Broadcasting correlated Gaussian sources with bandwidth expansion

We study hybrid digital-analog (HDA) joint source-channel coding schemes for 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 ¿_i ² and wants to estimate the ith component of the source, S_i. We consider HDA coding schemes with bandwidth expansion and analyze the region of (squared-error) distortion pairs that are simultaneously achievable. We first adapt an HDA scheme proposed by Reznic, Feder and Zamir in for broadcasting a single common source and use it to provide an achievable distortion region for broadcasting correlated sources. We also consider a three-layered coding scheme, which we refer to by the HWZ scheme, and which consists of an analog layer and two layers each consisting of a Wyner-Ziv coder followed by a channel coder. We also examine numerical examples which indicate that the HWZ scheme performs similarly to the adapted Reznic-Feder-Zamir scheme. For comparison, we adapt the outer bound for the set of all achievable distortion pairs in broadcasting correlated Gaussian sources with matched source-channel bandwidth to the bandwidth expansion case.