Approximate characterizations for the Gaussian broadcasting distortion region

We consider the joint source-channel coding problem of sending a Gaussian source over a K-user Gaussian broadcast channel with bandwidth mismatch. A new outer bound to the achievable distortion region is derived using the technique of introducing more than one additional auxiliary random variable, which was previously used to derive sum-rate lower bound for the Gaussian multiple description problem. By combining this outer bound with the source-channel-separation-based achievable region, we provide approximate characterizations of the achievable distortion region within constant multiplicative factors.