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

Cited by in corpus (4)

• Polarization for arbitrary discrete memoryless channels
• Polar Codes: Characterization of Exponent, Bounds, and Constructions
• Polar Codes are Optimal for Lossy Source Coding
• A Class of Transformations that Polarize Symmetric Binary-Input Memoryless Channels