Related papers: A note on the polar decomposition in metric spaces
We consider the joint design of polar coding and higher-order modulation schemes for ever increased spectral efficiency. The close connection between the polar code construction and the multi-level coding approach is described in detail.…
We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution,…
In this note we show that an unbounded regular operator $t$ on Hilbert $C^*$-modules over an arbitrary $C^*$ algebra $ \mathcal{A}$ has polar decomposition if and only if the closures of the ranges of $t$ and $|t|$ are orthogonally…
We prove that a conformal mapping defined on the unit disk belongs to a weighted Bergman space if and only if certain integrals involving the harmonic measure converge. With the aid of this theorem, we give a geometric characterization of…
In this paper, we investigate a coupled polar code architecture that supports both local and global decoding. This local-global construction is motivated by practical applications in data storage and transmission where reduced-latency…
We present a novel analysis method for measurements of polarization transferred in $A(\vec{e},e'\vec{N})$ experiments, which can be applied to other kinds of polarization measurements as well. In this method the polarization transfer…
An example of a coherent measurement for the direct evaluation of the degree of polarization of a single-mode optical beam is presented. It is applied to the case of great practical importance where depolarization is caused by polarization…
We provide a generalization of the normal mode decomposition for non-symmetric or locality constrained situations. This allows for instance to locally decouple a bipartitioned collection of arbitrarily correlated oscillators up to…
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…
Special class of Finsler metrics that can be decomposed to the product of two Riemannian metrics is considered. Based on such decomposition a new kind of Finsler gravity is suggested. Physical applications of Finsler decomposed metric are…
The main purpose of this paper is to present the generalization of the inequalities between the modulus of the polar derivative and the polynomial itself, depending on consideration of the zeros inside and outside of a closed disk and the…
We present all real quantum mechanical potentials in a two-dimensional Euclidean space that have the following properties: 1. They allow separation of variables of the Schr\"odinger equation in polar coordinates, 2. They allow an…
In-line polarimeters perform non-destructive polarization measurements of optical signals, and play a critical role in monitoring and controlling the polarization environment in for example optical networks. While current in-line…
In Euclidean space condensers with variable potential levels and the presence of a free part at the boundary are studied. The asymptotic formula of the modulus of such condenser is obtained when the plates are pulled into points. The…
Polar commutative n-complex numbers of the form u=x_0+h_1x_1+h_2x_2+...+h_{n-1}x_{n-1} are introduced in n dimensions, the variables x_0,...,x_{n-1} being real numbers. The polar n-complex number can be represented, in an even number of…
This work is on fast encoding and decoding of polar codes. We propose and detail 8-bit and 16-bit parallel decoders that can be used to reduce the decoding latency of the successive-cancellation decoder. These decoders are universal and can…
A couple of orthogonal coordinates for dipole geometry are proposed for numerical simulations of plasma geophysics in the Earth's dipole magnetic field. These coordinates have proper metric profiles along field lines in contrast to the…
We obtain several analogs of real polar decomposition for even dimensional matrices. In particular, we decompose a non-degenerate matrix as a product of a Hamiltonian and an anti-symplectic matrix and under additional requirements we…
We study here the error of numerical integration on metric measure spaces adapted to a decomposition of the space into disjoint subsets. We consider both the error for a single given function, and the worst case error for all functions in a…
Polarization is well known for its ability to decompose diffuse and specular reflections. However, the existing decomposition methods only focus on direct reflection and overlook multiple reflections, especially specular inter-reflection.…