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### Abstract

Feedback can considerably simplify the task of approaching and achieving the performance limits predicted by information theory. This paper determines some of the potential offered by feedback in a typical sensor network situation that could be termed monitoring: the task is to monitor an underlying physical reality at the highest possible fidelity. Since the sensed signals are often analog, and the communication channels noisy, it will not generally be possible to exactly communicate the sensed signals. Rather, such sensor network scenarios involve both a compression and a communication problem. It is well known that in general, these two tasks must be addressed jointly for optimal performance, but optimal performance is generally unknown. Instead, this paper focuses on the scaling behavior of performance, i.e., its dependence on the number of nodes in the network.