TY - JOUR

T1 - Multicasting in large wireless networks

T2 - Bounds on the minimum energy per bit

AU - Jain, Aman

AU - Kulkarni, Sanjeev R.

AU - Verdu, Sergio

N1 - Funding Information:
Manuscript received March 10, 2009; revised February 24, 2010; accepted May 25, 2010. Date of current version December 27, 2010. This work was supported in part by the National Science Foundation under Grants CCF-06-35154 and CNS-09-05398, the National Science Foundation Science & Technology Center under Grant CCF-0939370 and the U.S. Army Research Office under grant W911NF-07-1-0185. The material in this paper was presented in part at the IEEE International Symposium on Information Theory, Seoul, South Korea, June 2009.

PY - 2011/1

Y1 - 2011/1

N2 - In this paper, we consider scaling laws for maximal energy efficiency of communicating a message to all the nodes in a wireless network, as the number of nodes in the network becomes large. Two cases of large wireless networks are studieddense random networks and constant density (extended) random networks. In addition, we also study finite size regular networks in order to understand how regularity in node placement affects energy consumption. We first establish an information-theoretic lower bound on the minimum energy per bit for multicasting in arbitrary wireless networks when the channel state information is not available at the transmitters. Upper bounds are obtained by constructing a simple flooding scheme that requires no information at the receivers about the channel states or the locations and identities of the nodes. The gap between the upper and lower bounds is only a constant factor for dense random networks and regular networks, and differs by a poly-logarithmic factor for extended random networks. Furthermore, we show that the proposed upper and lower bounds for random networks hold almost surely in the node locations as the number of nodes approaches infinity.

AB - In this paper, we consider scaling laws for maximal energy efficiency of communicating a message to all the nodes in a wireless network, as the number of nodes in the network becomes large. Two cases of large wireless networks are studieddense random networks and constant density (extended) random networks. In addition, we also study finite size regular networks in order to understand how regularity in node placement affects energy consumption. We first establish an information-theoretic lower bound on the minimum energy per bit for multicasting in arbitrary wireless networks when the channel state information is not available at the transmitters. Upper bounds are obtained by constructing a simple flooding scheme that requires no information at the receivers about the channel states or the locations and identities of the nodes. The gap between the upper and lower bounds is only a constant factor for dense random networks and regular networks, and differs by a poly-logarithmic factor for extended random networks. Furthermore, we show that the proposed upper and lower bounds for random networks hold almost surely in the node locations as the number of nodes approaches infinity.

KW - Cooperative communication

KW - minimum energy per bit

KW - multicasting

KW - wideband communication

KW - wireless networks

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U2 - 10.1109/TIT.2010.2090228

DO - 10.1109/TIT.2010.2090228

M3 - Article

AN - SCOPUS:78650855428

VL - 57

SP - 14

EP - 32

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 1

M1 - 5673782

ER -