This paper addresses the set-membership filtering problem with communication constraints for a class of discrete time-varying systems in the presence of unknown-but-bounded process and measurement noises. The dynamic coder and decoder are proposed to model the digital communication channel to transmit the error between the current measurement output and the last time quantized measurement output rather than the current measurement output. This strategy will reduce the channel communication burden by transmitting fewer bits. A time-varying linear matrix inequality approach is developed to solve the set-membership filtering problem and a sufficient condition for the existence of set-membership filter is derived. A recursive convex optimization algorithm is provided to determine a state estimation ellipsoid that is a set of states compatible with quantized measurement and unknown-but-bounded process and measurement noises. Simulation results demonstrate the effectiveness of the proposed method.