This paper addresses the actuator fault estimation sliding-mode observer (SMO) design problem of linear continuous-time systems over digital communication channels. This problem frequently occurred in a network environment where data has to be quantized before being transmitted via digital communication channels. Traditional observers (linear Luenberger observer, Walcott-ZaK SMO) are not effective to solve this design issue since the effects of signal quantization will degrade estimation performances evidently. In this paper, a new descriptor SMO method is presented to overcome this difficult problem. It is shown that, if the quantizer density is larger than root 2 - 1, the designed observer can compensate quantization errors completely, and the fault vector can be reconstructed despite of signal quantization. Finally, a simulation example with the F-404 aircraft engine model is proposed to demonstrate the effectiveness of the proposed robust digital observer design approach.