相关论文: Source and Channel Polarization over Finite Fields…
Let $D_n(x;a)$ and $E_n(x;a)\in\mathbb F_q[x]$ be Dickson polynomials of first and second kind respectively, where $\mathbb F_q$ is a finite field with $q$ elements. In this article we show explicitly the irreducible factors these…
In this work, we develop a perturbation theory to analyze resonant states near a bound state in the continuum (BIC) in photonic crystal slabs. The theory allows us to rigorously determine the asymptotic behavior of $Q$-factor and the…
It is shown that polar coding schemes achieve the known achievable rate regions for several multi-terminal communications problems including lossy distributed source coding, multiple access channels and multiple descriptions coding. The…
Let $\mathbb{F}_q$ be the finite field with $q$ elements, where $q$ is a prime power and $n$ be a positive integer. In this paper, we explore the factorization of $f(x^{n})$ over $\mathbb{F}_q$, where $f(x)$ is an irreducible polynomial…
We develop a nonperturbative approach to the bulk polarization of crystalline electric insulators in $d\geq1$ dimensions. Formally, we define polarization via the response to background fluxes of both charge and lattice translation…
We report on IXPE, NICER and XMM-Newton observations of the magnetar 1E 2259+586. We find that the source is significantly polarized at about or above 20% for all phases except for the secondary peak where it is more weakly polarized. The…
In this paper we investigate the polarization property of the radiation amplified by astronomical masers in the presence of a strong magnetic field. Our model explicitly takes into account the broadband nature of the radiation field and the…
Following the approach by R. K\"otter and F. R. Kschischang, we study network codes as families of k-dimensional linear subspaces of a vector space F_q^n, q being a prime power and F_q the finite field with q elements. In particular,…
We generalize three results of M. Aguiar, which are valid for Loday's dendriform algebras, to arbitrary dendriform algebras, i.e., dendriform algebras associated to algebras satisfying any given set of relations. We define these dendriform…
The global polarization of $\Lambda/{\bar \Lambda}$ and the splitting of ${\bar \Lambda}-\Lambda$ polarization induced by rotation and magnetic field has been investigated in a dynamical quark model by taking into account the axial vector…
Multi-frequency radio polarimetry of the diffuse Galactic synchrotron background gives new viewpoints on the Galactic magnetic field. Rotation measure maps reveal magnetic structures on arcminute to degree scales, such as a ring in…
We first find the combinatorial degree of any map $f:V\to F$ where $F$ is a finite field and $V$ is a finite-dimensional vector space over $F$. We then simplify and generalize a certain construction due to Chein and Goodaire that was used…
A multilevel coded modulation scheme is studied that uses solely binary polar codes and Honda-Yamamoto probabilistic shaping. The scheme is shown to achieve the capacity of discrete memoryless channels with input alphabets of cardinality a…
The photon-induced process of electron-positron pair creation in a strong homogeneous magnetic field, provided that the polarization of particles is arbitrary, has been considered. The polarization of a photon is described in terms of the…
A decoding algorithm for polar codes with binary 16$\times$16 kernels with polarization rate 0.51828 and scaling exponents 3.346 and 3.450 is presented. The proposed approach exploits the relationship of the considered kernels and the…
We show that it is possible to generate continuous-wave fields and pulses of polarization squeezed light by sending classical, linearly polarized laser light twice through an atomic sample which causes an optical Faraday rotation of the…
The role of polarization in the topology of quantum emitter chains is investigated theoretically, whereby "polarization" refers to the transition dipole moments of the emitters. We show that, if the chain is zigzag-shaped, different…
We consider the problem of polar coding for transmission over $m$-user multiple access channels. In the proposed scheme, all users encode their messages using a polar encoder, while a joint successive cancellation decoder is deployed at the…
For paraxial light beams and electromagnetic fields, the Stokes vector and polarization matrix provide equivalent scalar measures of optical chirality, widely used in linear optics. However, growing interest in non-paraxial fields, with…
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…