Exponent Trade-off for Hypothesis Testing Over Noisy Channels

The distributed hypothesis testing (DHT) problem is considered, in which the joint distribution of a pair of sequences present at separated terminals, is governed by one of two possible hypotheses. The decision needs to be made by one of the terminals (the "decoder"). The other terminal (the "encoder") uses a noisy channel in order to help the decoder with the decision. This problem can be seen as a generalization of the side-information variant of the DHT problem, where the rate-limited link is replaced by a noisy channel. A recent work by Salehkalaibar and Wigger has derived an achievable Stein exponent for this problem, by employing concepts from the DHT scheme of Shimokawa et al., and from unequal error protection coding for a single special message. In this work we extend the view to a trade-off between the two error exponents, additionally building on multiple codebooks and two special messages with unequal error protection. As a by product, we also present an achievable exponent trade-off for a rate-limited link, which generalizes Shimokawa et al..