Modern Coding Theory by T. Richardson and R. Urbanke

This book is our attempt to summarize the state-of-the-art of iterative channel coding. Two other popular names which describe the same area are probabilistic coding and codes on graphs. Iterative decoding was originally devised by Gallager in 1960 in his remarkable thesis and then long forgotten. It was rediscovered by Berrou, Glavieux, and hitimajshima in 1993 in the form of turbo codes, and then independently in the mid 90’s by MacKay and McNeal, Sipser and Spielman, as well as Luby, Mitzenmacher, Shokrollahi, Spielman, and Steman in a form much closer to Gallager’s original construction. Iterative techniques have had a strong impact on coding theory and practice and, more generally, on the whole of communications.