Capacity of 3D erasure networks

Cheol Jeong, Won Yong Shin

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1 Citation (Scopus)


In this paper, we introduce a large-scale 3D erasure network, where $n$ wireless nodes are randomly distributed in a cuboid of nλ× nμ × nν with λ +μ +ν =1$ for λ ,μ , ν >0$ , and completely characterize its capacity scaling laws. Two fundamental path-loss attenuation models (i.e., exponential and polynomial power-law models) are used to suitably model an erasure probability for packet transmission. Then, under the two erasure models, we introduce a routing protocol using percolation highway in 3D space, and then analyze its achievable throughput scaling laws. It is shown that, under the two erasure models, the aggregate throughput scaling nmin{1-λ ,1-μ ,1-ν } can be achieved in the 3D erasure network. This implies that the aggregate throughput scaling n2/3 can be achieved in 3D cubic erasure networks, while n can be achieved in 2D square erasure networks. The gain comes from the fact that, compared with 2D space, more geographic diversity can be exploited via 3D space, which means that generating more simultaneous percolation highways is possible. In addition, cut-set upper bounds on the capacity scaling are derived to verify that the achievable scheme based on the 3D percolation highway is order-optimal within a polylogarithmic factor under certain practical operating regimes on the decay parameters.

Original languageEnglish
Article number7470564
Pages (from-to)2900-2912
Number of pages13
JournalIEEE Transactions on Communications
Issue number7
Publication statusPublished - 2016 Jul

Bibliographical note

Funding Information:
This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2054577) and by the Ministry of Science, ICT & Future Planning (MSIP) (2015R1A2A1A15054248).

Publisher Copyright:
© 1972-2012 IEEE.

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering


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