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Sharing of information is crucial in sensor networks to allow collective processing of observations made by distributed sensors. Our goal is to efficiently retrieve the distributed sensor measurements at a central processor or to share the information among all sensors. To achieve this goal with a minimum number of channel accesses, it naturally involves the compression of the distributed source data and an optimal scheduling of the transmissions to reduce the number of redundant transmissions. In this paper, we utilize a content-based group testing approach to derive a joint source coding and multiple access scheduling method without the initial knowledge of the statistics of the sensor field. The group testing multiple access (GTMA) scheme proposed in this paper is obtained by choosing groups through a tree splitting algorithm that adapts the branching of the tree according to the progressively estimated statistics of the sensor field. We show that this method overcomes the difficulty of applying the algebraic distributed source coding schemes to a large number of sensors and for arbitrary or unknown statistics of the sensor field.