Information geometry of Iterative Algorithms

Iterative methods are of fundamental importance in today`s advanced wireless communication systems. In particular, various variants of turbo algorithms and of expectation-maximization algorithms have been successfully applied in the context of decoding, demodulation, channel estimation, equalization, multiuser detection, and MIMO systems. This grant application for a one-year Erwin Schrödinger Fellowship proposes research focusing on the information geometry of these iterative algorithms. Information geometry is concerned with the intrinsic geometric properties of the manifold of probability density/mass functions and provides a powerful and intuitive approach for the investigation of iterative algorithms. The research directions to be pursued in the course of the fellowship fall within the following two general categories: Analysis: I plan to develop an information geometric framework for the interpretation of various iterative methods used in wireless communications. I expect that this framework allows to deepen the understanding of the mechanisms underlying iterative algorithms and to characterize their asymptotic behavior. Design: Based on this information geometric picture, I intend to devise improved design methods for iterative algorithms and for the communications schemes in which they are used. Furthermore, I will attempt to formulate novel iterative algorithms using the insights provided by information geometry. The proposed research will be performed at the Laboratoire des Signaux et Systèmes which is jointly operated by the Centre National du Recherche Scientifique (CNRS), the Ecole Superiéure d`Electricité (Supélec), and the Université de Paris-Sud. At this institution, considerable expert knowledge on iterative algorithms in general and specifically on their information geometric aspects is available.