[IEEE Trans. on Information Theory, November 2000, pp. 2666-2670]
Partial Characterization of the Positive Capacity Region of Two-Dimensional
Asymmetric Run Length Constrained Channels
Akiko Kato and Kenneth Zeger
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 (d1,k1) run length constraint horizontally and
the one-dimensional (d2,k2) run length constraint vertically.
For given d1, k1, d2, and k2, the asymmetric two-dimensional
capacity is defined as
Cd1,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 x n binary patterns.
We determine whether the capacity is positive or is zero,
for many choices of (d1,k1,d2,k2).