Log-logarithmic Time Pruned Polar Coding

Hsin-Po Wang, Iwan M. Duursma
2020 IEEE Transactions on Information Theory  
A pruned variant of polar coding is proposed for binary erasure channel (BEC). Fix any BEC. For sufficiently small ε > 0, we construct a series of capacity achieving codes with block length N = ε −4.9 , code rate R = Capacity − O(ε), block error probability P = ε, and encoding and decoding time complexity bC = O(log|log ε|) per information bit. The given per-bit complexity bC is log-logarithmic in N, in Capacity − R, and in P. Beyond BEC, there is a generalization: Fix a prime q and fix a
more » ... ric, q-ary-input, discrete-output memoryless channel. For sufficiently small ε > 0, we construct a series of error correction codes with block length N = ε −constant , code rate R = Capacity − O(ε), block error probability P = ε, and encoding and decoding time complexity bC = O(log|log ε|) per information bit. Over general channels, this family of codes has the lowest per-bit time complexity among all capacity-achieving codes known to date.
doi:10.1109/tit.2020.3041523 fatcat:ii3k5ibdabd7vjszqngut5lvm4