Séminaire ICI : Roope Vehkalahti
Titre du séminaire et orateur
Capacity and Geometry of Numbers in Fading Channels.
Roope Vehkalahti, Univ. Turku (Finlande).
Date et lieu
Jeudi 9 juin 2016, 14h30.
ENSEA, salle 384.
During the last fifteen years multiple-input multiple-output (MIMO) channels have slowly replaced single antenna channels as a main subject of study in information theory. In such channel the message signal is transmitted from multiple antennas unlike in the traditional one-antenna transmission. In addition the system may also contain several receiving antennas. Interest in such channels faced a sudden rise of interest when in 1999 Telatar proved that in the presence of Gaussian noise and ergodic fading the capacity of multiple antenna channel is considerably higher than that of a single antenna system. One of the key challenges in all of coding theory is to build capacity achieving structured codes. So far, and in most MIMO channel models, known coding strategies leave at least a constant gap to capacity and lack structure. In the case of classical single antenna Gaussian channels there exist a rich theory of lattice codes developed to attack these questions. In the heart of this theory are sphere packing arguments that prove that the performance of a lattice code can be roughly estimated by the size of a geometrical invariant of the lattice. This connection has been extremely fruitful and has motivated a large body of work connecting algebra, geometry and information theory. In recent joint work with L.Luzzi we proved that an analogous theory exists in fading MIMO channels. Based on this observation we developed a general theory that connects capacity questions and geometric properties of multiple antenna lattices codes. Building on this theory and on number theoretic existence results we constructed and analyzed capacity approaching coding schemes for several single user fading channel models.
Roope Vehkalahti received the M.Sc. and Ph.D. degrees from the University of Turku, Finland, in 2003 and 2008, respectively, both in pure mathematics. Since September 2003, he has been with the Department of Mathematics, University of Turku, Finland. In 2011-2012 he was visiting Swiss Federal Institute of Technology, Lausanne (EPFL). His research interest include applications of algebra and number theory to information theory.