Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

A kötelező előtanulmányi rend az adott szak honlapján és képzési programjában található.

Widespread concepts of and tasks to be solved by telecommunications can be described by a more or less unified theory. Aim of this subject is to present basics of and applied approaches in this theory. Main topics dealt with are information theory, decision- and estimation theory as well as theory of digital communications.

1. Introduction: task of telecommunication; sources of information, messages, interferers, noise; main blocks of communication systems, their function; digital and analog communication. Brief mathematical introduction: stochastic processes
2. Basics of information theory, definition of basic concepts, presentation via examples.
3. Source coding: purpose, effectiveness, coding of sources without and with memory. The first coding theorem of Shanon (Cource coding theorem)
4. Methods of source coding: Huffman-code; LZW code; arithmetic codes (encoder/decoder)
5. The transmission channel: mutual information; concept of the channel capacity. Typical channels: BSC, DMC, AWGN). Shannon bound. The second coding theorem of Shannon (Channel coding theorem).
6. Channel coding. Concept of message space, of code space. Classifying of errors. Hamming distance. Laws of code construction Singleton, Hamming bound, MDS, perfect code.
7. Methods of binary linear channel coding: heuristic coding, code vectors, generator matrix and polynomial, parity check matrix and polynomial. Hamming codes  
8. Non-binary linear channel coding methods: finite fields; operations over Galois-fields. Non-binary Hamming codes, Reed-Solomon codes, cyclic codes
9. Basics of decision theory; decision problems in communication. Binary decision, Bayes (minimum risk) decision; likelihood ratio, ML criterion, sufficient statistics, MAP decision.  
10. Basics of estimation theory: parameter estimation tasks; random parameters, cost functions, MMSE and MAP estimation; deterministic parameters, likelihood function, estimators, biased and unbiased types; Cramer-Rao bound, efficient estimators.
11. Transmission of digital signals over analog channels. The concept of complex envelope. Signal sets; the signal space. Signal sets of 2D, examples: PSK, QAM; higher dimensionality: orthogonal, regular simplex signal set. Optimum receivers in AWGN channels: correlation, matched filter.
12. Performance of noisy channels. Band limited channels, choice of signal waveform, Nyquist criterion.
13. Channel coding and modulation in channels with memory. Convolutional coding, trellis coding. Continous phase modulation. The Viterbi algorithm.
14. Fading channels; Rayleigh- and Rice-fading. Error probability in fading channels. Principles of spread spectrum transmission, the DS and the FH system.

During the relevant semester: One written mid-term exam. The mid-term exam is absolved with or above 50% of the maximum score. Not absolved with scores below 50% of the maximum score.

With absolved mid-term exam during the examination periode: One written exam absolved with the given percents of the maximum score as follows: 50% - 62,5%: pass (2); 62,5% - 75%: satisfactory (3); 75% - 87,5%: good (4); 87,5% - 100%: excellent (5). The mark is failed (1) below 50% of the maximum score.

J. G. Proakis, M. Salehi: Communication Systems Engineering (Prentice Hall, 2002)

Th. M. Cover, J. A. Thomas: Elements of Information Theory (Wiley, 2006)

H. L. Van Trees: Detection, Estimation, and Modulation Theory, Vol I (Wiley)