On the geometry of wireless network multicast in 2-D
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Medard_On the geometry.pdf
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Author(s)
Thakur, Mohit
Fawaz, Nadia
Medard, Muriel
Date Issued
October 2011
Journal
Proceedings on the IEEE International Symposium on Information Theory Proceedings (ISIT), 2011
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Thakur, Mohit, Nadia Fawaz, and Muriel Medard. “On the Geometry of Wireless Network Multicast in 2-D.” IEEE International Symposium on Information Theory Proceedings (ISIT), 2011. 1628–1632.
Version
Author's final manuscript
Abstract
We provide a geometric solution to the problem of optimal relay positioning to maximize the multicast rate for low SNR networks. The network we consider consists of a single source, multiple receivers and the only intermediate and locatable node as the relay. We construct network the hypergraph of the system nodes from the underlying information theoretic model of low-SNR regime that operates using superposition coding and FDMA in conjunction (which we call the "achievable hypergraph model"). We make the following contributions. 1) We show that the problem of optimal relay positioning maximizing the multicast rate can be completely decoupled from the flow optimization by noticing and exploiting geometric properties of multicast flow. 2) All the flow maximizing the multicast rate is sent over at most two paths, in succession. The relay position depends on only one path (out of the two), irrespective of the number of receiver nodes in the system. Subsequently, we propose simple and efficient geometric algorithms to compute the optimal relay position. 3) Finally, we show that in our model at the optimal relay position, the difference between the maximized multicast rate and the cut-set bound is minimum. We solve the problem for all (P[subscript s],[subscript Pr]) pairs of source and relay transmit powers and the path loss exponent α ≥ 2.
Description
31 May 2011
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Research Laboratory of Electronics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1109/ISIT.2011.6033820
