  We consider the joint source-channel coding problem of sending a Gaussian
source on 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 symmetric Gaussian
multiple description problem. By combining this outer bound with the
achievability result based on source-channel separation, we provide approximate
characterizations of the achievable distortion region within constant
multiplicative factors. Furthermore, we show that the results can be extended
to general broadcast channels, and the performance of the source-channel
separation based approach is also within the same constant multiplicative
factors of the optimum.
