Intersensor Collaboration in Distributed Quantization Networks

Several key results in distributed source coding offer the intuition that little improvement in compression can be gained from intersensor communication when the information is coded in long blocks. However, when sensors are restricted to code their observations in small blocks (e.g., one) or desire fidelity of a computation applied to source realizations, intelligent collaboration between sensors can greatly reduce distortion. For networks where sensors are allowed to "chat" using a side channel that is unobservable at the fusion center, we provide asymptotically-exact characterization of distortion performance and optimal quantizer design in the high-resolution (low-distortion) regime using a framework called distributed functional scalar quantization (DFSQ). The key result is that chatting can dramatically improve performance even when intersensor communication is at very low rate. We also solve the rate allocation problem when communication links have heterogeneous costs and provide a detailed example to demonstrate the theoretical and practical gains from chatting. This example for maximum computation gives insight on the gap between chatting and distributed networks, and how to optimize the intersensor communication.