Entropy bounds for constrained two-dimensional random fields

The maximum entropy and thereby the capacity of two-dimensional (2-D) field s given by certain constraints on configurations is considered. Upper and l ower bounds are derived. A new class of 2-D processes yielding good lower b ounds is introduced. Asymptotically, the process achieves capacity for cons traints with limited long-range effects. The processes are general and may also be applied to, e.g., data compression of digital images. Results are g iven for the binary hard square model, which is a 2-D run-length-limited mo del and some other 2-D models with simple constraints.