New Bounds on the Capacity of Multidimensional Run-Length Constraints

We examine the well-known problem of determining the capacity of multidimensional run-length-limited constrained systems. By recasting the problem, which is essentially a combinatorial counting problem, into a probabilistic setting, we are able to derive new lower and upper bounds on the capacity of $(0,k)$-RLL systems. These bounds are better than all previously-known analytical bounds for $k\geqslant 2$, and are tight asymptotically. Thus, we settle the open question: what is the rate at which the capacity of $(0,k)$-RLL systems converges to 1 as $k\rightarrow\infty$? We also provide the first nontrivial upper bound on the capacity of general $(d,k)$-RLL systems.