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We consider a pilot-assisted interleave-division multiple access (IDMA) system transmitting over block-fading channels. We describe this system in terms of a factor graph and use the sum-product algorithm to develop a receiver that performs joint data detection and channel estimation. Suitable approximations to the messages passed by the sum-product algorithm yield an implementation with a complexity that scales linearly with the number of users. Simulation results demonstrate large performance gains compared to classical receivers performing separate channel estimation and data detection.