On the geometry of wireless network multicast in 2-D
31 May 2011
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2012
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| Online Access: | http://hdl.handle.net/1721.1/73692 https://orcid.org/0000-0003-4059-407X |
| _version_ | 1811088511393071104 |
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| author | Thakur, Mohit Fawaz, Nadia Medard, Muriel |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Thakur, Mohit Fawaz, Nadia Medard, Muriel |
| author_sort | Thakur, Mohit |
| collection | MIT |
| description | 31 May 2011 |
| first_indexed | 2024-09-23T14:03:19Z |
| format | Article |
| id | mit-1721.1/73692 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:03:19Z |
| publishDate | 2012 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/736922022-09-28T17:59:19Z On the geometry of wireless network multicast in 2-D Thakur, Mohit Fawaz, Nadia Medard, Muriel Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Research Laboratory of Electronics Medard, Muriel 31 May 2011 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. 2012-10-10T13:28:39Z 2012-10-10T13:28:39Z 2011-10 2011-07 Article http://purl.org/eprint/type/ConferencePaper 978-1-4577-0594-6 978-1-4577-0596-0 2157-8095 http://hdl.handle.net/1721.1/73692 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. https://orcid.org/0000-0003-4059-407X en_US http://dx.doi.org/10.1109/ISIT.2011.6033820 Proceedings on the IEEE International Symposium on Information Theory Proceedings (ISIT), 2011 Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Thakur, Mohit Fawaz, Nadia Medard, Muriel On the geometry of wireless network multicast in 2-D |
| title | On the geometry of wireless network multicast in 2-D |
| title_full | On the geometry of wireless network multicast in 2-D |
| title_fullStr | On the geometry of wireless network multicast in 2-D |
| title_full_unstemmed | On the geometry of wireless network multicast in 2-D |
| title_short | On the geometry of wireless network multicast in 2-D |
| title_sort | on the geometry of wireless network multicast in 2 d |
| url | http://hdl.handle.net/1721.1/73692 https://orcid.org/0000-0003-4059-407X |
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