We formulate a new problem which bridges between source coding and enhancement in wireless acoustic sensor networks. We consider a network of wireless microphones, each of which encoding its own measurement under a covariance matrix distortion constraint and sending it to a fusion center. To process the data at the center, we use a recent spatio-temporal prediction filter. We assume that a weighted sum-rate for the network is specified. The problem is to allocate optimal distortion matrices to the nodes in order to achieve a maximum output SNR at the fusion center after processing the received data, while the weighted sum-rate for the network is no more than the specified value. We formulate this problem as an optimization problem for which we derive a set of equalities imposed on the solution by studying the KKT conditions. In particular, for the special case of scalar sources with two microphones and a sum-rate constraint, we derive the distortion allocation in closed form and will show that if the given sum-rate is higher than a critical value, the stationary points from the KKT conditions lead to distortion allocations which maximize the output SNR of the filter