On Distributed Hypothesis Testing with Constant-Bit Communication Constraints

In this paper, we consider the distributed hypothesis testing (DHT) problem where two nodes are constrained to transmit constant bits to a central decoder. In such cases, we show that in order to achieve the optimal error exponents, it suffices to consider the empirical distributions of observed data sequences and encode them to the transmission bits. With such a coding strategy, we develop a geometric approach in the distribution spaces to show the optimal achievable error exponents and coding scheme for the following cases: (i) both nodes can transmit log 2 3 bits; (ii) one of the nodes can transmit 1 bit, and the other node is not constrained; (iii) the joint distribution of the nodes are conditionally independent given one hypothesis. Our approach essentially reveals new potentials for characterizing the precise error exponents for DHT with general communication constraints.