Distributed Sequential Hypothesis Testing With Zero-Rate Compression

In this paper, we consider sequential testing over a single-sensor, a single-decision center setup. At each time, instant t, the sensor gets k samples $(k \gt 0)$ and describes the observed sequence until time t to the decision center over a zero-rate noiseless link. The decision center sends a single bit of feedback to the sensor to request for more samples for compression/testing or to stop the transmission. We have characterized the optimal exponent of type-II error probability under the constraint that type-I error probability does not exceed a given threshold $\varepsilon \in(0,1)$ and also when the expectation of the number of requests from decision center is smaller than n which tends to infinity. Interestingly, the optimal exponent coincides with that for fixed-length hypothesis testing with zero-rate communication constraints.