Infoscience

Conference paper

On the scaling of Polar Codes: II. The behavior of un-polarized channels

Hassani, S. Hamed; Alishahi, Kasra; Urbanke, Rudiger
  • Presented at: 2010 IEEE International Symposium on Information Theory, Austin, TX, Jul 13, 2010
  • Published in: 2010 Ieee International Symposium On Information Theory (ISBN: 978-1-4244-6960-4), p. 879-883
  • Series: IEEE International Symposium on Information Theory
  • Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa, 2010

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 lim(n ->infinity) 1/n ln P(Zn is an element of [a, b]), where Z(n) is the Bhattacharyya process. The quantity P( Z(n) is an element of[a, b]) represents the fraction of sub-channels that are still un-polarized at time n.

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Record created on 2012-01-12, modified on 2012-05-22

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