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We consider a new source coding problem motivated by the following distributed estimation task in a clustered sensor network. Suppose there are multiple uncorrelated signal sources in the field that we are interested in, however, these sources cannot be directly observed by the sensors. Sensors within each cluster communicate directly with their corresponding cluster-head (CH) to report their observations, which are mixtures of all signal sources in the field, corrupted by noise. Based on the collected data, the CHs estimate the sources and collaborate to improve these initial estimates. Under stringent energy constraint, which prohibits the sensors within a cluster to jointly encode their correlated observations, we propose to employ distributed source coding (DSC) to encode sensorspsila correlated data. In particular, we propose a practically simple, and yet effective, encoding algorithm for sensors, a data reconstruction scheme for CHs, and the corresponding rate allocation policy. We investigate the trade off between rate and mean square error (MSE) performance for the proposed algorithms. Numerical evaluations testify the effectiveness of the proposed methods.