Optimal Error Exponent of Type-Based Distributed Hypothesis Testing over AWGN Channels

This paper investigates the distributed hypothesis testing (DHT) problem over AWGN channels, where the distributed nodes are restricted to transmit functions of the empirical distributions of the observed data sequences due to practical computational constraints. The goal of this problem is to design the transmitted signals of the distributed nodes, so that the decision center can make a decision based on the received signals with the maximal decision error exponent. In order to solve this problem, we first propose a mixture coding strategy for each node, which combines the decode-and-forward and amplify-and-forward strategies, and then the achievable error exponent is computed. Moreover, we present a genie-aided approach to prove the converse result, thereby demonstrating the optimality of the achievable error exponent. In summary, our results provide coding guidance for distributed systems, and could be applied to more complicated problems.