Bounds on the capacity of constrained two-dimensional codes

Bounds on the capacity of constrained two-dimensional (2-D) codes are presented. The bounds of Calkin and Wilf (see SIAM J. Discr. Math., vol.11, no.1, p.54-60, 1998) apply to first-order symmetric constraints. The bounds are generalized in a weaker form to higher order and nonsymmetric constraints. Results are given for constraints specified by run-length limits or a minimum distance between pixels of a given value.