Universal bounds on the scaling behavior of polar codes

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.

Presented at:
Internationel Symposium on Information Theory ISIT2012, Boston, Massachusetts, USA, 1-6 July, 2012

 Record created 2012-09-25, last modified 2018-09-13

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