A Fundamental Limit of Distributed Hypothesis Testing Under Memoryless Quantization

We consider a distributed binary hypothesis testing setup where multiple nodes send quantized information to a central processor, which is oblivious to the nodes’ statistics. We study the regime where the type-II error decays exponentially and the type-I error vanishes. For memoryless quantization, we characterize a tradeoff curve that yields a lower bound for the feasible region of type-II error exponents and the average number of bits sent under the null hypothesis. Moreover, we show that the tradeoff curve is approached at high rates with lattice quantization.