  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., 1), 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, especially
if the fusion center desires fidelity of a nonlinear computation applied to
source realizations rather than fidelity in representing the sources
themselves. 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.
