Hypothesis Testing over a Noisy Channel

A point to point hypothesis testing problem involving two parties, one referred to as the observer and the other as the detector, is studied. The observer observes a discrete memoryless source and communicates its observations to the detector over a discrete memoryless channel. The detector performs a binary hypothesis test on the probability distribution of the observer's observation. The trade-off between the type 1 error probability and the type 2 error exponent is explored. We obtain a single-letter characterization of the optimal type 2 error exponent for a given constraint on the type 1 error probability. We also show that a strong converse holds, in the sense that, the optimal type 2 error exponent is independent of the constraint on the type 1 error probability.