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

We consider the problem of sending a bivariate Gaussian source S = (S-1, S-2) 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(2)(i) 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. [1] and Prabhakaran et al. [2], 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. [3] from the matched source-channel bandwidth case to the bandwidth mismatch case.