Log-logarithmic Time Pruned Polar Coding on Binary Erasure Channels
release_mfax67rzczdwff6c7xx5cgpjri
by
Hsin-Po Wang, Iwan Duursma
2018
Abstract
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].
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