We consider an AWGN multiple access channel in which two correlated senders send information to a common receiver. In order to reduce the required transmission power, each one of the senders is encoded independently using a standard turbo code. The correlation model is not assumed to be known at the encoder. The decoder consists of two turbo decoders, each associated to a different sender, which exchange extrinsic information to exploit the correlation existing between the senders. The resulting performance is close to the theoretical limits obtained when separation between source and channel coding is assumed. This occurs even when the correlation between senders and the noise variance are unknown at the decoder site, since they can be estimated jointly with the decoding process with little performance degradation.