We propose a distributed source coding system for data collected by sensor networks. It uses a feedback channel between the sensors and the gateway node (i.e., the joint decoder) but, unlike previous systems, the encoding process is driven by the decoder. Compression is performed using distributed arithmetic coding, which is extended to adaptively estimate the source probabilities. Specifically, the decoder estimates marginal and conditional probabilities, and sends them back to the sensors to drive the distributed arithmetic coding process. This reduces the decoding delay, and potentially eliminates the need of rate-compatible Slepian-Wolf codes.