Master of Science - Communications Systems Theory

Outline of Courses:

Communication and Information Theory

• Review of algebra, probability and Fourier analysis.
• Information and entropy.
• Lossless coding techniques.
• Lossy coding techniques.
• Rate distortion.
• Practical source coding systems.
• Chanel capacity.
• Modulation.
• Error control.
• Block codes.
• Convolutional codes and decoding techniques.
• Separation principle.
• Interaction of source and channel coding.
• Broadcast and multi-use channels and networks.
• Wireless channels and packet channels.

Cryptology and Security

• Introduction to Mathematical cryptographic systems including finite fields, public key cryptography, RSA, Discrete log and knapsack.
• Primality and factoring.
• Cryptographic Security in Internet, Kerberos, Firewalls, email-security, electronic payment, security in mobile networks.

Stochastic Models for Communication I,II

• Review of probability theory and Hilbert space theory.
• Markov chains with countable states in discrete-time. Applications to multiple access and digital communications.
• Gibbs fields with finite number of sites. Application to image processing and sythesis.
• Renewal theory and continuous-time Markov chains. Application to queuing theory.
• Time series and random signals. Application to data compression and traffic modelling.

Wavelets & Applications: Advanced Digital Signal Processing

• This course presents and overview of filter banks and wavelets, their construction and properties, their relation to subband coding as well as some generalisations.
• The point of view is expansion into orthogonal and biorthogonal bases, and overcomplete expansions (frames).
• The time-frequency properties of such bases will be studied.
• Applications to image and video compresssion and representation are discussed.

Computer Algebra Systems

• Introduction to algorithms in algebra and number theory.
• Design of Computer Algebra Systems like MAPLE and GAP.
• Practical experience in using, designing and implementing algorithms in the GAP language.
• Monoids and Groups, Permutations and Permutation Groups; Polynomials, Factorisation, Finite Fields, Computers and Coding Theory.
• Investigation of large permutation groups (and related codes) on a computer.
• Visualisation of algebra using animated web pages.