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Entropy 2015, 17(9), 6462-6480; doi:10.3390/e17096462

Subspace Coding for Networks with Different Level Messages

The State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an 710071, China
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Author to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 6 July 2015 / Revised: 31 August 2015 / Accepted: 14 September 2015 / Published: 21 September 2015
(This article belongs to the Section Information Theory)
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Abstract

We study the asymptotically-achievable rate region of subspace codes for wireless network coding, where receivers have different link capacities due to the access ways or the faults of the intermediate links in the network. Firstly, an outer bound of the achievable rate region in a two-receiver network is derived from a combinatorial method. Subsequently, the achievability of the outer bound is proven by code construction, which is based on superposition coding. We show that the outer bound can be achieved asymptotically by using the code presented by Koetter and Kschischang, and the outer bound can be exactly attained in some points by using a q-analog Steiner structure. Finally, the asymptotically-achievable rate region is extended to the general case when the network has m receivers with different levels. View Full-Text
Keywords: network coding; error correcting; achievable rate region; projective spaces; Kruskal–Katona theorem; block design network coding; error correcting; achievable rate region; projective spaces; Kruskal–Katona theorem; block design
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Cai, F.; Cai, N.; Guo, W. Subspace Coding for Networks with Different Level Messages. Entropy 2015, 17, 6462-6480.

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