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Distributed source coding (DSC) has recently been considered as an efficient approach to data compression in wireless sensor networks (WSN). Using this coding method multiple sensor nodes compress their correlated observations without inter-node communications. Therefore energy and bandwidth can be efficiently saved. In this paper, we investigate a random-binning based DSC scheme for remote source estimation in WSN and its performance of estimated signal to distortion ratio (SDR). With the introduction of a detailed power consumption model for wireless sensor communications, we quantitatively analyze the overall network energy consumption of the DSC scheme. We further propose a novel energy-aware transmission protocol for the DSC scheme, which flexibly optimizes the DSC performance in terms of either SDR or energy consumption, by adapting the source coding and transmission parameters to the network conditions. Simulations validate the energy efficiency of the proposed adaptive transmission protocol.