This paper addresses the state estimation and stabilization for linear discrete-time descriptor systems. It is assumed that the estimator and controller can only receive the transmitted sequence of finite coded signals via a limited digital communication channel. Both coder-decoder and coder-decoder-controller procedures are proposed, in which a compensation term is introduced to meet the compatible requirement. In addition, an effective method for selecting the compensation term is presented. Detection and stabilization conditions in terms of linear matrix inequality are obtained. Finally, an example is given to illustrate the effectiveness of design procedures. (C) 2009 Elsevier Ltd. All rights reserved.