2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105551These are the notes for two lectures delivered at the Les Houches summer school Mathematical Statistical Mechanics, held in July 2005. I review some basic notions on sparse graph error correcting codes with emphasis on `modern' aspects, such as, iterative belief propagation decoding. Relations with statistical mechanics, inference and random combinatorial optimization are stressed, as well as some general mathematical ideas and open problems.delivered in Les Houches, July 2005Statistical MechanicsDisordered Systems and Neural Networkstext