Distributed Remote Vector Gaussian Source Coding for Wireless Acoustic Sensor Networks

In this paper, we consider the problem of remote vector Gaussian source coding for a wireless acoustic sensor network. Each node receives messages from multiple nodes in the network and decodes these messages using its own measurement of the sound field as side information. The node´s measurement and the estimates of the source resulting from decoding the received messages are then jointly encoded and transmitted to a neighbouring node in the network. We show that for this distributed source coding scenario, one can encode a so-called conditional sufficient statistic of the sources instead of jointly encoding multiple sources. We focus on the case where node measurements are in form of noisy linearly mixed combinations of the sources and the acoustic channel mixing matrices are invertible. For this problem, we derive the rate-distortion function for vector Gaussian sources and under covariance distortion constraints.