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Recently, battery-powered wireless sensor network (WSN) technology has been applied on various environment detections. The capacity of the battery, however, limits the working time of the sensor. The conventional censoring scheme, in which either the entire log-likelihood ratio (LLR) value is transmitted or only a single-bit indicating signal, namely “1,” is sent to the fusion center (FC) if the LLR falls within the “send” region, has been introduced for reduced communication rate in a parallel fusion network where decisions made at local nodes need to be communicated to an FC. In this paper, a new sensor-censoring scheme is proposed to further exploit its energy-efficiency capability. As opposed to conventional censoring schemes, the proposed scheme allows each sensor to transmit a binary decision, i.e., either “1” or “-1,” to the FC only when the reliability of its observation on the environment is beyond a given level. The binary hypothesis on the phenomenon of the environment in WSNs has been assumed, and the error performance of the binary code applied for data transmission to the FC under the considered censoring strategy has been analyzed. Under the proposed censoring scheme, the main problem of this paper is to minimize the fusion errors via obtaining the optimum energy saving rate. The result obtained from the conducted examples confirms that the goal of energy saving by the proposed scheme is archived.