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Asymptotically optimal and bandwith-efficient decentralized detection

We consider decentralized detection for wireless sensor networks. A sequential scheme based on level-triggered sampling is proposed. In the proposed scheme, sensors compute log-likelihood ratio (LLR) of their local observations, sample local LLR using level-triggered sampling and transmit a single bit at each sampling time to a fusion center (FC). At each sampling time excess LLR over (below) sampling threshold is linearly encoded in time. The FC, upon receiving a bit from a sensor, decodes excess LLR and updates approximate global LLR, which it uses as test statistic. An SPRT-like test is used by the FC to reach a final decision. We show that the proposed scheme achieves order-2 asymptotic optimality by using only a single bit for each sample, thanks to time-encoding the overshoot.