A Model for the Two-dimensional no Isolated Bits Constraint

Søren Forchhammer; Torben Vaarby Laursen

doi:10.1109/ISIT.2006.261993

A Model for the Two-dimensional no Isolated Bits Constraint

Søren Forchhammer, Torben Vaarby Laursen

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Abstract

A stationary model is presented for the two-dimensional (2-D) no isolated bits (n.i.b.) constraint over an extended alphabet defined by the elements within 1 by 2 blocks. This block-wise model is based on a set of sufficient conditions for a Pickard random field (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 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

Original language	English
Title of host publication	IEEE International Symposium on Information Theory, 2006
Publisher	IEEE
Publication date	2006
ISBN (Print)	1-4244-0505-X
DOIs	https://doi.org/10.1109/ISIT.2006.261993
Publication status	Published - 2006
Event	2006 IEEE International Symposium on Information Theory - Seattle, United States Duration: 9 Jul 2006 → 14 Jul 2006 http://www.isit2006.org/

Conference

Conference	2006 IEEE International Symposium on Information Theory
Country/Territory	United States
City	Seattle
Period	09/07/2006 → 14/07/2006
Internet address	http://www.isit2006.org/

Bibliographical note

Copyright: 2006 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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title = "A Model for the Two-dimensional no Isolated Bits Constraint",

abstract = "A stationary model is presented for the two-dimensional (2-D) no isolated bits (n.i.b.) constraint over an extended alphabet defined by the elements within 1 by 2 blocks. This block-wise model is based on a set of sufficient conditions for a Pickard random field (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 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",

author = "S{\o}ren Forchhammer and Laursen, {Torben Vaarby}",

note = "Copyright: 2006 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; 2006 IEEE International Symposium on Information Theory, ISIT 2006 ; Conference date: 09-07-2006 Through 14-07-2006",

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AU - Laursen, Torben Vaarby

N1 - Copyright: 2006 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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N2 - A stationary model is presented for the two-dimensional (2-D) no isolated bits (n.i.b.) constraint over an extended alphabet defined by the elements within 1 by 2 blocks. This block-wise model is based on a set of sufficient conditions for a Pickard random field (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 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

AB - A stationary model is presented for the two-dimensional (2-D) no isolated bits (n.i.b.) constraint over an extended alphabet defined by the elements within 1 by 2 blocks. This block-wise model is based on a set of sufficient conditions for a Pickard random field (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 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

U2 - 10.1109/ISIT.2006.261993

DO - 10.1109/ISIT.2006.261993

M3 - Article in proceedings

SN - 1-4244-0505-X

BT - IEEE International Symposium on Information Theory, 2006

PB - IEEE

T2 - 2006 IEEE International Symposium on Information Theory

Y2 - 9 July 2006 through 14 July 2006

ER -

A Model for the Two-dimensional no Isolated Bits Constraint

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