  We consider the problem of determining the trade-off between the rate and the
block-length of polar codes for a given block error probability when we use the
successive cancellation decoder. We take the sum of the Bhattacharyya
parameters as a proxy for the block error probability, and show that there
exists a universal parameter $\mu$ such that for any binary memoryless
symmetric channel $W$ with capacity $I(W)$, reliable communication requires
rates that satisfy $R< I(W)-\alpha N^{-\frac{1}{\mu}}$, where $\alpha$ is a
positive constant and $N$ is the block-length. We provide lower bounds on
$\mu$, namely $\mu \geq 3.553$, and we conjecture that indeed $\mu=3.627$, the
parameter for the binary erasure channel.
