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.