Error probability analysis for data fusion of end-nodes in tree networks

In the preceding works on the tree networks composed of binary symmetric channel (BSC), the path diversity effects are discussed in [8]-[10]. In [9], it is shown that the error probability of majority decision at the fusion center is almost constant regardless of network size. This constant property of error probability has not been discussed theoretically. In this paper, a new approach of signal-to-noise ratio (SNR) is proposed for the theoretical explanation on the constant property. A random tree network is presented to model a network with a large number of nodes randomly deployed over a field. The error probability of random tree network is analyzed for data fusion of end-nodes by SNR, which is shown to be useful to explain the constant property. Based on the analytical expressions, the effects of system parameters on error probability of random tree network are demonstrated.