Related papers: Polar Codes for Quantum Reading
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…
Here we concerned with quantum key distribution - a way to establish common cryptographic key between several parties. The work proposes a combination between quantum key distribution and systematic polar coding (an error correction…
We prove polarization theorems for arbitrary classical-quantum (cq) channels. The input alphabet is endowed with an arbitrary Abelian group operation and an Ar{\i}kan-style transformation is applied using this operation. It is shown that as…
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 a family of capacity-achieving codes that have explicit and low-complexity construction, encoding, and decoding algorithms. Decoding of polar codes is based on the successive-cancellation decoder, which decodes in a bit-…
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…
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 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 present a method of constructing rate-compatible polar codes that are capacity-achieving with low-complexity sequential decoders. The proposed code construction allows for incremental retransmissions at different rates in order to adapt…
Most existing works of polar codes focus on the analysis of block error probability. However, in many scenarios, bit error probability is also important for evaluating the performance of channel codes. In this paper, we establish a new…
This paper investigates universal polar coding schemes. In particular, a notion of ordering (called convolutional path) is introduced between probability distributions to determine when a polar compression (or communication) scheme designed…
We prove that, for all binary-input symmetric memoryless channels, polar codes enable reliable communication at rates within $\epsilon > 0$ of the Shannon capacity with a block length, construction complexity, and decoding complexity all…
Polar codes are constructed for m-user multiple access channels (MAC) whose input alphabet size is a prime number. The block error probability under successive cancelation decoding decays exponentially with the square root of the block…
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,…
Information-theoretic work for wiretap channels is mostly based on random coding schemes. Designing practical coding schemes to achieve information-theoretic security is an important problem. By applying the two recently developed…
A pruned variant of polar coding is reinvented for all binary erasure channels. For small $\varepsilon>0$, we construct codes with block length $\varepsilon^{-5}$, code rate $\text{Capacity}-\varepsilon$, error probability $\varepsilon$,…
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…
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,…
The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Ar{\i}kan proved that…
A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name of quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the…