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This paper considers a decentralized robust state estimation problem for uncertain systems via a data-rate constrained sensor network. The uncertainties of the systems satisfy an integral quadratic constraint. The sensor network consists of spatially distributed sensors that take the measurements of a system, and a fusion center where the state estimation is carried out. The communications from the sensors to the fusion center are through data-rate constrained communication channels. We propose an estimation scheme which involves coders and a decoder-estimator, and their construction is based on the robust Kalman filtering techniques.