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arXiv · 1307.5510

Improved Bounds on the Finite Length Scaling of Polar Codes

Dina Goldin·David Burshtein
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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.

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Dina Goldin, David Burshtein. 2013-07-21. Improved Bounds on the Finite Length Scaling of Polar Codes. https://arxiv.org/abs/1307.5510

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