Causal Coding and Feedback in Gaussian Sensor Networks

Summary

Varaiya and Walrand found an elegant insight regarding the use of feedback in a causal coding context: While generally useful, feedback becomes useless when the channel is sufficiently symmetric. The goal of this note is to extend this insight to scenarios inspired by sensor networks. Specifically, two such scenarios are considered: a situation with a single sensor but where the source is observed through a noisy channel, and a genuine network scenario where all source and noise distributions are assumed to be Gaussian. For the latter, it is shown that feedback is useless if source and channel bandwidth are equal, but that, if the latter is larger, feedback is strictly useful. Varaiya and Walrand establish their results via dynamic programming arguments. It is unclear to date whether such arguments can be extended to the distributed scenario considered in the present chapter. Instead, our results are established via information-theoretic bounds.