Constraints for two-dimensional recording media

We give a simple model for interferences occurring in 2 dimensional(2-D) bit patterned media for digital recording. We investigate some constraints induced from the model. Some lower bounds of capacities of 2-D constraints are derived. A sufficient condition for the positivity of the capacity of a 2-D constraint is given. We also give an encoding algorithm for the constraint which works well with few exceptions. The algorithm can also be regarded as a representation of the 2-D constraint.