TY - GEN
T1 - New bounds on the capacity of multi-dimensional RLL-constrained systems
AU - Schwartz, Moshe
AU - Vardy, Alexander
PY - 2006/7/6
Y1 - 2006/7/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33745662157&partnerID=8YFLogxK
U2 - 10.1007/11617983_22
DO - 10.1007/11617983_22
M3 - Conference contribution
AN - SCOPUS:33745662157
SN - 3540314237
SN - 9783540314233
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 225
EP - 234
BT - Applied Algebra, Algebraic Algorithms and Error-Correcting Codes - 16th International Symposium, AAECC-16, Proceedings
T2 - 16th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-16
Y2 - 20 February 2006 through 24 February 2006
ER -