New bounds on the capacity of multi-dimensional RLL-Constrained systems

Authors:
Moshe Schwartz;Alexander Vardy
Affiliations:
University of California San Diego, La Jolla, CA;University of California San Diego, La Jolla, CA
Venue:
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Year:
2006

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Abstract

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.