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The 1-Vertex Transfer Matrix and Accurate Estimation of Channel Capacity
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago.
KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Kondenserade materiens teori.
Department of Mathematics and Mathematical Statistics, Umeå University.
2010 (Engelska)Ingår i: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 56, nr 8, s. 3692-3699Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
2010. Vol. 56, nr 8, s. 3692-3699
Nyckelord [en]
Channel capacity, multidimensional codes, optical storage, phrases, transfer matrices
Nationell ämneskategori
Teknik och teknologier
Identifikatorer
URN: urn:nbn:se:kth:diva-26684DOI: 10.1109/TIT.2010.2050802ISI: 000282001700004Scopus ID: 2-s2.0-77954618228OAI: oai:DiVA.org:kth-26684DiVA, id: diva2:373139
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QC 20101130Tillgänglig från: 2010-11-30 Skapad: 2010-11-26 Senast uppdaterad: 2022-06-25Bibliografiskt granskad

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