Block Pickard Models for Two-Dimensional Constraints

Søren Forchhammer; Jørn Justesen

doi:10.1109/TIT.2009.2027505

Block Pickard Models for Two-Dimensional Constraints

Søren Forchhammer, Jørn Justesen

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Abstract

In Pickard random fields (PRF), the probabilities of finite configurations and the entropy of the field can be calculated explicitly, but only very simple structures can be incorporated into such a field. Given two Markov chains describing a boundary, an algorithm is presented which determines whether a PRF consistent with the distribution on the boundary and a 2-D constraint exists. Iterative scaling is used as part of the algorithm, which also determines the conditional probabilities yielding the maximum entropy for the given boundary description if a solution exists. A PRF is defined for the domino tiling constraint represented by a quaternary alphabet. PRF models are also presented for higher order constraints, including the no isolated bits (n.i.b.) constraint, and a minimum distance 3 constraint by defining super symbols on blocks of binary symbols.

Original language	English
Journal	I E E E Transactions on Information Theory
Volume	55
Issue number	10
Pages (from-to)	4626-4634
ISSN	0018-9448
DOIs	https://doi.org/10.1109/TIT.2009.2027505
Publication status	Published - 2009

Bibliographical note

Copyright: 2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE

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abstract = "In Pickard random fields (PRF), the probabilities of finite configurations and the entropy of the field can be calculated explicitly, but only very simple structures can be incorporated into such a field. Given two Markov chains describing a boundary, an algorithm is presented which determines whether a PRF consistent with the distribution on the boundary and a 2-D constraint exists. Iterative scaling is used as part of the algorithm, which also determines the conditional probabilities yielding the maximum entropy for the given boundary description if a solution exists. A PRF is defined for the domino tiling constraint represented by a quaternary alphabet. PRF models are also presented for higher order constraints, including the no isolated bits (n.i.b.) constraint, and a minimum distance 3 constraint by defining super symbols on blocks of binary symbols.",

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