  We consider the problem of distributed joint source-channel coding of
correlated Gaussian sources over a Gaussian Multiple Access Channel (GMAC).
There may be side information at the decoder and/or at the encoders. First we
specialize a general result (for transmission of correlated sources over a MAC
with side information) to obtain sufficient conditions for reliable
transmission over a Gaussian MAC. This system does not satisfy the
source-channel separation. We study and compare three joint source-channel
coding schemes available in literature. We show that each of these schemes is
optimal under different scenarios. One of the schemes, Amplify and Forward (AF)
which simplifies the design of encoders and the decoder, is optimal at low SNR
but not at high SNR. Another scheme is asymptotically optimal at high SNR. The
third coding scheme is optimal for orthogonal Gaussian channels. We also show
that AF is close to the optimal scheme for orthogonal channels even at high
SNR.
