On Independence and Capacity of Multidimensional Semiconstrained Systems
Abstract
We find a new formula for the limit of the capacity of certain sequences of
multidimensional semiconstrained systems as the dimension tends to infinity. We
do so by generalizing the notion of independence entropy, originally studied in
the context of constrained systems, to the study of semiconstrained systems.
Using the independence entropy, we obtain new lower bounds on the capacity of
multidimensional semiconstrained systems in general, and $d$-dimensional
axial-product systems in particular. In the case of the latter, we prove our
bound is asymptotically tight, giving the exact limiting capacity in terms of
the independence entropy. We show the new bound improves upon the best-known
bound in a case study of $(0,k,p)$-RLL.