On Optimal Distributed Joint Source-Channel Coding for Correlated Gaussian Sources over Gaussian Channels

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.