Related papers: A Simple Proof of Fast Polarization
The paper investigates the emerging field of low-complexity non-binary polar code (NB-PC) decoders. It shows that customizing each kernel of an NB-PC decoder through offline analysis can significantly reduce the overall decoding complexity.…
The Stokes parameters have been found in the framework of quantum electrodynamics for the description of polarization of radiation emitted by relativistic positrons channeled between (110) planes in Si crystal. The degree of polarization,…
Wyner's work on wiretap channels and the recent works on information theoretic security are based on random codes. Achieving information theoretical security with practical coding schemes is of definite interest. In this note, the attempt…
This study examines multilevel channel polarization for a certain class of erasure channels that the input alphabet size is an arbitrary composite number. We derive limiting proportions of partially noiseless channels for such a class. The…
We analyze polarization-adjusted convolutional codes using the algebraic representation of polar and Reed-Muller codes. We define a large class of codes, called generalized polynomial polar codes which include PAC codes and Reverse PAC…
Optical neural networks are emerging as a powerful and versatile tool for processing optical signals directly in the optical domain with superior speed, integrability, and functionality. Their application to optical polarization enables…
A method of ultrafast switching of ferroelectric polarization is suggested. The method is based on the interaction of a ferroelectric sample with the feedback field of a resonator in which the sample is inserted. The polarization reversal…
In this paper, we investigate the fundamentals of puncturing and shortening for polar codes, based on binary domination which plays a key role in polar code construction. We first prove that the orders of encoder input bits to be made…
We prove an explicit formula for the Bergman kernel of polarized abelian varieties. As applications, we show that if two positive line bundles represent the same first Chern class and have identical Bergman kernel functions for some tensor…
We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…
(Electric) polarization tensors describe part of the leading order term of asymptotic voltage perturbations caused by low volume fraction inhomogeneities of the electrical properties of a medium. They depend on the geometry of the support…
The investigation of polarized light of protoplanetary disks is key for constraining the dust properties, disk morphology and embedded magnetic fields. However, different polarization mechanisms and the diversity of dust grain shapes and…
The construction of polar codes with code length $n=2^m$ involves $m$ layers of polar transforms. In this paper, we observe that after each layer of polar transforms, one can swap certain pairs of adjacent bits to accelerate the…
Polarized targets evolved into indispensable tools in particle and nuclear physics. However, the polarized solid target is degraded by high-intense beam irradiation, known as radiation damage due to target heating and radical generation. We…
We report a fast, room temperature detection scheme for the polarization ellipticity of laser radiation, with a bandwidth that stretches from the infrared to the terahertz range. The device consists of two elements, one in front of the…
A consistent factorization theorem is presented in the framework of effective field theories. Conventional factorization suffers from infrared divergences in the soft and collinear parts. We present a factorization theorem in which the…
We present a fast method for estimating the cosmic microwave background polarization power spectra using unbiased estimates of heuristically-weighted correlation functions. This extends the O(N_pix^(3/2)) method of Szapudi et al. (2001) to…
In this work, we address the low-complexity construction of shortened and punctured polar codes from a unified view. While several independent puncturing and shortening designs were attempted in the literature, our goal is a unique,…
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…
The asymptotic performance of a polar code under successive cancellation decoding is determined by the exponent of its polarizing matrix. We first prove that the partial distances of a polarizing matrix constructed from the Kronecker…