In a wireless sensor network, a fusion center may receive incorrect information from local sensors, with some probabilities of transmission errors, due to channel fading. To cope with such a problem, we generalize the likelihood-ratio-test method of Chen and Willett (2005)  and derive optimal local sensor compression rules that minimize the Bayesian cost under a given fusion rule and transmission error probabilities. Our proposed method is able to operate without conditional independence between sensor data, which is often required by existing methods. Numerical examples are also used to validate the performance through receiver operating characteristics curves. These examples highlight the interesting features of our method compared to those in ideal situations.