紹介
This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. It is accessible to graduate students and researchers without a specific training in any of these fields. The selected topics include spin glasses, error correcting codes, satisfiability, and are central to each field. The approach focuses on large random instances and adopts a common probabilistic formulation in terms of graphical models. It presents message passing algorithms like belief propagation and survey propagation, and their use in decoding and constraint satisfaction solving. It also explains analysis techniques like density evolution and the cavity method, and uses them to study phase transitions.
目次
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
