Capacity of 3D erasure networks

Cheol Jeong, Won Yong Shin

Research output: Contribution to journalArticle

Abstract

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
Volume64
Issue number7
DOIs
Publication statusPublished - 2016 Jul

Fingerprint

Scaling laws
Throughput
Routing protocols
Polynomials

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Jeong, Cheol ; Shin, Won Yong. / Capacity of 3D erasure networks. In: IEEE Transactions on Communications. 2016 ; Vol. 64, No. 7. pp. 2900-2912.
@article{20663dd058b7455eba8365b3ef9c849b,
title = "Capacity of 3D erasure networks",
abstract = "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.",
author = "Cheol Jeong and Shin, {Won Yong}",
year = "2016",
month = "7",
doi = "10.1109/TCOMM.2016.2569580",
language = "English",
volume = "64",
pages = "2900--2912",
journal = "IEEE Transactions on Communications",
issn = "0096-1965",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "7",

}

Capacity of 3D erasure networks. / Jeong, Cheol; Shin, Won Yong.

In: IEEE Transactions on Communications, Vol. 64, No. 7, 7470564, 07.2016, p. 2900-2912.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Capacity of 3D erasure networks

AU - Jeong, Cheol

AU - Shin, Won Yong

PY - 2016/7

Y1 - 2016/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84978768157&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84978768157&partnerID=8YFLogxK

U2 - 10.1109/TCOMM.2016.2569580

DO - 10.1109/TCOMM.2016.2569580

M3 - Article

AN - SCOPUS:84978768157

VL - 64

SP - 2900

EP - 2912

JO - IEEE Transactions on Communications

JF - IEEE Transactions on Communications

SN - 0096-1965

IS - 7

M1 - 7470564

ER -