Abstract :
A binary sequence satisfies a one-dimensional (d,k) run length constraint if every run of zeros has length at least d and at most k. A two-dimensional binary pattern is (d1,k1,d2 ,k2)-constrained if it satisfies the one-dimensional (d 1,k1) run length constraint horizontally and the one-dimensional (d2,k2) run length constraint vertically. For given d1, k1, d2, and k 2, the asymmetric two-dimensional capacity is defined as C d1,k1,d2,k2=limm,n→∞ (1/(mn)) log2 Nm,n(d1,k1,d2,k2) where Nm,n(d1,k1,d2,k2) denotes the number of (d1 ,k1,d2,k2)-constrained m×n binary patterns. We determine whether the capacity is positive or is zero, for many choices of (d1,k1,d2,k 2)
Keywords :
binary sequences; channel capacity; 1D run length constraint; 2D asymmetric run length constrained channels; asymmetric two-dimensional capacity; binary patterns; binary sequence; partial characterization; positive capacity region; two-dimensional binary pattern; Binary sequences; Codes; Information theory; Optical recording; Physics;
