Abstract :
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 Cd,k is defined as Cd,k=limm,n→∞log2Nm,n d,k/mn, where Nm,nd,k 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
Keywords :
binary codes; channel capacity; runlength codes; 1D run-length constraints; 2D binary patterns; binary codes; binary sequence; bounds; channel capacity; encoding algorithms; rectangular patterns; two-dimensional run-length constrained channels; Binary codes; Binary sequences; Channel capacity; Digital recording; Equations; Extrapolation; Merging; Physics;
