Log-logarithmic Time Pruned Polar Coding
Hsin-Po Wang, Iwan Duursma

TL;DR
This paper introduces a pruned polar coding method for binary erasure channels that achieves capacity with extremely low encoding and decoding complexity, specifically log-logarithmic in key parameters, marking a significant advancement.
Contribution
It presents the first explicit family of capacity-achieving codes with log-logarithmic per-bit complexity, extending the concept to q-ary symmetric channels and achieving the fastest known complexity.
Findings
Capacity-achieving codes with block length N=ε^{-5} for small ε
Per-bit complexity is O(log|log ε|), the second lowest after repeat-accumulate codes
Generalization to q-ary channels with complexity O(log|log ε|)
Abstract
A pruned variant of polar coding is proposed for binary erasure channels. For sufficiently small , we construct a series of capacity achieving codes with block length , code rate , error probability , and encoding and decoding time complexity per information bit. The given per-bit complexity is log-logarithmic in , in , and in ; no known family of codes possesses this property. It is also the second lowest after repeat-accumulate codes and their variants. While random codes and classical polar codes are the only two families of capacity-achieving codes whose , , , and were written down as explicit functions, our construction gives the third family. Then we generalize the result to: Fix a…
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