It appears that the proposed list decoder bridges the gap between successive-cancellation and maximum-likelihood decoding of polar codes, and devise an efficient, numerically stable, implementation taking only O(L · n log n) time and O( L · n) space.Expand

An efficient closest point search algorithm, based on the Schnorr-Euchner (1995) variation of the Pohst (1981) method, is implemented and is shown to be substantially faster than other known methods.Expand

A polynomial-time soft-decision decoding algorithm for Reed-Solomon codes is developed and it is shown that the asymptotic performance can be approached as closely as desired with a list size that does not depend on the length of the code.Expand

A method for efficiently constructing polar codes is presented and analyzed, proving that for any fixed ε > 0 and all sufficiently large code lengths n, polar codes whose rate is within ε of channel capacity can be constructed in time and space that are both linear in n.Expand

It is proved that the family of binary Reed-Muller codes (of all orders) is at most a constant times their conventional redundancy, and general bounds on the stopping redundancy of linear codes are derived.Expand

This work aims to increase the throughput of polar decoding hardware by an order of magnitude relative to successive-cancellation decoders and is more than 8 times faster than the current fastest polar decoder.Expand

Polar codes are used to construct a coding scheme that achieves the secrecy capacity of general wiretap channels, as long as both C 1 and C 2 are symmetric and binary-input.Expand

We introduce a new family of error-correcting codes that have a polynomial-time encoder and a polynomial-time list-decoder, correcting a fraction of adversarial errors up to /spl tau//sub M/ = 1 -… Expand

It is shown that the problem of computing the minimum distance of a binary linear code is NP-hard, and the corresponding decision problem is NP-complete. This result constitutes a proof of the… Expand

Polar codes are used to construct a coding scheme that achieves the secrecy capacity for a wide range of wiretap channels, and the construction works for any instantiation of the wiretap channel model, as long as both C1 and C2 are symmetric and binary-input, and C1 is degraded with respect to C1.Expand