On the capacity of two-dimensional run-length constrained channels

Two-dimensional binary patterns that satisfy one-dimensional (d, k) run-length constraints both horizontally and vertically are considered. For a given d and k, the capacity C_d,k is defined as C_d,k=lim_m,n→∞log₂N_m,n ^d,k/mn, where N_m,n^d,k denotes the number of m×n rectangular patterns that satisfy the two-dimensional (d,k) run-length constraint. Bounds on C_d,k are given and it is proven for every d⩾1 and every k>d that C_d,k=0 if and only if k=d+1. Encoding algorithms are also discussed