#### Overview

The last fifteen years have seen dramatic changes and great improvements in the area of coding theory. Rather than relying on algebraic code constructions it is now recognized that suitably confined “random structures” combined with low complexity iterative decoding algorithms can achieve astonishing performance at unprecendentedly low complexity. This new approach to coding is usually referred to as “iterative decoding.” This paradigm shift poses many new challenging problems but also represents an enormous opportunity. We decided to take full advantage of this opportunity, and to make the analysis and design of these iterative coding systems the present focus of LTHC. In particular, we are interested in a sound understanding of the basic principles underlying such coding systems. The pool of applications which derive significant benefit from any improvement in this area is large and contains many of the most prevalent communication systems today, e.g., wireless systems, optical links operating at rates as high as 40gbits/s and magnetic or holographic storage systems.