# W. Chen - Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany

## Contact Details

NameW. Chen |
||

AffiliationInstitute of Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany |
||

CityPotsdam |
||

CountryGermany |
||

## Pubs By Year |
||

## External Links |
||

## Pub CategoriesMathematics - Mathematical Physics (5) Mathematical Physics (5) Computer Science - Computer Vision and Pattern Recognition (5) Quantum Physics (3) Physics - Mesoscopic Systems and Quantum Hall Effect (3) Mathematics - Probability (3) Physics - Atomic Physics (3) Physics - Strongly Correlated Electrons (3) Mathematics - Analysis of PDEs (3) Solar and Stellar Astrophysics (2) Statistics - Machine Learning (2) Computer Science - Information Theory (2) Physics - Optics (2) Mathematics - Information Theory (2) Computer Science - Networking and Internet Architecture (2) Physics - Materials Science (2) High Energy Physics - Phenomenology (2) Nuclear Theory (2) Astrophysics of Galaxies (2) Physics - Soft Condensed Matter (1) High Energy Astrophysical Phenomena (1) Physics - Accelerator Physics (1) Physics - Biological Physics (1) Earth and Planetary Astrophysics (1) Computer Science - Computational Complexity (1) Computer Science - Data Structures and Algorithms (1) Physics - Physics and Society (1) Computer Science - Learning (1) Physics - Superconductivity (1) Quantitative Biology - Quantitative Methods (1) Computer Science - Artificial Intelligence (1) Physics - Statistical Mechanics (1) Mathematics - Dynamical Systems (1) Mathematics - Metric Geometry (1) Mathematics - Combinatorics (1) High Energy Physics - Lattice (1) High Energy Physics - Experiment (1) Physics - Plasma Physics (1) Mathematics - Number Theory (1) Computer Science - Computation and Language (1) |

## Publications Authored By W. Chen

**Authors:**Tao Hong, Masashige Matsumoto, Yiming Qiu, Wangchun Chen, Thomas R. Gentile, Shannon Watson, Firas F. Awwadi, Mark M. Turnbull, Sachith E. Dissanayake, Harish Agrawal, Rasmus Toft-Petersen, Bastian Klemke, Kris Coester, Kai P. Schmidt, David A. Tennant

**Category:**Physics - Strongly Correlated Electrons

Spontaneous symmetry-breaking quantum phase transitions play an essential role in condensed matter physics. The collective excitations in the broken-symmetry phase near the quantum critical point can be characterized by fluctuations of phase and amplitude of the order parameter. The phase oscillations correspond to the massless Nambu$-$Goldstone modes whereas the massive amplitude mode, analogous to the Higgs boson in particle physics, is prone to decay into a pair of low-energy Nambu$-$Goldstone modes in low dimensions. Read More

Apollonian gaskets are formed by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We experimentally study the pair correlation, electrostatic energy, and nearest neighbor spacing of centers of circles from Apollonian gaskets. Even though the centers of these circles are not uniformly distributed in any `ambient' space, after proper normalization, all these statistics seem to exhibit some interesting limiting behaviors. Read More

In this short article, we state a Hopf type lemma for fractional equations and the outline of its proof. We believe that it will become a powerful tool in applying the method of moving planes on fractional equations to obtain qualitative properties of solutions. Read More

For a general dyadic grid, we give a Calder\'{o}n-Zygmund type decomposition, which is the principle fact about the multilinear maximal function $\mathfrak{M}$ on the upper half-spaces. Using the decomposition, we study the boundedness of $\mathfrak{M}.$ We obtain a natural extension to the multilinear setting of Muckenhoupt's weak-type characterization. Read More

In this paper, we consider nonlinear equations involving the fractional p-Laplacian $$ (-\lap)_p^s u(x)) \equiv C_{n,s,p} PV \int_{\mathbb{R}^n} \frac{|u(x)-u(y)|^{p-2}[u(x)-u(y)]}{|x-z|^{n+ps}} dz= f(x,u).$$ We prove a {\em maximum principle for anti-symmetric functions} and obtain other key ingredients for carrying on the method of moving planes, such as {\em a key boundary estimate lemma}. Then we establish radial symmetry and monotonicity for positive solutions to semilinear equations involving the fractional p-Laplacian in a unit ball and in the whole space. Read More

We demonstrate direct laser cooling of a gas of rubidium 87 atoms to quantum degeneracy. The method does not involve evaporative cooling, is fast, and induces little atom loss. The atoms are trapped in a two-dimensional optical lattice that enables cycles of cloud compression to increase the density, followed by degenerate Raman sideband cooling to decrease the temperature. Read More

