We investigate the behavior of lossy source coding and joint source-channel
coding (JSCC) with finite block-length. In both cases we fix the probability
that the distortion exceeds a prescribed threshold. In source coding, the excess
coding rate is inversely proportional (to the first order) to the square root of
the block length. We coin the proportion constant source dispersion. This result
is the dual of a corresponding channel coding result, where the dispersion above
corresponds to the channel dispersion. In the JSCC setting, we show a similar
result for the distortion threshold that can be guaranteed to within the
excess-distortion probability. The gap between this threshold and the optimal
average distortion is governed by a constant that we coin the JSCC dispersion.