  We study a distributed hypothesis testing setup where peripheral nodes send
quantized data to the fusion center in a memoryless fashion. The
\emph{expected} number of bits sent by each node under the null hypothesis is
kept limited. We characterize the optimal decay rate of the mis-detection
(type-II error) probability provided that false alarms (type-I error) are rare,
and study the tradeoff between the communication rate and maximal type-II error
decay rate. We resort to rate-distortion methods to provide upper bounds to the
tradeoff curve and show that at high rates lattice quantization achieves
near-optimal performance. We also characterize the tradeoff for the case where
nodes are allowed to record and quantize a fixed number of samples. Moreover,
under sum-rate constraints, we show that an upper bound to the tradeoff curve
is obtained with a water-filling solution.
