Sending Gaussian Source on Bandwidth-Mismatched Gaussian Channel with Improved Robustness

It is well-known that optimal digital coding schemes based on the source-channel separation principle suffer from the ``threshold effect" that they are sensitive to the channel condition. If the channel condition is worse than what the code is designed for, the code will fail to decode completely; on the other hand, if the channel condition is in fact better, a digital code can not provide any performance improvement. There exist more robust joint source-channel coding schemes in the literature which can achieve optimal performance for a given channel condition, and at the same time, either being useful when the channel condition is worse, or offering performance improvement when the channel condition is better, but not both. In this paper, we propose several schemes which use hybrid analog and digital signaling to provide benefits in both cases {\em simultaneously}, while still keeping it optimal for a given target channel condition. We further show that compared to the best known optimal schemes designed for the target channel condition, which takes into account only the worse channel condition, or only the better channel condition, these new set of schemes can in fact achieve the same performances for the better and the worse channel conditions simultaneously.