  Improved bounds on the blocklength required to communicate over binary-input
channels using polar codes, below some given error probability, are derived.
For that purpose, an improved bound on the number of non-polarizing channels is
obtained. The main result is that the blocklength required to communicate
reliably scales at most as $O((I(W)-R)^{-5.77})$ where $R$ is the code rate and
$I(W)$ the symmetric capacity of the channel, $W$. The results are then
extended to polar lossy source coding at rate $R$ of a source with symmetric
distortion-rate function $D(\cdot)$. The blocklength required scales at most as
$O((D_N-D(R))^{-5.77})$ where $D_N$ is the actual distortion.
