Block Pickard Models for Two-Dimensional Constraints

Publication: Research - peer-reviewJournal article – Annual report year: 2009

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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 languageEnglish
JournalI E E E Transactions on Information Theory
Publication date2009
Volume55
Issue10
Pages4626-4634
ISSN0018-9448
DOIs
StatePublished

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