Testing Against Independence with an Eavesdropper

TL;DR

This paper investigates a distributed hypothesis testing problem with an eavesdropper, characterizing the maximum error decay rate under communication, error, and security constraints for testing against independence.

Contribution

It provides a novel characterization of the maximum type-II error exponent in a secure distributed hypothesis testing scenario against independence.

Findings

Maximized type-II error exponent under security constraints.

Derived bounds for error probabilities with an eavesdropper.

Characterized optimal trade-offs between communication rate, error, and security.

Abstract

We study a distributed binary hypothesis testing (HT) problem with communication and security constraints, involving three parties: a remote sensor called Alice, a legitimate decision centre called Bob, and an eavesdropper called Eve, all having their own source observations. In this system, Alice conveys a rate R description of her observation to Bob, and Bob performs a binary hypothesis test on the joint distribution underlying his and Alice's observations. The goal of Alice and Bob is to maximise the exponential decay of Bob's miss-detection (type II-error) probability under two constraints: Bob's false alarm-probability (type-I error) probability has to stay below a given threshold and Eve's uncertainty (equivocation) about Alice's observations should stay above a given security threshold even when Eve learns Alice's message. For the special case of testing against independence, we characterise the largest possible type-II error exponent under the described type-I error probability and security constraints.