New Bounds on the Capacity of Multi-dimensional RLL-Constrained Systems

We examine the well-known problem of determining the capacity of multi-dimensional 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 bounds for k ≥ 2, and are even 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 → ∞? While doing so, we also provide the first ever non-trivial upper bound on the capacity of general (d,k)-RLL systems.