Distributed Symmetric Function Computation in Noisy Wireless Sensor Networks

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 {().....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 r^alpha units of energy to transmit each bit, where r is the transmission range of the sensor.