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In this work, we analyze the throughput, delay, and energy efficiency of random access sensor networks that employ Slepian-Wolf distributed source coding (DSC) and study the impact of MAC protocol design on these performances. Suppose that N sensors observe correlated information from the environment and that their local data are sent to a sink node through direct transmission links. To eliminate data redundancy, we allow sensors to encode their local messages using the Slepian-Wolf DSC method. We assume that sensors are ordered sequentially and that each sensor's message is compressed by exploiting the joint data statistics between itself and the sensors earlier in the sequence. Due to properties of DSC, a message can be decoded only if all messages transmitted by sensors earlier in the sequence are successfully decoded. The loss of one message may cause failure in decoding many other messages. Hence, the sensors' messages are not of equal importance and should be given different transmission priorities by the MAC. Based on the properties of DSC, we provide analytical tools to study the throughput, delay, and energy efficiency of slotted ALOHA random access protocols. Utilizing these tools, we compare between the performance of different transmission probability assignments and study the impact of MAC protocol design on the performance of these systems. Furthermore, an adaptive MAC protocol is also proposed to improve upon the throughput and delay of the original system.