Journal article
Block Pickard Models for Two-Dimensional Constraints
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.
| Language: | English |
|---|---|
| Publisher: | IEEE |
| Year: | 2009 |
| Pages: | 4626-4634 |
| ISSN: | 15579654 and 00189448 |
| Types: | Journal article |
| DOI: | 10.1109/TIT.2009.2027505 |
| ORCIDs: | Forchhammer, Søren |
2-D constraints 2-D entropy Codes Constraint optimization Entropy H infinity control Iterative algorithms Iterative methods Markov chain Markov processes PRF model Pickard random fields Probability distribution Two dimensional displays binary symbol block Pickard random field model conditional probability domino tiling constraint entropy finite configuration higher-order constraint iterative methods iterative scaling maximum entropy minimum distance <emphasis emphasistype="italic"><formula formulatype="inline"> <tex Notation="TeX">$3$</tex></formula></emphasis> constraint minimum distance constraint n.i.b. constraint no-isolated-bits constraint probability quaternary alphabet random processes super symbol two-dimensional (2-D) capacity two-dimensional constraint
