On the Correlation Between Polarized BECs

Abstract

We consider the $2^n$ channels synthesized by the $n$-fold application of Arıkan's polar transform to a binary erasure channel (BEC). The synthetic channels are BECs themselves, and we show that, asymptotically for almost all these channels, the pairwise correlations between their erasure events are extremely small: the correlation coefficients vanish faster than any exponential in $n$. Such a fast decay of correlations allows us to conclude that the union bound on the block error probability of polar codes is very tight.

9 pages, Extended version of a paper submitted to ISIT 2013

References in corpus (1)

• On the Correlation Between Polarized BECs

Cited by in corpus (7)

• On the Correlation Between Polarized BECs
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• Modular Arithmetic Erasure Channels and Their Multilevel Channel Polarization
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