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Type: Journal article
Title: Capacity analysis of linear operator channels over finite fields
Author: Yang, S.
Ho, S.W.
Meng, J.
Yang, E.H.
Citation: IEEE Transactions on Information Theory, 2014; 60(8):4880-4901
Publisher: IEEE
Issue Date: 2014
ISSN: 0018-9448
Statement of
Shenghao Yang, Siu-Wai Ho, Jin Meng and En-Hui Yang
Abstract: Motivated by communication through a network employing linear network coding, capacities of linear operator channels (LOCs) with arbitrarily distributed transfer matrices over finite fields are studied. Both the Shannon capacity C and the subspace coding capacity C SS are analyzed. By establishing and comparing lower bounds on C and upper bounds on C SS , various necessary conditions and sufficient conditions such that C = C SS are obtained. A new class of LOCs such that C = C SS is identified, which includes LOCs with uniform-given-rank transfer matrices as special cases. It is also demonstrated that C SS is strictly less than C for a broad class of LOCs. In general, an optimal subspace coding scheme is difficult to find because it requires to solve the maximization of a nonconcave function. However, for an LOC with a unique subspace degradation, C SS can be obtained by solving a convex optimization problem over rank distribution. Classes of LOCs with a unique subspace degradation are characterized. Since LOCs with uniform-given-rank transfer matrices have unique subspace degradations, some existing results on LOCs with uniform-given-rank transfer matrices are explained from a more general way.
Keywords: Channel coding; degradation; network coding; symmetric matrices; vectors; random variables
Rights: © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
DOI: 10.1109/TIT.2014.2326976
Grant ID: 2011CBA00300
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Electrical and Electronic Engineering publications

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