Data fusion in a relay network

The distributed detection of a binary source communicated through parallel relays to a common fusion point is examined. There is independent noise on the links from the source to the relays and noiseless but limited alphabet size communication from the relays to the fusion point. We show that if the link from one relay to the fusion point is limited to an M-ary alphabet, then maximum a posteriori probability (MAP) detection at the fusion point can be achieved using at most an (M+1)-ary alphabet from the other relay. The solution structure for the optimal relay and fusion strategies is characterized for arbitrary channels, and the complete solution is provided to the additive Gaussian noise channel.