Reflections on the Broadcast Channel: Progress and Challenges
Professor Shlomo Shamai
Department of Electrical Engineering
Technion - Israel Institute of Technology
The classical Gaussian broadcast channel is addressed in a perspective of traditional and novel information theoretic concepts and techniques, touching also upon implications on practical wireless systems. We start by introducing the standard broadcast channel, and briefly review some basic results on its capacity region. We specialize to the scalar Gaussian model and provide a new proof for the converse based on a fundamental relation between mutual information and minimum-mean square error estimation. Extending the picture to the Gaussian vector channel, we overview basic concepts that led to the full characterization of the capacity region of this non-degraded broadcast model, namely: 'dirty paper' coding, multiple access-broadcast duality aspects, Sato and degraded marginal based techniques, as well as basic concepts of the enhanced channel, and extremal inequalities. We further touch on several relevant issues arising in networks: the role of channel-state information, the impact of fading, SNR scaling laws, multiplexing gains, and compound settings. Our aim is to highlight some interesting yet unsolved problems, the solution of which will carry significant theoretical and practical implications. The theory is used to demonstrate the impact on an idealistic cellular wireless down link (the Wyner model), where cell-site co-processing is highlighted. Some unresolved questions are emphasized, and practical approaches based on zero-forcing precoding and scheduling, are discussed. Time permitting, a broader outlook on the Gaussian broadcast channel be given touching on advanced concepts such as: user conferencing, joint source-channel coding, cognitive systems and secrecy in the broadcast regime. We conclude by contrasting the large number of results and techniques with these as-yet unsolved fundamental problems concerning broadcast channels which play a dominant role in modern communications.
Shlomo Shamai (Shitz) received the B.Sc., M.Sc., and Ph.D. degrees in electrical engineering from the Technion - Israel Institute of Technology, in 1975, 1981 and 1986 respectively. During 1975-1985 he was with the Communications Research Labs in the capacity of a Senior Research Engineer. Since 1986 he is with the Department of Electrical Engineering, Technion - Israel Institute of Technology, where he is now the William Fondiller Professor of Telecommunications. His research interests encompass a wide spectrum of topics in information theory and statistical communications.
Dr. Shamai (Shitz) is an IEEE Fellow and a member of the Union Radio Scientifique Internationale (URSI). He is the recipient of the 1999 van der Pol Gold Medal of URSI, and a co-recipient of the 2000 IEEE Donald G. Fink Prize Paper Award, the 2003, and the 2004 joint IT/COM societies paper award. He is also the recipient of 1985 Alon Grant for distinguished young scientists and the 2000 Technion Henry Taub Prize for Excellence in Research. He has served as Associate Editor for the SHANNON THEORY OF THE IEEE TRANSACTIONS ON INFORMATION THEORY, and also serves on the Board of Governors of the Information Theory Society.