Distributed Hypothesis Testing Under A Covertness Constraint

TL;DR

This paper investigates distributed hypothesis testing under a covertness constraint, characterizing the achievable Stein exponent for partially-connected channels and proposing schemes that improve detection performance without shared secrets.

Contribution

It provides a characterization of the Stein exponent under covertness constraints for DMCs and introduces coding schemes that do not require secret keys and achieve exponential covertness.

Findings

Stein exponent equals the non-warden exponent for certain channels.

Proposed schemes improve the local exponent at the decision center.

Covertness constraint vanishes exponentially fast with observation length.

Abstract

We study distributed hypothesis testing under a covertness constraint in the non-alert situation, which requires that under the null-hypothesis an external warden be unable to detect whether communication between the sensor and the decision center is taking place. We characterize the achievable Stein exponent of this setup when the channel from the sensor to the decision center is a partially-connected discrete memoryless channel (DMC), i.e., when certain output symbols can only be induced by some of the inputs. The Stein-exponent in this case, does not depend on the specific transition law of the DMC and equals Shalaby and Papamarcou's exponent without a warden but where the sensor can send $k$ noise-free bits to the decision center, for $k$ a function that is sublinear in the observation length $n$. For fully-connected DMCs, we propose an achievable Stein-exponent and show that it can improve over the local exponent at the decision center. All our coding schemes do not require that the sensor and decision center share a common secret key, as commonly assumed in covert communication. Moreover, in our schemes the divergence covertness constraint vanishes (almost) exponentially fast in the obervation length $n$, again, an atypical behaviour for covert communication.