Related papers: Performance of polar codes for quantum and private…
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 consider the problem of determining the trade-off between the rate and the block-length of polar codes for a given block error probability when we use the successive cancellation decoder. We take the sum of the Bhattacharyya parameters…
We consider achieving the rates in the capacity region of a multi-level 3-receiver broadcast channel, in which the second receiver is degraded with respect to the first receiver, with degraded message sets. We propose a two-level chaining…
Over any discrete memoryless channel, we build codes such that: for one, their block error probabilities and code rates scale like random codes'; and for two, their encoding and decoding complexities scale like polar codes'. Quantitatively,…
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 consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
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 prove that, for the binary erasure channel (BEC), the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but do so under the best possible scaling of their block length as a~function of the gap to…
We report experimental studies on the effect of the depolarizing quantum channel on weak-pulse BB84 and SARG04 quantum cryptography. The experimental results show that, in real world conditions in which channel depolarization cannot be…
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…
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…
We consider explicit polar constructions of blocklength $n\rightarrow\infty$ for the two extreme cases of code rates $R\rightarrow1$ and $R\rightarrow0.$ For code rates $R\rightarrow1,$ we design codes with complexity order of $n\log n$ in…
We consider the fundamental protocol of dense coding of classical information assuming that noise affects both the forward and backward communication lines between Alice and Bob. Assuming that this noise is described by the same quantum…
We show that polar codes asymptotically achieve the whole capacity-equivocation region for the wiretap channel when the wiretapper's channel is degraded with respect to the main channel, and the weak secrecy notion is used. Our coding…
We consider a queue-channel model that captures the waiting time-dependent degradation of information bits as they wait to be transmitted. Such a scenario arises naturally in quantum communications, where quantum bits tend to decohere…
Transmission of information reliably and efficiently across channels is one of the fundamental goals of coding and information theory. In this respect, efficiently decodable deterministic coding schemes which achieve capacity provably have…
A pruned variant of polar coding is proposed for binary erasure channels. For sufficiently small $\varepsilon>0$, we construct a series of capacity achieving codes with block length $N=\varepsilon^{-5}$, code rate…
Being attracted by the property of classical polar code, researchers are trying to find its analogue in quantum fields, which is called quantum polar code. The first step and the key to design quantum polar code is to find out for the…
We develop a low-complexity polar coding scheme for the discrete memoryless broadcast channel with confidential messages under strong secrecy and randomness constraints. Our scheme extends previous work by using an optimal rate of uniform…
It is shown that for any binary-input discrete memoryless channel $W$ with symmetric capacity $I(W)$ and any rate $R <I(W)$, the probability of block decoding error for polar coding under successive cancellation decoding satisfies $P_e \le…