This study investigates the ultraslow diffusion by a spatial structural derivative, in which the exponential function exp(x)is selected as the structural function to construct the local structural derivative diffusion equation model. The analytical solution of the diffusion equation is a form of Biexponential distribution. Its corresponding mean squared displacement is numerically calculated, and increases more slowly than the logarithmic function of time. Read More

This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, L\'evy and stretched Gaussian noises, to exact value of the selected functions including linear equations, polynomial and exponential equations, and the maximum absolute and the mean square errors are calculated for the different cases. L\'evy and stretched Gaussian distributions have many applications in fractional and fractal calculus. Read More

Despite the recent success of deep-learning based semantic segmentation, deploying a pre-trained road scene segmenter to a city whose images are not presented in the training set would not achieve satisfactory performance due to dataset biases. Instead of collecting a large number of annotated images of each city of interest to train or refine the segmenter, we propose an unsupervised learning approach to adapt road scene segmenters across different cities. By utilizing Google Street View and its time-machine feature, we can collect unannotated images for each road scene at different times, so that the associated static-object priors can be extracted accordingly. Read More

**Authors:**Derek Ward-Thompson, Kate Pattle, Pierre Bastien, Ray S. Furuya, Woojin Kwon, Shih-Ping Lai, Keping Qiu, David Berry, Minho Choi, Simon Coudé, James Di Francesco, Thiem Hoang, Erica Franzmann, Per Friberg, Sarah F. Graves, Jane S. Greaves, Martin Houde, Doug Johnstone, Jason M. Kirk, Patrick M. Koch, Jungmi Kwon, Chang Won Lee, Di Li, Brenda C. Matthews, Joseph C. Mottram, Harriet Parsons, Andy Pon, Ramprasad Rao, Mark Rawlings, Hiroko Shinnaga, Sarah Sadavoy, Sven van Loo, Yusuke Aso, Do-Young Byun, Eswariah Chakali, Huei-Ru Chen, Mike C. -Y. Chen, Wen Ping Chen, Tao-Chung Ching, Jungyeon Cho, Antonio Chrysostomou, Eun Jung Chung, Yasuo Doi, Emily Drabek-Maunder, Stewart P. S. Eyres, Jason Fiege, Rachel K. Friesen, Gary Fuller, Tim Gledhill, Matt J. Griffin, Qilao Gu, Tetsuo Hasegawa, Jennifer Hatchell, Saeko S. Hayashi, Wayne Holland, Tsuyoshi Inoue, Shu-ichiro Inutsuka, Kazunari Iwasaki, Il-Gyo Jeong, Ji-hyun Kang, Miju Kang, Sung-ju Kang, Koji S. Kawabata, Francisca Kemper, Gwanjeong Kim, Jongsoo Kim, Kee-Tae Kim, Kyoung Hee Kim, Mi-Ryang Kim, Shinyoung Kim, Kevin M. Lacaille, Jeong-Eun Lee, Sang-Sung Lee, Dalei Li, Hua-bai Li, Hong-Li Liu, Junhao Liu, Sheng-Yuan Liu, Tie Liu, A-Ran Lyo, Steve Mairs, Masafumi Matsumura, Gerald H. Moriarty-Schieven, Fumitaka Nakamura, Hiroyuki Nakanishi, Nagayoshi Ohashi, Takashi Onaka, Nicolas Peretto, Tae-Soo Pyo, Lei Qian, Brendan Retter, John Richer, Andrew Rigby, Jean-François Robitaille, Giorgio Savini, Anna M. M. Scaife, Archana Soam, Motohide Tamura, Ya-Wen Tang, Kohji Tomisaka, Hongchi Wang, Jia-Wei Wang, Anthony P. Whitworth, Hsi-Wei Yen, Hyunju Yoo, Jinghua Yuan, Chuan-Peng Zhang, Guoyin Zhang, Jianjun Zhou, Lei Zhu, Philippe André, C. Darren Dowell, Sam Falle, Yusuke Tsukamoto

**Category:**Astrophysics of Galaxies

We present the first results from the B-fields In STar-forming Region Observations (BISTRO) survey, using the Sub-millimetre Common-User Bolometer Array 2 (SCUBA-2) camera, with its associated polarimeter (POL-2), on the James Clerk Maxwell Telescope (JCMT) in Hawaii. We discuss the survey's aims and objectives. We describe the rationale behind the survey, and the questions which the survey will aim to answer. Read More

