Distributed Hypothesis Testing over Noisy Broadcast Channels

This paper studies binary hypothesis testing with a single sensor that communicates with two decision centers over a memoryless broadcast channel. The main focus lies on the tradeoff between the two type-II error exponents achievable at the two decision centers. In our proposed scheme, we can partially mitigate this tradeoff when the transmitter has a probability larger than 1/2 to distinguish the alternate hypotheses at the decision centers, i.e., the hypotheses under which the decision centers wish to maximize their error exponents. In the cases where these hypotheses cannot be distinguished at the transmitter (because both decision centers have the same alternative hypothesis or because the transmitter’s observations have the same marginal distribution under both hypotheses), our scheme shows an important tradeoff between the two exponents. The results in this paper thus reinforce the previous conclusions drawn for a setup where communication is over a common noiseless link. Compared to such a noiseless scenario, here, however, we observe that even when the transmitter can distinguish the two hypotheses, a small exponent tradeoff can persist, simply because the noise in the channel prevents the transmitter to perfectly describe its guess of the hypothesis to the two decision centers.

Privacy-Aware Distributed Hypothesis Testing

A distributed binary hypothesis testing (HT) problem involving two parties, a remote observer and a detector, is studied. The remote observer has access to a discrete memoryless source, and communicates its observations to the detector via a rate-limited noiseless channel. The detector observes another discrete memoryless source, and performs a binary hypothesis test on the joint distribution of its own observations with those of the observer. While the goal of the observer is to maximize the type II error exponent of the test for a given type I error probability constraint, it also wants to keep a private part of its observations as oblivious to the detector as possible. Considering both equivocation and average distortion under a causal disclosure assumption as possible measures of privacy, the trade-off between the communication rate from the observer to the detector, the type II error exponent, and privacy is studied. For the general HT problem, we establish single-letter inner bounds on both the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs. Subsequently, single-letter characterizations for both trade-offs are obtained (i) for testing against conditional independence of the observer’s observations from those of the detector, given some additional side information at the detector; and (ii) when the communication rate constraint over the channel is zero. Finally, we show by providing a counter-example where the strong converse which holds for distributed HT without a privacy constraint does not hold when a privacy constraint is imposed. This implies that in general, the rate-error exponent-equivocation and rate-error exponent-distortion trade-offs are not independent of the type I error probability constraint.