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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.
E. Arıkan, “Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels,” submitted to IEEE Trans. Inform. Theory,
2007
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B. Hajek, June 2007 · 2007
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