Quantizer Design for Decentralized MMSE Estimation

Conceptual and practical encoding/decoding, aimed at accurately reproducing remotely collected observations, has been heavily investigated since the pioneering works by Shannon about source coding. However, when the goal is not to reproduce the observables, but making inference about an embedded parameter and the scenario consists of many unconnected remote nodes, the landscape is less certain. We consider a multi-terminal system designed for efficiently estimating a random parameter according to the MMSE criterion. The analysis is limited to scalar quantizers followed by a joint entropy encoder, and it is performed in the high-resolution regime where the mathematics is easier