Improved Bounds on the Finite Length Scaling of Polar Codes

Abstract

Improved bounds on the blocklength required to communicate over binary-input channels using polar codes, below some given error probability, are derived. For that purpose, an improved bound on the number of non-polarizing channels is obtained. The main result is that the blocklength required to communicate reliably scales at most as $O((I(W)-R{)}^{-5.77})$ where $R$ is the code rate and $I(W)$ the symmetric capacity of the channel, $W$. The results are then extended to polar lossy source coding at rate $R$ of a source with symmetric distortion-rate function $D(\cdot )$. The blocklength required scales at most as $O((D_N-D(R){)}^{-5.77})$ where $D_N$ is the actual distortion.

submitted for publication, IEEE Transactions on Information Theory

References in corpus (4)

• Polarization for arbitrary discrete memoryless channels
• Rate-Dependent Analysis of the Asymptotic Behavior of Channel Polarization
• On the scaling of Polar codes: I. The behavior of polarized channels
• Universal Bounds on the Scaling Behavior of Polar Codes

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