The beginning of 21st century provided us with many answers about how to reach the channel capacity. Polarization and spatial coupling are two techniques for achieving the capacity of binary memoryless symmetric channels under low-complexity decoding algor ...
The recently introduced polar codes constitute a breakthrough in coding theory due to their capacity-achieving property. This goes hand in hand with a quasilinear construction, encoding, and successive cancellation list decoding procedures based on the Plo ...
Polar coding solutions demonstrate excellent performance under the list decoding that is challenging to implement in hardware due to the path sorting operations. As a potential solution to this problem, permutation decoding recently became a hot research t ...
Cryptographic key exchange protocols traditionally rely on computational conjectures such as the hardness of prime factorization(1) to provide security against eavesdropping attacks. Remarkably, quantum key distribution protocols such as the Bennett-Brassa ...
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 representatives of such codes and can be considered as two extreme cases. Reed-Mul ...
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 number of outer codes, and on-demand construction of codewords of these code ...
In this paper, we consider low-complexity decoding of second-order Reed-Muller codes. A class of polynomial-time algorithms, based on the projections onto first-order codes, is studied. An old representative of this class, originally developed for binary s ...
In this paper, we consider the problem of decoding Reed-Muller (RM) codes in binary erasure channel. We propose a novel algorithm, which exploits several techniques, such as list recursive (successive cancellation) decoding based on Plotkin decomposition, ...
