Hybrid digital-analog joint source-channel coding for broadcasting correlated Gaussian sources

We consider the transmission of a bivariate Gaussian source S = (S₁, S₂) across a power-limited two-user Gaussian broadcast channel. User i (i = 1, 2) observes the transmitted signal corrupted by Gaussian noise with power sigma_i ² and wants to estimate S_i. We study hybrid digital-analog (HDA) joint source-channel coding schemes and analyze these schemes to obtain achievable (squared-error) distortion regions. Two cases are considered: 1) source and channel bandwidths are equal, 2) broadcasting with bandwidth compression. We adapt HDA schemes of Wilson et al. and Prabhakaran et al. to provide various achievable distortion regions for both cases. Using numerical examples, we demonstrate that for bandwidth compression, a three-layered coding scheme consisting of analog, superposition, and Costa coding performs well compared to the other provided HDA schemes. In the case of matched bandwidth, a three-layered coding scheme with an analog layer and two layers, each consisting of a Wyner-Ziv coder followed by a Costa coder, performs best.