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

Signals and Systems, Infocommunication

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; digitl 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 (of source coding)
4. Methods of source coding: Huffman-code; LZW code; arithmetic codes (szószerint: encoder)
5. The transmission channel: mutual information; concept of the channel capacity. Typical channels: BSC, DMC, AWGN). Shannon bound. The second coding theorem of Shannon (of channel coding).
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 (SZERINTEM AZ OPT. SIGN. SET ELŐSZÖR AZ AWGN-HEZ TARTOZNA.)
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.

Six lectures/ fortnight

During the relevant semester: 4 written exams. Maximum score for each exam is 15 points. Exam result vs. score: 0-4 points: 0; 4.5-7 points: failed (1); 7.5-9 points: pass (2); 9.5-11 points: satisfactory (3); 11.5-13 points: good (4); 13.5-15 points: excellent (5). Exam not written is taken as 0. The mark is failed (1) if there are less than two exams of score pass or better. If there are at least two better-than-failed exams, the mark is the average rounded-to-an-integer of the best two scores.

By appointment with the lecturer

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)