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The 1-vertex transfer matrix and accurate estimation of channel capacity
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2010 (English)In: IEEE Transactions on Information Theory, ISSN 0018-9448, Vol. 57, no 8, 3692-3699 p.Article in journal (Refereed) Published
Abstract [en]

The notion of a 1-vertex transfer matrix for multidimensional codes is introduced. It is shown that the capacity of such codes, or the topological entropy, can be expressed as the limit of the logarithm of spectral radii of 1-vertex transfer matrices. Storage and computations using the 1-vertex transfer matrix are much smaller than storage and computations needed for the standard transfer matrix. The method is applied to estimate the first 15 digits of the entropy of the 2-D (0, 1) run length limited channel. A large-scale computation of eigenvalues for the (0, 1) run length limited channel in 2-D and 3-D have been carried out. This was done in order to be able to compare the computational cost of the new method with the standard transfer matrix and have rigorous bounds to compare the estimates with. This in turn leads to improvements on the best previous lower and upper bounds for these channels.

Place, publisher, year, edition, pages
IEEE , 2010. Vol. 57, no 8, 3692-3699 p.
Keyword [en]
channel capacity, multidimensional codes, optical storage, phrases, transfer matrices, independent sets, entropy, graph, z(d)
National Category
Computer Science Information Systems
URN: urn:nbn:se:umu:diva-41317DOI: 10.1109/Tit.2010.2050802ISI: 000282001700004OAI: diva2:405611

652JM Times Cited:0 Cited References Count:15

Available from: 2011-03-23 Created: 2011-03-23 Last updated: 2015-08-31Bibliographically approved

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Lundow, P. H.Markström, Klas
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