On the Sufficiency of Power Control for a Class of Channels with Feedback

We show that, for a particular class of channels that we believe applies to many physical problems of interest, the utility of feedback, insofar as channel capacity is concerned, is simply for allowing the transmitter to perform power control. This class of channels, which assumes noiseless feedback but allows for the feedback to be of arbitrary rate, includes channels that model slow, flat fading channels with variable input power. Thus our result gives some guidance on the design of effective transmission schemes for slow, flat fading channels with feedback. Some technical results relating to the capacity of channels with noiseless feedback are also demonstrated and a dynamic programming formulation for the optimal power control policy problem is proposed

Modern Coding Theory: The Statistical Mechanics and Computer Science Point of View

These are the notes for a set of lectures delivered by the two authors at the Les Houches Summer School on `Complex Systems' in July 2006. They provide an introduction to the basic concepts in modern (probabilistic) coding theory, highlighting connections with statistical mechanics. We also stress common concepts with other disciplines dealing with similar problems that can be generically referred to as `large graphical models'. While most of the lectures are devoted to the classical channel coding problem over simple memoryless channels, we present a discussion of more complex channel models. We conclude with an overview of the main open challenges in the field.Comment: Lectures at Les Houches Summer School on `Complex Systems', July 2006, 44 pages, 25 ps figure