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

Hassani, S. H ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1109/ISIT.2010.5513585
  3. Publisher: 2010
  4. Abstract:
  5. 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 →∞ 1/n ln ℙ(Zn ∈ [a,b]), where Z n is the Bhattacharyya process. The quantity ℙ (Zn ∈ [a,b]) represents the fraction of sub-channels that are still un-polarized at time n
  6. Keywords:
  7. Binary erasure channel ; Escape rate ; Polar codes ; Subchannels ; Upper and lower bounds ; Information theory
  8. Source: IEEE International Symposium on Information Theory - Proceedings, 13 June 2010 through 18 June 2010, Austin, TX ; 2010 , Pages 879-883 ; 21578103 (ISSN) ; 9781424469604 (ISBN)
  9. URL: http://ieeexplore.ieee.org/document/5513585