Distributed Hypothesis Testing with Collaborative Detection

A detection system with a single sensor and two detectors is considered, where each of the terminals observes a memoryless source sequence, the sensor sends a message to both detectors and the first detector sends a message to the second detector. Communication of these messages is assumed to be error-free but rate-limited. The joint probability mass function (pmf) of the source sequences observed at the three terminals depends on an M-ary hypothesis (M >= 2), and the goal of the communication is that each detector can guess the underlying hypothesis. Detector k, k = 1; 2, aims to maximize the error exponent under hypothesis i(k), i(k) is an element of {1;...;M}, while ensuring a small probability of error under all other hypotheses. We study this problem in the case in which the detectors aim to maximize their error exponents under the same hypothesis (i. e., i(1) = i(2)) and in the case in which they aim to maximize their error exponents under distinct hypotheses (i. e., i(1) not equal i2). For the setting in which i(1) = i(2), we present an achievable exponents region for the case of positive communication rates, and show that it is optimal for a specific case of testing against independence. We also characterize the optimal exponents region in the case of zero communication rates. For the setting in which i(1) not equal i(2), we characterize the optimal exponents region in the case of zero communication rates.