TY - JOUR

T1 - Distributed symmetric function computation in noisy wireless sensor networks

AU - Srikant, R.

AU - Dullerud, Geir E.

N1 - Funding Information: Manuscript received July 8, 2006; revised March 13, 2007. The research was supported by a Vodafone Fellowship, AFOSR URI Grant F49620-01-1-0365, and NSF Grant CNS 05-19535. The material in this correspondence was presented in part at the 4th International Symposium on Modeling and Optimization in Mobile, Ad-Hoc, and Wireless Networks, Boston, MA, April 2006.

PY - 2007

Y1 - 2007

N2 - In this correspondence, we consider a wireless sensor network consisting of n sensors, and each sensor has a measurement, which is an integer value belonging to the set {0,⋯,m-1}, so that it can be represented by [log2 m] bits. The network has a special node called the fusion center whose goal is to compute a symmetric function of these measurements. The problem studied is to minimize the total transmission energy used by the network when computing this function, subject to the constraint that this computation be correct with high probability. We assume the wireless channels are binary symmetric channels with a probability of error p, and that each sensor uses ralpha units of energy to transmit each bit, where r is the transmission range of the sensor. For constant m, the main result in this correspondence is an algorithm whose energy usage is κ ⌈log2 m⌉ n(log log n) (8 √ n/log n)α, where κ = ⌈ 4/-log(4p(1-p))⌉. Then, we consider the case where the sensor network observes N events. In this case, we demonstrate a network algorithm which has energy usage Θ(n(√n/log n)α) per event if the number of events satisfies N = Ω(loglog n).

AB - In this correspondence, we consider a wireless sensor network consisting of n sensors, and each sensor has a measurement, which is an integer value belonging to the set {0,⋯,m-1}, so that it can be represented by [log2 m] bits. The network has a special node called the fusion center whose goal is to compute a symmetric function of these measurements. The problem studied is to minimize the total transmission energy used by the network when computing this function, subject to the constraint that this computation be correct with high probability. We assume the wireless channels are binary symmetric channels with a probability of error p, and that each sensor uses ralpha units of energy to transmit each bit, where r is the transmission range of the sensor. For constant m, the main result in this correspondence is an algorithm whose energy usage is κ ⌈log2 m⌉ n(log log n) (8 √ n/log n)α, where κ = ⌈ 4/-log(4p(1-p))⌉. Then, we consider the case where the sensor network observes N events. In this case, we demonstrate a network algorithm which has energy usage Θ(n(√n/log n)α) per event if the number of events satisfies N = Ω(loglog n).

KW - Binary symmetric channel

KW - Function computation

KW - Reception diversity

KW - Sensor network

KW - Wireless network

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U2 - 10.1109/TIT.2007.909156

DO - 10.1109/TIT.2007.909156

M3 - Article

SN - 0018-9448

VL - 53

SP - 4826

EP - 4833

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 12

ER -