Related papers: Polar codes for classical-quantum channels
Polar codes, invented by Arikan in 2009, are known to achieve the capacity of any binary-input memoryless output-symmetric channel. One of the few drawbacks of the original polar code construction is that it is not universal. This means…
We analyze the practical performance of quantum polar codes, by computing rigorous bounds on block error probability and by numerically simulating them. We evaluate our bounds for quantum erasure channels with coding block lengths between…
The problem of polar coding for an arbitrary sequence of independent binary-input memoryless symmetric (BMS) channels $\left\{W_i\right\}_{i=1}^{N}$ is considered. The sequence of channels is assumed to be completely known to both the…
Ar{\i}kan's polar coding, is by now a well studied technique that allows achieving the symmetric capacity of binary input memoryless channels with low complexity encoding and decoding, provided that the polar decoding architecture is used…
Arikan's recursive code construction is designed to polarize a collection of memoryless channels into a set of good and a set of bad channels, and it can be efficiently decoded using successive cancellation. It was recently shown that the…
Polar coding is a recently proposed coding technique that can provably achieve the channel capacity. The polar code structure, which is based on the original 2x2 generator matrix, polarises the channels, i.e., a portion of the channel…
Ar{\i}kan's polar coding technique is based on the idea of synthesizing $n$ channels from the $n$ instances of the physical channel by a simple linear encoding transformation. Each synthesized channel corresponds to a particular input to…
A capacity-achieving scheme based on polar codes is proposed for reliable communication over multi-channels which can be directly applied to bit-interleaved coded modulation schemes. We start by reviewing the ground-breaking work of polar…
We present a rate-compatible polar coding scheme that achieves the capacity of any family of channels. Our solution generalizes the previous results [1], [2] that provide capacity-achieving rate-compatible polar codes for a degraded family…
Optical communication channels are ultimately quantum-mechanical in nature, and we must therefore look beyond classical information theory to determine their communication capacity as well as to find efficient encoding and decoding schemes…
Polar codes, introduced recently by Ar\i kan, are the first family of codes known to achieve capacity of symmetric channels using a low complexity successive cancellation decoder. Although these codes, combined with successive cancellation,…
We define a new phenomenon for communication over noisy quantum channels. The investigated solution is called polaractivation and based on quantum polar encoding. Polaractivation is a natural consequence of the channel polarization effect…
We provide a purely quantum version of polar codes, achieving the symmetric coherent information of any qubit-input quantum channel. Our scheme relies on a recursive channel combining and splitting construction, where a two-qubit gate…
In this thesis we analyse the type of states and ensembles which achieve the capacity for certain quantum channels carrying classical information. We first concentrate on the product-state capacity of a particular quantum channel, that is,…
A method for efficiently constructing polar codes is presented and analyzed. Although polar codes are explicitly defined, straightforward construction is intractable since the resulting polar bit-channels have an output alphabet that grows…
Progress in designing channel codes has been driven by human ingenuity and, fittingly, has been sporadic. Polar codes, developed on the foundation of Arikan's polarization kernel, represent the latest breakthrough in coding theory and have…
Arikan's polar coding method is extended to two-user multiple-access channels. It is shown that if the two users of the channel use the Arikan construction, the resulting channels will polarize to one of five possible extremals, on each of…
We construct a new secret-key assisted polar coding scheme for private classical communication over a quantum or classical wiretap channel. The security of our scheme rests on an entropic uncertainty relation, in addition to the channel…
Inspired by classical polar codes, whose coding rate can asymptotically achieve the Shannon capacity, researchers are trying to find its analogue in quantum information field, which are called quantum polar codes. However, no one has…
A fully general strong converse for channel coding states that when the rate of sending classical information exceeds the capacity of a quantum channel, the probability of correctly decoding goes to zero exponentially in the number of…