On the rate of channel polarization

A bound is given on the rate of channel polarization. As a corollary, an earlier bound on the probability of error for polar coding is improved. Specifically, it is shown that, for any binary-input discrete memoryless channel W with symmetric capacity I(W) and any rate R < I(W), the polar-coding block-error probability under successive cancellation decoding satisfies P-e(N, R) <= 2(-N beta) for any beta < 1/2 when the block-length N is large enough.