Optimal Distortion-Power Tradeoffs in Sensor Networks: Gauss-Markov Random Processes

TL;DR

This paper analyzes the fundamental limits of sensor networks in accurately reconstructing Gauss-Markov processes, establishing bounds and optimal schemes for minimal distortion under power constraints.

Contribution

It provides explicit bounds and an order-optimal scheme for joint source-channel coding in sensor networks observing Gauss-Markov processes.

Findings

Bounds on minimum expected distortion are tight for Gauss-Markov processes.

Order-optimal coding schemes are identified under sum power constraints.

Minimum distortion scales with power constraint in a quantifiable manner.

Abstract

We investigate the optimal performance of dense sensor networks by studying the joint source-channel coding problem. The overall goal of the sensor network is to take measurements from an underlying random process, code and transmit those measurement samples to a collector node in a cooperative multiple access channel with feedback, and reconstruct the entire random process at the collector node. We provide lower and upper bounds for the minimum achievable expected distortion when the underlying random process is stationary and Gaussian. In the case where the random process is also Markovian, we evaluate the lower and upper bounds explicitly and show that they are of the same order for a wide range of sum power constraints. Thus, for a Gauss-Markov random process, under these sum power constraints, we determine the achievability scheme that is order-optimal, and express the minimum achievable expected distortion as a function of the sum power constraint.