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

Two-dimensional binary patterns that satisfy onedimensional (d; k) run-length constraints both horizontally and vertically are considered. For a given d and k, the capacity Cd; k is defined as Cd; k = limm;n!1 log2N (d; k) m;n =mn, where N (d; k) m;n denotes the number of m n rectangular patterns that satisfy the two-dimensional (d; k) run-length constraint. Bounds on Cd; k are given and it is proven for every d 1 and every k > d that Cd; k = 0 if and only if k = d+ 1. Encoding algorithms are also discussed.