Distortion bounds for broadcasting with bandwidth expansion

We consider the problem of transmitting a Gaussian source over a Gaussian broadcast channel with p>1 channel uses per source sample. Our goal is to minimize simultaneously the squared-error distortion D₁ at receiver 1 (connected to the good channel) and D₂ at receiver 2 (connected to the bad channel). The distortion region, defined as the set of all simultaneously-achievable distortion pairs (D₁, D₂), is yet unknown. A separation-based system, consisting of a successive refinement source encoder followed by a broadcast channel encoder, is suboptimal. A variant of the problem is that of sending a Gaussian source over an AWGN channel, where the SNR is unknown except that SNR>SNR_min where SNR_min is known. In these conditions, the distortion cannot decay faster than 1/(SNR) as the SNR improves.