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We study the properties of error correcting codes for noise models in the presence of asymmetries and/or correlations by means of the entanglement fidelity and the code entropy. First, we consider a dephasing Markovian memory channel and…
Despite the extreme error-correction performance, the amount of computation of sequential decoding of the polarization-adjusted convolutional (PAC) codes is random. In sequential decoding of convolutional codes, the computational cutoff…
In this paper, we introduce stitched polar codes, a novel generalization of Ar{\i}kan's regular polar codes. Our core methodology reconfigures the fundamental polarization process by stitching additional structures to enhance the…
Knill, Laflamme, and Milburn (KLM) proved that it is possible to build a scalable universal quantum computer using only linear-optics elements and conditional dynamics [Nature (London) {\bf 409}, 46 (2001)\cite{Knill}]. However, the…
Polarization-adjusted convolutional (PAC) codes were recently proposed and arouse the interest of the channel coding community because they were shown to approach theoretical bounds for the (128,64) code size. In this letter, we propose…
Due to their fast decoding algorithms, quantum generalizations of low-density parity check, or LDPC, codes have been investigated as a solution to the problem of decoherence in fragile quantum states. However, the additional twisted inner…
Inspired by classical polar codes, whose coding rate can asymptotically achieve the Shannon capacity, researchers are trying to find its analogue in quantum information field, which are called quantum polar codes. However, no one has…
The channel polarization behavior of polar codes under noise with memory is investigated. By introducing a genie-aided channel model, we first show that the polarized subchannels still converge to extremal channels under the standard polar…
A framework is proposed that allows for a joint description and optimization of both binary polar coding and the multilevel coding (MLC) approach for $2^m$-ary digital pulse-amplitude modulation (PAM). The conceptual equivalence of polar…
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…
In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some…
A polar coding scheme for fading channels is proposed in this paper. More specifically, the focus is Gaussian fading channel with a BPSK modulation technique, where the equivalent channel could be modeled as a binary symmetric channel with…
Qutrits, the triple level quantum systems in various forms, have been proposed for quantum information processing recently. By the methods presented in this paper a bi-photonic qutrit, which is encoded with the polarizations of two photons…
In crystalline solids, the electronic polarization follows the \emph{generalized Neumann's principle}, under which all crystallographic point groups can, in principle, support ferroelectric polarization. However, in high-symmetry…
The paper presents bounds on the achievable rates and the decoding complexity of low-density parity-check (LDPC) codes. It is assumed that the communication of these codes takes place over statistically independent parallel channels where…
Progress in designing channel codes has been driven by human ingenuity and, fittingly, has been sporadic. Polar codes, developed on the foundation of Arikan's polarization kernel, represent the latest breakthrough in coding theory and have…
Density Functional Theory (DFT) calculations were used to evaluate polarity of group III nitrides, such as aluminum nitride (AlN), gallium nitride (GaN) and indium nitride (InN) providing physically sound quantitative measure of polarity of…
The information-theoretic unconditional security offered by quantum key distribution has spurred the development of larger quantum communication networks. However, as these networks grow so does the strong need to reduce complexity and…
Research on polar codes has been constantly gaining attention over the last decade, by academia and industry alike, thanks to their capacity-achieving error-correction performance and low-complexity decoding algorithms. Recently, they have…
Binary linear block codes (BLBCs) are essential to modern communication, but their diverse structures often require tailor-made decoders, increasing complexity. This work introduces enhanced polar decoding ($\mathsf{PD}^+$), a universal…