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https://hdl.handle.net/2440/123760
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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 1557-9654 |
Statement of Responsibility: | 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 2011CBA00301 61033001 61361136003 http://purl.org/au-research/grants/arc/DP1094571 |
Published version: | http://dx.doi.org/10.1109/tit.2014.2326976 |
Appears in Collections: | Aurora harvest 4 Electrical and Electronic Engineering publications |
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