Related papers: Efficient Quantum Polar Coding
Known strategies for sending bits at the capacity rate over a general channel with classical input and quantum output (a cq channel) require the decoder to implement impractically complicated collective measurements. Here, we show that a…
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…
In the Shannon lecture at the 2019 International Symposium on Information Theory (ISIT), Ar{\i}kan proposed to employ a one-to-one convolutional transform as a pre-coding step before the polar transform. The resulting codes of this…
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…
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…
One of the primary goals of information theory is to provide limits on the amount of information it is possible to send through various types of communication channels, and to understand the encoding methods that will allow one to achieve…
We study the problem of decoding classical information encoded on quantum states at the output of a quantum channel, with particular focus on increasing the communication rates towards the maximum allowed by Quantum Mechanics. After a brief…
We obtain a lower bound on the maximum number of qubits, $Q^{n, \epsilon}(\mathcal{N})$, which can be transmitted over $n$ uses of a quantum channel $\mathcal{N}$, for a given non-zero error threshold $\epsilon$. To obtain our result, we…
The polar codes introduced by Arikan in 2009 achieve the capacity of binary-input discrete memoryless channels (BIDMCs) with low complexity encoding and decoding. Identifying the unreliable synthetic channels, generated by Arikan…
Polar codes are able to achieve the capacity of memoryless channels under successive cancellation (SC) decoding. Soft Cancellation (SCAN) is a soft-output decoder based on the SC schedule, useful in iterative decoding and concatenation of…
We introduce a new quantum communication protocol for the transmission of quantum information under collective noise. Our protocol utilizes a decoherence-free subspace in such a way that an optimal asymptotic transmission rate is achieved,…
In this paper, we propose a comprehensive Polar coding solution that integrates reliability calculation, rate matching and parity-check coding. Judging a channel coding design from the industry's viewpoint, there are two primary concerns:…
The more than thirty years old issue of the information capacity of quantum communication channels was dramatically clarified during the last period, when a number of direct quantum coding theorems was discovered. To considerable extent…
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…
Good quantum error-correcting codes that fulfill practical considerations, such as simple encoding circuits and efficient decoders, are essential for functional quantum information processing systems. Quantum polar codes satisfy some of…
This paper presents polar coding schemes for the 2-user discrete memoryless broadcast channel (DM-BC) which achieve Marton's region with both common and private messages. This is the best achievable rate region known to date, and it is…
Polar codes provably achieve the capacity of a wide array of channels under successive decoding. This assumes infinite precision arithmetic. Given the successive nature of the decoding algorithm, one might worry about the sensitivity of the…
We consider lossy source compression of a binary symmetric source using polar codes and the low-complexity successive encoding algorithm. It was recently shown by Arikan that polar codes achieve the capacity of arbitrary symmetric…
We propose quantum dense coding protocol for optical images. This protocol extends the earlier proposed dense coding scheme for continuous variables [S.L.Braunstein and H.J.Kimble, Phys.Rev.A 61, 042302 (2000)] to an essentially multimode…
Polar codes are an exciting new class of error correcting codes that achieve the symmetric capacity of memoryless channels. Many decoding algorithms were developed and implemented, addressing various application requirements: from…