# Subject description - A0B01TIK

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A0B01TIK Information Theory and Coding
Roles:V Extent of teaching:4P+2S
Department:13101 Language of teaching:CS
Guarantors:Hamhalter J. Completion:Z,ZK
Lecturers:Gollová A., Hamhalter J. Credits:8
Tutors:Gollová A., Hamhalter J. Semester:L

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

Webpage:

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 BPOI1 Computer Systems V – BPOI_BO Common courses V – BPOI3 Software Systems V – BPOI2 Computer and Information Science V – BPKYR1 Robotics V – BPKYR_BO Common courses V – BPKYR3 Systems and Control V – BPKYR2 Sensors and Instrumentation V – BPKME1 Communication Technology V – BPKME5 Komunikace a elektronika V – BPKME_BO Common courses V – BPKME4 Network and Information Technology V – BPKME3 Applied Electronics V – BPKME2 Multimedia Technology V – BPEEM1 Applied Electrical Engineering V – BPEEM_BO Common courses V – BPEEM2 Electrical Engineering and Management V – BMI(ECTS) Manager Informatics V – BWM(ECTS) Web and Multimedia V – BIS(ECTS) Intelligent Systems V – BSI(ECTS) Software Engineering V –

 Page updated 4.6.2020 09:51:27, semester: Z,L/2020-1, L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)