Log-logarithmic Time Pruned Polar Coding on Binary Erasure Channels

12/19/2018

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by   Hsin-Po Wang, et al.

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A pruned variant of polar coding is reinvented for all binary erasure channels. For small ε>0, we construct codes with block length ε^-5, code rate Capacity-ε, error probability ε, and encoding and decoding time complexity O(N|ε|) per block, equivalently O(|ε|) per information bit (Propositions 5 to 8). This result also follows if one applies systematic polar coding [Arıkan 10.1109/LCOMM.2011.061611.110862] with simplified successive cancelation decoding [Alamdar-Yazdi-Kschischang 10.1109/LCOMM.2011.101811.111480], and then analyzes the performance using [Guruswami-Xia arXiv:1304.4321] or [Mondelli-Hassani-Urbanke arXiv:1501.02444].