Gaussian Sensor Networks with Adversarial Nodes

TL;DR

This paper analyzes Gaussian sensor networks with adversarial sensors, showing how coordination affects optimal strategies and demonstrating that uncoded communication is optimal, with digital methods being suboptimal.

Contribution

It introduces a new analysis of sensor networks with adversaries, highlighting the role of coordination and characterizing optimal strategies in different settings.

Findings

Coordination enables optimal strategies for both transmitters and adversaries.

Uncoded communication is optimal; digital compression is suboptimal.

Different strategies emerge depending on whether sensors can coordinate or are fixed.

Abstract

This paper studies a particular sensor network model which involves one single Gaussian source observed by many sensors, subject to additive independent Gaussian observation noise. Sensors communicate with the receiver over an additive Gaussian multiple access channel. The aim of the receiver is to reconstruct the underlying source with minimum mean squared error. The scenario of interest here is one where some of the sensors act as adversary (jammer): they strive to maximize distortion. We show that the ability of transmitter sensors to secretly agree on a random event, that is "coordination", plays a key role in the analysis. Depending on the coordination capability of sensors and the receiver, we consider two problem settings. The first setting involves transmitters with coordination capabilities in the sense that all transmitters can use identical realization of randomized encoding for each transmission. In this case, the optimal strategy for the adversary sensors also requires coordination, where they all generate the same realization of independent and identically distributed Gaussian noise. In the second setting, the transmitter sensors are restricted to use fixed, deterministic encoders and this setting, which corresponds to a Stackelberg game, does not admit a saddle-point solution. We show that the the optimal strategy for all sensors is uncoded communications where encoding functions of adversaries and transmitters are in opposite directions. For both settings, digital compression and communication is strictly suboptimal.