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
^−Nβ
for any β ≪ 1/2 when the block-length N is large enough.