A novel crystal configuration of sandwiched S-Mo-Se structure (Janus SMoSe) at the monolayer limit has been synthesized and carefully characterized in this work. By controlled sulfurization of monolayer MoSe2 the top layer of selenium atoms are substituted by sulfur atoms while the bottom selenium layer remains intact. The peculiar structure of this new material is systematically investigated by Raman, photoluminescence and X-ray photoelectron spectroscopy and confirmed by transmission-electron microscopy and time-of-flight secondary ion mass spectrometry. Read More

In this work, a second order smoothed particle hydrodynamics is derived for the study of relativistic heavy ion collisions. The hydrodynamical equation of motion is formulated in terms of the variational principle. In order to describe the fluid of high energy density but of low baryon density, the entropy is taken as the base quantity for the interpolation. Read More

We develop an empirical behavioural order-driven (EBOD) model, which consists of an order placement process and an order cancellation process. Price limit rules are introduced in the definition of relative price. The order placement process is determined by several empirical regularities: the long memory in order directions, the long memory in relative prices, the asymmetric distribution of relative prices, and the nonlinear dependence of the average order size and its standard deviation on the relative price. Read More

To increase the scalability of Software Defined Networks (SDNs), flow aggregation schemes have been proposed to merge multiple mouse flows into an elephant aggregated flow for traffic engineering. In this paper, we first notice that the user bit-rate requirements of mouse flows are no longer guaranteed in the aggregated flow since the flow rate decided by the TCP allocation is usually different from the desired bit-rate of each user. To address the above issue, we present a novel architecture, named Flexible Flow And Rate Management (F$^2$ARM), to control the rates of only a few flows in order to increase the scalability of SDN, while leaving the uncontrolled flows managed by TCP. Read More

Coupled Linear Boltzmann Transport and hydrodynamics (CoLBT-hydro) is developed for simultaneous and event-by-event simulations of jet transport and jet-induced medium excitation in high-energy heavy-ion collisions. This is made possible by a GPU parallelized (3+1)D hydrodynamics that has a source term from the energy-momentum deposition by propagating jet shower partons and provides real time update of the bulk medium evolution for subsequent jet transport. Hadron spectra in $\gamma$-jet events of Au+Au collisions at RHIC are calculated for the first time that include hadrons from both the modified jet and jet-induced medium excitation. Read More

We study the problem of single-image depth estimation for images in the wild. We collect human annotated surface normals and use them to train a neural network that directly predicts pixel-wise depth. We propose two novel loss functions for training with surface normal annotations. Read More

The graphene/MoS2 heterojunction formed by joining the two components laterally in a single plane promises to exhibit a low-resistance contact according to the Schottky-Mott rule. Here we provide an atomic-scale description of the structural, electronic, and magnetic properties of this type of junction. We first identify the energetically favorable structures in which the preference of forming C-S or C-Mo bonds at the boundary depends on the chemical conditions. Read More

Person re-identification (ReID) is an important task in wide area video surveillance which focuses on identifying people across different cameras. Recently, deep learning networks with a triplet loss become a common framework for person ReID. However, the triplet loss pays main attentions on obtaining correct orders on the training set. Read More

Band gap tuning in two-dimensional transitional metal dichalcogenides (TMDs) is crucial in fabricating new optoelectronic devices. High resolution photoluminescence (PL) microscopy is needed for accurate band gap characterization. We performed tip-enhanced photoluminescence (TEPL) measurements of monolayer MoSe2 with nanoscale spatial resolution, providing an improved characterization of the band gap correlated with the topography compared with the conventional far field spectroscopy. Read More

Motivation: Single cell transcriptome sequencing (scRNA-Seq) has become a revolutionary tool to study cellular and molecular processes at single cell resolution. Among existing technologies, the recently developed droplet-based platform enables efficient parallel processing of thousands of single cells with direct counting of transcript copies using Unique Molecular Identifier (UMI). Despite the technology advances, statistical methods and computational tools are still lacking for analyzing droplet-based scRNA-Seq data. Read More

Let $N(\leq m,n)$ denote the number of partitions of $n$ with rank not greater than $m$, and let $M(\leq m,n)$ denote the number of partitions of $n$ with crank not greater than $m$. Bringmann and Mahlburg observed that $N(\leq m,n)\leq M(\leq m,n)\leq N(\leq m+1,n)$ for $m<0$ and $1\leq n\leq 100$. They also pointed out that these inequalities can be restated as the existence of a re-ordering $\tau_n$ on the set of partitions of $n$ such that $|\text{crank}(\lambda)|-|\text{rank}(\tau_n(\lambda))|=0$ or $1$ for all partitions $\lambda$ of $n$, that is, the rank and the crank are nearly equal distributions over partitions of $n$. Read More

