Achievable rate-exponent region for parallel distributed detection via binary symmetric channels

Distributed detection with multiple sensors and a fusion center over binary symmetric channels has been investigated. The fusion center receives noisy observations of the local binary decisions. A fundamental tradeoff between achievable information rate and the error exponent of the missing probability exists. The tradeoff is well characterized by the rate-exponent region. The paper first derived a closed-form analytic expression for the error exponent and information rate by means of the theory of relative entropy typical set. Second, the properties of the optimal error exponent and information rate are discussed in detail. It was demonstrated that they are monotonically decreasing in the bit error probability of the binary symmetric channel. Simulation results validated the conclusions.