Log-Logarithmic Time Pruned Polar Coding

@article{Wang2021LogLogarithmicTP,
  title={Log-Logarithmic Time Pruned Polar Coding},
  author={Hsin-Po Wang and Iwan M. Duursma},
  journal={IEEE Transactions on Information Theory},
  year={2021},
  volume={67},
  pages={1509-1521}
}
A pruned variant of polar coding is proposed for binary erasure channel (BEC). Fix any BEC. For sufficiently small <inline-formula> <tex-math notation="LaTeX">$\varepsilon >{0}$ </tex-math></inline-formula>, we construct a series of capacity achieving codes with block length <inline-formula> <tex-math notation="LaTeX">$\text {N}=\varepsilon ^{-{4.9}}$ </tex-math></inline-formula>, code rate <inline-formula> <tex-math notation="LaTeX">$\text {R}=\text {Capacity}-\text {O}(\varepsilon)$ </tex… 

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This work analyzes the latency of the simplified successive cancellation (SSC) decoding scheme for polar codes proposed by Alamdar-Yazdi and Kschischang and shows that most of the latency reduction arises from the parallel decoding of subcodes of rate 0 or 1.

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