Related papers: Multilevel Polarization for Quantum Channels
Polar coding, introduced 2008 by Arikan, is the first (very) efficiently encodable and decodable coding scheme whose information transmission rate provably achieves the Shannon bound for classical discrete memoryless channels in the…
Channel polarization is a method of constructing capacity achieving codes for symmetric binary-input discrete memoryless channels (B-DMCs) [1]. In the original paper, the construction complexity is exponential in the blocklength. In this…
Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with "usual" polar codes, the block error probability under successive cancellation decoding is…
Quantum Key Distribution (QKD) enables two parties to establish a common secret key that is information-theoretically secure by transmitting random bits that are encoded as qubits and sent over a quantum channel, followed by classical…
We construct concatenated capacity-achieving quantum codes for noisy optical quantum channels. We demonstrate that the error-probability of capacity-achieving quantum polar encoding can be reduced by the proposed low-complexity…
Polar codes are the first capacity achieving and efficiently implementable codes for classical communication. Recently they have also been generalized to communication over classical-quantum and quantum channels. In this work we present our…
We investigate the generation of EPR pairs between three observers in a general causally structured setting, where communication occurs via a noisy quantum broadcast channel. The most general quantum codes for this setup take the form of…
We provide a complete proof of the security of quantum cryptography against any eavesdropping attack including coherent measurements even in the presence of noise. Polarization-based cryptographic schemes are shown to be equivalent to…
We study the performance of common quantum stabilizer codes in the presence of asymmetric and correlated errors. Specifically, we consider the depolarizing noisy quantum memory channel and perform quantum error correction via the five and…
We introduce an error resilient distributed computing method based on an extension of the channel polarization phenomenon to distributed algorithms. The method leverages an algorithmic split operation that transforms two identical compute…
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…
We present a quantum process-tomography protocol based on a low-degree ansatz for the quantum channel, i.e. when it can be expressed as a fixed-degree polynomial in terms of Pauli operators. We demonstrate how to perform tomography of such…
Similar to existing codes, puncturing and shortening are two general ways to obtain an arbitrary code length and code rate for polar codes. When some of the coded bits are punctured or shortened, it is equivalent to a situation in which the…
This study examines multilevel channel polarization for a certain class of erasure channels that the input alphabet size is an arbitrary composite number. We derive limiting proportions of partially noiseless channels for such a class. The…
As quantum computers approach the fault tolerance threshold, diagnosing and characterizing the noise on large scale quantum devices is increasingly important. One of the most important classes of noise channels is the class of Pauli…
The construction of polar codes for channels other than BECs requires sorting of all bit channels and then selecting the best $K$ of them for a block length $N=2^n$. In this paper, two types of partial orders (PO) of polar codes are…
A major challenge in quantum communication is addressing the negative effects of noise on channel capacity, especially for completely depolarizing channels, where information transmission is inherently impossible. The concept of indefinite…
In this paper, we propose a new class of nonbinary polar codes with two-stage polarization for ultra-reliable and low-latency communications (URLLC), where the outer (symbol-level) polarization is achieved by using a 2X2 q-ary matrix [1 0;…
A method of channel polarization, proposed by Arikan, allows us to construct efficient capacity-achieving channel codes. In the original work, binary input discrete memoryless channels are considered. A special case of $q$-ary channel…
Polar encoding, described by Arikan in IEEE Transactions on Information Theory, Vol. 55, No. 7, July 2009, was a milestone for telecommunications. A Polar code distributes information among high and low-capacity channels, showing the…