Groupe d’études et de recherche en analyse des décisions

Markov chain Monte Carlo methods for two-dimensional constrained models

Mehdi Molkaraie Universitat Pompeu Fabra de Barcelona, Espagne

We discuss Markov chain Monte Carlo methods (Gibbs sampling) to compute the capacity (the free energy) of two-dimensional constrained channels. A straightforward binary case is described as follows. On a square gird of size \(N=M \times M\), we consider the constraint that no two, horizontally or vertically, adjacent variables can both have value 1. The goal is then to count the number of valid configurations in a given model.