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 On the Correlation Between Polarized BECs


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We consider the $2^n$ channels synthesized by the $n$-fold application of Ar\i{}kans 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.



Autor: Mani Bastani Parizi; Emre Telatar

Fuente: https://archive.org/







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