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Constrained Codes as Networks of Relations

Schwartz, Moshe and Bruck, Jehoshua (2007) Constrained Codes as Networks of Relations. In: 2007 IEEE International Symposium on Information Theory. IEEE , Piscataway, NJ, pp. 1386-1390. ISBN 978-1-4244-1397-3. https://resolver.caltech.edu/CaltechAUTHORS:20170424-171247108

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Abstract

We revisit the well-known problem of determining the capacity of constrained systems. While the one-dimensional case is well understood, the capacity of two-dimensional systems is mostly unknown. When it is non-zero, except for the (1,∞ )- RLL system on the hexagonal lattice, there are no closed-form analytical solutions known. Furthermore, for the related problem of counting the exact number of constrained arrays of any given size, only exponential-time algorithms are known. We present a novel approach to finding the exact capacity of two-dimensional constrained systems, as well as efficiently counting the exact number of constrained arrays of any given size. To that end, we borrow graph-theoretic tools originally developed for the field of statistical mechanics, tools for efficiently simulating quantum circuits, as well as tools from the theory of the spectral distribution of Toeplitz matrices.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ISIT.2007.4557416DOIArticle
http://ieeexplore.ieee.org/document/4557416/PublisherArticle
http://resolver.caltech.edu/CaltechPARADISE:2007.ETR082Related ItemTechnical Report
ORCID:
AuthorORCID
Schwartz, Moshe0000-0002-1449-0026
Bruck, Jehoshua0000-0001-8474-0812
Additional Information:© 2007 IEEE. This work was supported in part by the Caltech Lee Center for Advanced Networking.
Funders:
Funding AgencyGrant Number
Caltech Lee Center for Advanced NetworkingUNSPECIFIED
DOI:10.1109/ISIT.2007.4557416
Record Number:CaltechAUTHORS:20170424-171247108
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170424-171247108
Official Citation:M. Schwartz and J. Bruck, "Constrained Codes as Networks of Relations," 2007 IEEE International Symposium on Information Theory, Nice, 2007, pp. 1386-1390. doi: 10.1109/ISIT.2007.4557416
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76884
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:25 Apr 2017 02:58
Last Modified:15 Nov 2021 17:03

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