On the Rate of Channel Polarization

Abstract

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 $\beta <\frac{1}{2}$ when the block-length $N$ is large enough.

Some minor corrections

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