On bi-directional lossy communication of correlated Gaussian sources

We investigate fundamental limits of lossy communication in a bi-directional (two-way), half-duplex relay channel, where users wish to exchange correlated Gaussian sources and do so by sending their data according to a two-phase transmission protocol. We first establish a general distortion inner bound using the data processing inequality. Based on uncoded transmission schemes, separate source and channel coding schemes, and a lattice coding scheme, we then develop several cooperative joint source-channel coding (JSCC) approaches. Furthermore, we compare the corresponding achievable distortion performances in terms of the correlation coefficient between Gaussian sources. This comparison particularly shows that separate source and channel coding in combination with decode-and-forward relaying achieves the best distortion values of any joint source-channel coding scheme in this paper.