Role | Recommended semester |
| MPEK8_2021 | Communication and information processing | PV | 2,4 |
| Page updated 23.4.2024 17:51:08, semester: Z/2024-5, Z,L/2023-4, Send comments about the content to the Administrators of the Academic Programs | Proposal and Realization: I. Halaška (K336), J. Novák (K336) |