Subject description - B0B01TIK

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B0B01TIK Information Theory and Coding
Roles:  Extent of teaching:4P+2S
Department:13101 Language of teaching:CS
Guarantors:  Completion:Z,ZK
Lecturers:  Credits:8
Tutors:  Semester:L

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:

Program Branch Role Recommended semester


Page updated 29.3.2024 14:51:28, 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)