A Model for the Two-Dimensional No Isolated Bits Constraint

Soren Forchhammer, Torben V. Laursen
2006 2006 IEEE International Symposium on Information Theory  
A stationary model is presented for the twodimensional (2-D) no isolated bits (n.i.b.) constraint over an extended alphabet dened by the elements within 1 by 2 blocks. This block-wise model is based on a set of sufcient conditions for a Pickard random eld (PRF) over an m−ary alphabet. Iterative techniques are applied as part of determining the model parameters. Given two Markov chains describing a boundary, an algorithm is presented which determines whether a certain PRF consistent with the
more » ... onsistent with the boundary 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. Optimizing over the parameters for a class of boundaries with certain symmetry properties, an entropy of 0.9156 is achieved for the n.i.b. constraint, providing a lower bound. An algorithm for iterative search for a PRF solution starting from a set of conditional probabilities is also presented. Authorized licensed use lim ited to: D anm arks T ekniske Inform ationscenter. D ownloa de d on N ove m be r 2 8 , 2 0 0 9 a t 1 8 :3 6 from IE E E X plore . R e strictions a pply.
doi:10.1109/isit.2006.261993 dblp:conf/isit/ForchhammerL06 fatcat:pogkk7ploreobhdlrz23grhsxa