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On the efficiency of polar-like decoding for symmetric codes
Kirill Ivanov, Rüdiger Urbanke
The recently introduced polar codes constitute a breakthrough in coding theory due to their capacityachieving property. This goes hand in hand with a quasilinear construction, enco…
Capacity-achieving codes: a review on double transitivity
Kirill Ivanov, Rüdiger L. Urbanke
Recently it was proved that if a linear code is invariant under the action of a doubly transitive permutation group, it achieves the capacity of erasure channel. Therefore, it is o…
Partially symmetric monomial codes
Kirill Ivanov, Rüdiger Urbanke
A framework of monomial codes is considered, which includes linear codes generated by the evaluation of certain monomials. Polar and Reed-Muller codes are the two best-known repres…
Fast Block Sequential Decoding of Polar Codes
Grigorii Trofimiuk, Nikolay Iakuba, Stanislav Rets +2
A reduced complexity sequential decoding algorithm for polar (sub)codes is described. The proposed approach relies on a decomposition of the polar (sub)code being decoded into a nu…