  This paper studies the minimum achievable source coding rate as a function of
blocklength $n$ and probability $\epsilon$ that the distortion exceeds a given
level $d$. Tight general achievability and converse bounds are derived that
hold at arbitrary fixed blocklength. For stationary memoryless sources with
separable distortion, the minimum rate achievable is shown to be closely
approximated by $R(d) + \sqrt{\frac{V(d)}{n}} Q^{-1}(\epsilon)$, where $R(d)$
is the rate-distortion function, $V(d)$ is the rate dispersion, a
characteristic of the source which measures its stochastic variability, and
$Q^{-1}(\epsilon)$ is the inverse of the standard Gaussian complementary cdf.
