We consider an AWGN multiple access channels in which two correlated senders transmit information to a common receiver. In order to reduce the required transmission power, each one of the senders is encoded independently using a concatenation of two LDGM codes. The joint decoder consists of two decoders, which exchange extrinsic information to exploit the correlation between the senders. Different interleaving schemes are investigated and analyzed. The resulting performance is very close to the theoretical limits obtained when separation between source and channel coding is assumed. Little performance degradation is observed when the correlation parameter and the noise variance are unknown at the decoder site, since they can be estimated jointly with the decoding process.