Information theory and statistics: a tutorial
Communications and Information Theory
Cascading methods for runlength-limited arrays
IEEE Transactions on Information Theory
The capacity and coding gain of certain checkerboard codes
IEEE Transactions on Information Theory
Stationary Markov random fields on a finite rectangular lattice
IEEE Transactions on Information Theory
Entropy bounds for constrained two-dimensional random fields
IEEE Transactions on Information Theory
On the capacity of two-dimensional run-length constrained channels
IEEE Transactions on Information Theory
Efficient coding schemes for the hard-square model
IEEE Transactions on Information Theory
Improved bit-stuffing bounds on two-dimensional constraints
IEEE Transactions on Information Theory
Extending models for two-dimensional constraints
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
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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.