Alignment-Based Network Coding for Two-Unicast-Z Networks
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Medard_Alignment based.pdf
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Author(s)
Zeng, Weifei
Cadambe, Viveck R.
Medard, Muriel
Date Issued
June 2016
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Zeng, Weifei et al. “Alignment-Based Network Coding for Two-Unicast-Z Networks.” IEEE Transactions on Information Theory 62, 6 (June 2016): 3183–3211 © 2016 Institute of Electrical and Electronics Engineers (IEEE)
Version
Original manuscript
Abstract
In this paper, we study the wireline two-unicast-Z communication network over directed acyclic graphs. The two-unicast-Z network is a two-unicast network where the destination intending to decode the second message has a priori side information of the first message. We make three contributions in this paper. First, we describe a new linear network coding algorithm for two-unicast-Z networks over the directed acyclic graphs. Our approach includes the idea of interference alignment as one of its key ingredients. For the graphs of a bounded degree, our algorithm has linear complexity in terms of the number of vertices, and the polynomial complexity in terms of the number of edges. Second, we prove that our algorithm achieves the rate pair (1, 1) whenever it is feasible in the network. Our proof serves as an alternative, albeit restricted to two-unicast-Z networks over the directed acyclic graphs, to an earlier result of Wang et al., which studied the necessary and sufficient conditions for the feasibility of the rate pair (1, 1) in two-unicast networks. Third, we provide a new proof of the classical max-flow min-cut theorem for the directed acyclic graphs.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Research Laboratory of Electronics
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DOI of Published Version
https://doi.org/10.1109/TIT.2016.2553676
