A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.

1. Introduction to Information Theory 2. Statistical physics and probability theory 3. Introduction to combinatorial optimization 4. Probabilistic toolbox 5. The Random Energy Model 6. Random Code Ensemble 7. Number partitioning 8. Introduction to replica theory 9. Factor graphs and graph ensembles 10. Satisfiability 11. Low-Density Parity-Check Codes 12. Spin glasses 13. Bridges: Inference and Monte Carlo 14. Belief propagation 15. Decoding with belief propagation 16. The assignment problem 17. Ising models on random graphs 18. Linear Boolean equations 19. The 1RSB cavity method 20. Random K-satisfiability 21. Glassy states in coding theory 22. An ongoing story

Marc Mezard , Laboratoire de Physique Theorique et Modeles Statistiques, Universite de Paris Sud, Orsay, France, Andrea Montanari , Electrical Engineering and Statistics Department, Stanford University, USA

`Combines an exceptionally broad coverage of non-trivial problems with a treatment of sufficient depth [...] A very valuable and unique book.' ACC Coolen, King's College London