An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
Graph Algorithms
Independent Sets in Regular Hypergraphs and Multidimensional Runlength-Limited Constraints
SIAM Journal on Discrete Mathematics
On Phase Transition in the Hard-Core Model on ${\mathbb Z}^d$
Combinatorics, Probability and Computing
Improved lower bounds on capacities of symmetric 2D constraints using Rayleigh quotients
IEEE Transactions on Information Theory
Constrained systems with unconstrained positions
IEEE Transactions on Information Theory
Tradeoff functions for constrained systems with unconstrained positions
IEEE Transactions on Information Theory
Constrained Codes as Networks of Relations
IEEE Transactions on Information Theory
Maximum runlength-limited codes with error control capabilities
IEEE Journal on Selected Areas in Communications
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We introduce a concept of independence entropy for symbolic dynamical systems. This notion of entropy measures the extent to which one can freely insert symbols in positions without violating the constraint defined by the shift space. We show that for a certain class of one-dimensional shift spaces X, the independence entropy coincides with the limiting, as d tends to infinity, topological entropy of the dimensional shift defined by imposing the constraints of X in each of the d cardinal directions. This is of interest because for these shift spaces independence entropy is easy to compute. Thus, while in these cases, the topological entropy of the d-dimensional shift (d驴2) is difficult to compute, the limiting topological entropy is easy to compute. In some cases, we also compute the rate of convergence of the sequence of d-dimensional entropies. This work generalizes earlier work on constrained systems with unconstrained positions.