New bounds on the capacity of multidimensional run-length constraints

Moshe Schwartz, Alexander Vardy

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 ≥ 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 → ∞? We also provide the first nontrivial upper bound on the capacity of general (d,k)-RLL systems.

Original languageEnglish
Article number5895090
Pages (from-to)4373-4382
Number of pages10
JournalIEEE Transactions on Information Theory
Issue number7
StatePublished - 1 Jul 2011


  • 2-D constrained coding
  • Constrained coding
  • multidimensional constraints
  • run-length limited coding

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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