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On the scaling of polar codes: II. The behavior of un-polarized channels | IEEE Conference Publication | IEEE Xplore

On the scaling of polar codes: II. The behavior of un-polarized channels


Abstract:

We provide upper and lower bounds on the escape rate of the Bhattacharyya process corresponding to polar codes where transmission takes place over the the binary erasure ...Show More

Abstract:

We provide upper and lower bounds on the escape rate of the Bhattacharyya process corresponding to polar codes where transmission takes place over the the binary erasure channel. More precisely, we bound the exponent of the number of sub-channels whose Bhattacharyya constant falls in a fixed interval [a, b]. Mathematically this can be stated as bounding the limit limn→8 1overn ln ℙ(Zn ∈ [a, b]), where Zn is the Bhattacharyya process. The quantity ℙ(Zn ∈ [a, b]) represents the fraction of sub-channels that are still un-polarized at time n.
Date of Conference: 13-18 June 2010
Date Added to IEEE Xplore: 23 July 2010
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Conference Location: Austin, TX, USA

References

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