Distributed Hypothesis Testing over Multi-Access Channels

Consider distributed hypothesis testing over multiple-access channels (MACs), where the receiver wishes to maximize the type-II error exponent under a constrained type-I error probability. For this setup, we propose a scheme that combines hybrid coding with a MAC-version of Borades unequal error protection. It achieves the optimal type-II error exponent for a generalization of testing against independence over an orthogonal MAC when the transmitters' sources are independent. In this case, hybrid coding can be replaced by the simpler separate source-channel coding. The paper also presents upper and lower bounds on the optimal type-II error exponent for generalized testing against independence of Gaussian sources over a Gaussian MAC. The bounds are close and significantly larger than a type-II error exponent that is achievable using separate source-channel coding.