On the Performance of Hybrid Digital-Analog Coding for Broadcasting Correlated Gaussian Sources

We consider the problem of sending 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 σ_i² and desires to estimate S_i. We study hybrid digital-analog (HDA) joint source-channel coding schemes and analyze the region of (squared-error) distortion pairs that are simultaneously achievable. Two cases are considered: 1) broadcasting with bandwidth compression, and 2) broadcasting with bandwidth expansion. We modify and adapt HDA schemes of Wilson et al. and Prabhakaran et al. , originally proposed for broadcasting a single common Gaussian source, in order to provide achievable distortion regions for broadcasting correlated Gaussian sources. For comparison, we also extend the outer bound of Soundararajan et al. from the matched source-channel bandwidth case to the bandwidth mismatch case.