The Asymptotic Capacity of Multi-Dimensional
Runlength-Limited Constraints and Independent
Sets in Hypergraphs
Erik Ordentlich, Ron M. Roth1
Information Theory Research Group
HP Laboratories Palo Alto
HPL-2002-348
December 17th , 2002*
E-mail: eord@hpl.hp.com, ronny@cs.technion.ac.il
regular graphs,
Hamming graphs,
linear hypergraphs,
multi-dimensional
constraints,
runlength- limited
constraints
Let C(n,d) be the Shannon capacity of the n-dimensional (d,Τ)runlength- limited (RLL) constraint. Denote by I(n,q) the number of
independent sets in the Hamming graph with vertices consisting of
all n-tuples over an alphabet of size q and edges connecting pairs of
vertices with Hamming distance 1. We show that limn ∆ Τ C(n,d) =
limn ∆ Τ (d+1) -n log2 I (n,d+1)=1/(d +1). Our method also leads to an
improvement of a previous bound by Alon on the number of
independent sets in regular graphs and to a generalization of this
bound to a family of hypergraphs, of which the Hamming graphs
can be thought of as a special case.
* Internal Accession Date Only
1
Computer Science Department, Technion, Haifa, 32000, Israel
 Copyright Hewlett-Packard Company 2002
Approved for External Publication
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