**Authors:**Qingyan Wang, Wenhao Zhang, Weiwei Chen, Ying Xing, Yi Sun, Ziqiao Wang, Jia-Wei Mei, Zhengfei Wang, Lili Wang, Xu-Cun Ma, Feng Liu, Qi-Kun Xue, Jian Wang

The discovery of high-temperature superconductivity in FeSe/STO has trigged great research interest to reveal a range of exotic physical phenomena in this novel material. Here we present a temperature dependent magnetotransport measurement for ultrathin FeSe/STO films with different thickness and protection layers. Remarkably, a surprising linear magnetoresistance (LMR) is observed around the superconducting transition temperatures but absent otherwise. Read More

Topological nodal line semimetals are characterized by the crossing of the conduction and valence bands along one or more closed loops in the Brillouin zone. Usually, these loops are either isolated or touch each other at some highly symmetric points. Here, we introduce a new kind of nodal line semimetal, dubbed "topological Hopf-link semimetal", that contains a pair of linked nodal loops. Read More

Understanding semantic similarity among images is the core of a wide range of computer vision applications. An important step towards this goal is to collect and learn human perceptions. Interestingly, the semantic context of images is often ambiguous as images can be perceived with emphasis on different aspects, which may be contradictory to each other. Read More

For multipartite entangled states, entanglement monogamy is an important property. We investigate the monogamy relations for multiqubit generalized W-class states. We present new analytical monogamy inequalities satisfied by the $x$-th power of the dual of convex-roof extended negativity, namely CRENOA, for $x\geq2$ and $x\leq0$. Read More

Network Function Virtualization (NFV) on Software-Defined Networks (SDN) can effectively optimize the allocation of Virtual Network Functions (VNFs) and the routing of network flows simultaneously. Nevertheless, most previous studies on NFV focus on unicast service chains and thereby are not scalable to support a large number of destinations in multicast. On the other hand, the allocation of VNFs has not been supported in the current SDN multicast routing algorithms. Read More

We study decay properties of the $P$-wave charmed baryons using the method of light-cone QCD sum rules, including the $S$-wave decays of the flavor $\mathbf{\bar 3}_F$ $P$-wave charmed baryons into ground-state charmed baryons accompanied by a pseudoscalar meson ($\pi$ or $K$) or a vector meson ($\rho$ or $K^*$), and the $S$-wave decays of the flavor $\mathbf{6}_F$ $P$-wave charmed baryons into ground-state charmed baryons accompanied by a pseudoscalar meson ($\pi$ or $K$). We study both two-body and three-body decays which are kinematically allowed. We find two mixing solutions from internal $\rho$- and $\lambda$-mode excitations, which can well describe both masses and decay properties of the $\Lambda_c(2595)$, $\Lambda_c(2625)$, $\Xi_c(2790)$ and $\Xi_c(2815)$. Read More

Ultracold plasmas (UCP) provide a well-controlled system for studying multiple aspects in plasma physics that include collisions and strong coupling effects. By applying a short electric field pulse to a UCP, a plasma electron center-of-mass (CM) oscillation can be initiated. In accessible parameter ranges, the damping rate of this oscillation is determined by the electron-ion collision rate. Read More

We prove disorder chaos at zero temperature for three types of diluted models with large connectivity parameter: $K$-spin antiferromagnetic Ising model for even $K\geq 2$, $K$-spin spin glass model for even $K\geq 2$, and random $K$-sat model for all $K\geq 2$. We show that modifying even a small proportion of clauses results in near maximizers of the original and modified Hamiltonians being nearly orthogonal to each other with high probability. We use a standard technique of approximating diluted models by appropriate fully connected models and then apply disorder chaos results in this setting, which include both previously known results as well as new examples motivated by the random $K$-sat model. Read More

We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi's prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero. Read More

This paper proposes a new route for applying the generative adversarial nets (GANs) to NLP tasks (taking the neural machine translation as an instance) and the widespread perspective that GANs can't work well in the NLP area turns out to be unreasonable. In this work, we build a conditional sequence generative adversarial net which comprises of two adversarial sub models, a generative model (generator) which translates the source sentence into the target sentence as the traditional NMT models do and a discriminative model (discriminator) which discriminates the machine-translated target sentence from the human-translated sentence. From the perspective of Turing test, the proposed model is to generate the translation which is indistinguishable from the human-translated one. Read More

