Related papers: Performance of polar codes for quantum and private…
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…
The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel's ultimate ability to transmit quantum information…
The min-sum approximation is widely used in the decoding of polar codes. Although it is a numerical approximation, hardly any penalties are incurred in practice. We give a theoretical justification for this. We consider the common case of a…
Quantum key distribution (QKD) has undergone significant development in recent decades, particularly with respect to free-space (air) and optical fiber channels. Here, we report the first proof-of-principle experiment for the BB84 protocol…
A method is proposed, called channel polarization, to construct code sequences that achieve the symmetric capacity $I(W)$ of any given binary-input discrete memoryless channel (B-DMC) $W$. The symmetric capacity is the highest rate…
Combined with one-time pad encryption scheme, quantum key distribution guarantees the unconditional security of communication in theory. However, error correction and privacy amplification in the post-processing phase of quantum key…
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…
Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel. This allows us to recover the no-cloning bound on the capacity of the quantum erasure channel, R is…
This paper studies the performance of block coding on an additive white Gaussian noise channel under different power limitations at the transmitter. Lower bounds are presented for the minimum error probability of codes satisfying maximal…
Polar code visibly approaches channel capacity in practice and is thereby a constituent code of the 5G standard. Compared to low-density parity-check code, however, the performance of short-length polar code has rooms for improvement that…
This article considers the performance of digital communication systems transmitting messages over finite-state erasure channels with memory. Information bits are protected from channel erasures using error-correcting codes; successful…
In this paper, we propose a low-complexity, secrecy capacity achieving polar coding scheme for the cognitive interference channel with confidential messages (CICC) under the strong secrecy criterion. Existing polar coding schemes for…
We examine the task of privacy amplification from information-theoretic and coding-theoretic points of view. In the former, we give a one-shot characterization of the optimal rate of privacy amplification against classical adversaries in…
In this paper, we derive analytic expressions for the success probability of decoding (Partial) Unit Memory codes in memoryless channels. An applications of this result is that these codes outperform individual block codes in certain…
In quantum error correction, the description of noise channel cannot be completely accurate, and fluctuation always appears in noise channel. It is found that when fluctuation of physical noise channel is considered, the average effective…
When classical or quantum information is broadcast to separate receivers, there exist codes that encrypt the encoded data such that the receivers cannot recover it when performing local operations and classical communication, but they can…
We derive the optimum second-order coding rates, known as second-order capacities, for erasure and list decoding. For erasure decoding for discrete memoryless channels, we show that second-order capacity is $\sqrt{V}\Phi^{-1}(\epsilon_t)$…
Fault-tolerant quantum computation with depolarization error often requires demanding error threshold and resource overhead. If the operations can maintain high noise bias -- dominated by dephasing error with small bit-flip error -- we can…
In 2008 Arikan proposed polar coding [arXiv:0807.3917] which we summarize as follows: (a) From the root channel $W$ synthesize recursively a series of channels $W_N^{(1)},\dotsc,W_N^{(N)}$. (b) Select sophisticatedly a subset $A$ of…
Consider a binary-input memoryless output-symmetric channel $W$. Such a channel has a capacity, call it $I(W)$, and for any $R<I(W)$ and strictly positive constant $P_{\rm e}$ we know that we can construct a coding scheme that allows…