NDLI: Capacity Analysis of Linear Operator Channels Over Finite Fields

Content Provider	IEEE Xplore Digital Library
Author	Shenghao Yang Siu-Wai Ho Jin Meng En-Hui Yang
Copyright Year	1963
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.
Sponsorship	IEEE Information Theory Society
Starting Page	4880
Ending Page	4901
Page Count	22
File Size	862053
File Format	PDF
ISSN	00189448
Volume Number	60
Issue Number	8
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Channel coding Degradation Network coding Symmetric matrices Vectors Random variables subspace coding Linear operator channel network coding
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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