The dispersion of joint source-channel coding

In this work we investigate the behavior of the distortion threshold that can be guaranteed in joint source- channel coding, to within a prescribed excess-distortion probability. We show that the gap between this threshold and the optimal average distortion is governed by a constant that we call the joint source-channel dispersion. This constant can be easily computed, since it is the sum of the source and channel dispersions, previously derived. The resulting performance is shown to be better than that of any separation-based scheme. For the proof, we use unequal error protection channel coding, thus we also evaluate the dispersion of that setting.