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.