Universal bounds on the scaling behavior of polar codes

Goli, A ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1109/ISIT.2012.6283641
  3. Publisher: IEEE , 2012
  4. Abstract:
  5. We consider the problem of determining the tradeoff between the rate and the block-length of polar codes for a given block error probability when we use the successive cancellation decoder. We take the sum of the Bhattacharyya parameters as a proxy for the block error probability, and show that there exists a universal parameter μ such that for any binary memoryless symmetric channel W with capacity I(W), reliable communication requires rates that satisfy R < I(W) - αN -1/μ, where α is a positive constant and N is the block-length. We provide lower bounds on μ, namely μ ≥ 3.553, and we conjecture that indeed μ = 3.627, the parameter for the binary erasure channel
  6. Keywords:
  7. Binary erasure channel ; Block error probability ; Lower bounds ; Memoryless ; Polar codes ; Positive constant ; Reliable communication ; Scaling behavior ; Successive cancellation ; Symmetric channels ; Universal parameters ; Communication channels (information theory)
  8. Source: IEEE International Symposium on Information Theory - Proceedings ; 2012 , Pages 1957-1961 ; 9781467325790 (ISBN)
  9. URL: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6283641