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We investigate the problem of transmiting independent sources over the Gaussian Multiple Access Channel (MAC) using a CDMA-like access scheme that allows users to transmit at different rates. Rather than using standard digital communications systems, we focus on analog joint source-channel coding techniques to encode each user’s source. We analyze the performance of the proposed scheme and demonstrate its optimality. Simulation results with practical analog joint source-channel codes optimized for point-to-point communications show that the resulting performance is very close to the theoretical limits.