  It is shown that for any binary-input discrete memoryless channel $W$ with
symmetric capacity $I(W)$ and any rate $R <I(W)$, the probability of block
decoding error for polar coding under successive cancellation decoding
satisfies $P_e \le 2^{-N^\beta}$ for any $\beta<\frac12$ when the block-length
$N$ is large enough.
