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Extending models for two-dimensional constraints

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Authors:
  • Forchhammer, Søren
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    Orcid logo0000-0002-6698-8870
    Department of Photonics Engineering, Technical University of Denmark
DOI:
10.1109/ISIT.2009.5206052
Abstract:
Random fields in two dimensions may be specified on 2 times 2 elements such that the probabilities of finite configurations and the entropy may be calculated explicitly. The Pickard random field is one example where probability of a new (non-boundary) element is conditioned on three previous elements. To extend the concept we consider extending such a field such that a vector or block of elements is conditioned on a larger set of previous elements. Given a stationary model defined on 2 times 2 elements, iterative scaling is used to define the extended model. The extended model may be used for models of two-dimensional constraints and as examples we apply it to the hard-square constraint and the no isolated bits (n.i.b) constraint. The iterative scaling can ensure that the entropy of the extension is optimized and that the entropy is increased compared to the initial model defined on 2 times 2 elements. Application to a simple stationary model with hidden states is also outlined. For the n.i.b constraint, the initial model is based on elements defined by blocks of (1 times 2) binary symbols.
ISBN:
9781424443123
Type:
Conference paper
Language:
English
Published in:
Proceedings, Isit, 2009
Keywords:
Main Research Area:
Science/technology
Publication Status:
Published
Review type:
Undetermined
Conference:
2009 IEEE International Symposium on Information Theory, 2009
Publisher:
IEEE
Submission year:
2009
Scientific Level:
Scientific
ID:
2171861176

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