  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 $(k>0)$ 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 $\epsilon\in (0,1)$ 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.
