It is expected that future generations of wireless communication systems will provide a wide variety of services such as voice, video, high speed data, and interactive multimedia for a variety of users ranging from the stationary to the highly mobile --- with speeds ranging from the pedestrian to high vehicular speeds --- and in a wide range of outdoor (urban downtown to rural) as well as indoor (homes, office buildings, factories, etc.) propagation environments commonly encountered in everyday life. Battery limitations in hand-held devices or laptops and the scarcity of bandwidth relative to the ambitions of such services dictate the need for designing systems in which these resources must be used as efficiently as possible.
This project will focus on developing a mathematical theory of two-dimensional ``space-time'' codes based on algebraic number theory for reliable, robust and resource-efficient data transmission over multi-antenna wireless communication links. Robustness of performance to a variety of channel conditions will be emphasized by considering general code design criteria as will problems related to efficient decodability. Scalable, high performance space-time codes that can be dynamically adapted to changing channel conditions due to changes in propagation environments, scattering geometries, and user mobility will be investigated. Questions of both existence and construction will be pursued. A new level of generality is introduced in this project so that knowledge acquired for code design for one model can be applied to other models. The long history of mathematics shows that the very level of generality itself can be a guide to what good codes should look like.