We study the inapproximability of the induced disjoint paths problem on an arbitrary $n$-node $m$-edge undirected graph, which is to connect the maximum number of the $k$ source-sink pairs given in the graph via induced disjoint paths. It is known that the problem is NP-hard to approximate within $m^{{1\over 2}-\varepsilon}$ for a general $k$ and any $\varepsilon>0$. In this paper, we prove that the problem is NP-hard to approximate within $n^{1-\varepsilon}$ for a general $k$ and any $\varepsilon>0$ by giving a simple reduction from the independent set problem. Read More

W4 is a giant H{\sc ii} region ionized by the OB stars of the cluster IC~1805. The H{\sc ii} region/cluster complex has been a subject of numerous investigations as it is an excellent laboratory for studying the feedback effect of massive stars on the surrounding region. However, the low-mass stellar content of the cluster IC~1805 remains poorly studied till now. Read More

The flow and deformation of macromolecules is ubiquitous in nature and industry, and an understanding of this phenomenon at both macroscopic and microscopic length scales is of fundamental and practical importance. Here we present the formulation of a general mathematical framework, which could be used to extract, from scattering experiments, the molecular relaxation of deformed polymers. By combining and modestly extending several key conceptual ingredients in the literature, we show how the anisotropic single-chain structure factor can be decomposed by spherical harmonics and experimentally reconstructed from its cross sections on the scattering planes. Read More

Purpose: To investigate the effect of realistic microstructural geometry on the susceptibility-weighted magnetic resonance (MR) signal in white matter (WM), with application to demyelination. Methods: Previous work has modeled susceptibility-weighted signals under the assumption that axons are cylindrical. In this work, we explore the implications of this assumption by considering the effect of more realistic geometries. Read More

We investigate the generation of entanglement (spin squeezing) in an optical-transition atomic clock through the coupling to a vacuum electromagnetic field that is enhanced by an optical cavity. We show that if each atom is prepared in a superposition of the ground state and a long-lived electronic excited state, and viewed as a spin-1/2 system, then the collective vacuum light shift entangles the atoms, resulting in a squeezed distribution of the ensemble collective spin. This scheme reveals that even a vacuum field can be a useful resource for entanglement and quantum manipulation. Read More

We study combinatorial multi-armed bandit with probabilistically triggered arms (CMAB-T) and semi-bandit feedback. We resolve a serious issue in the prior CMAB-T studies where the regret bounds contain a possibly exponentially large factor of $1/p^*$, where $p^*$ is the minimum positive probability that an arm is triggered by any action. We address this issue by introducing triggering probability moderated (TPM) bounded smoothness conditions into the general CMAB-T framework, and show that many applications such as influence maximization bandit and combinatorial cascading bandit satisfy such TPM conditions. Read More

Saliency computation has become a popular research field for many applications due to the useful information provided by saliency maps. For a saliency map, local relations around the salient regions in multi-channel perspective should be taken into consideration by aiming uniformity on the region of interest as an internal approach. And, irrelevant salient regions have to be avoided as much as possible. Read More

The local electronic and atomic structures of the high-quality single crystal of SrFeO3-{delta} ({delta}~0.19) were studied using temperature-dependent x-ray absorption and valence-band photoemission spectroscopy (VB-PES) to investigate the origin of anisotropic resistivity in the ab-plane and along the c-axis close to the region of thermal hysteresis (near temperature for susceptibility maximum, Tm~78 K). All experiments herein were conducted during warming and cooling processes. Read More

Apollo-type NEA (3200) Phaethon, classified at the B/F-type taxonomy, probably the main mass of the Phaethon-Geminid stream complex (PGC), can be the most metamorphic C-complex asteroid in our solar system, since it is heated up to ~1000 K by the solar radiation around its perihelion passages. Hence, its surface material may be easily decomposed in near-sun environment. Phaethon's spectrum exhibits extremely blue-slope in the VIS-NIR region (so-called Phaethon Blue). Read More

We investigate the energy landscape of the spherical mixed even p-spin model near its maximum energy. We relate the distance between pairs of near maxima to the support of the Parisi measure at zero temperature. We then provide an algebraic relation that characterizes one-step replica symmetric breaking Parisi measures. Read More

In this paper, we aim to obtain the optimal delay-power tradeoff and the corresponding optimal scheduling policy for arbitrary i.i.d. Read More

Some short-period, detached binary systems have recently been reported to experience very rapid orbital decay, much faster than is expected from the angular-momentum loss caused by gravitational radiation alone. As these systems contain fully convective stars, magnetic braking is not believed to be operative, making the large orbital-period derivative puzzling. Here we explore whether a resonant interaction between the binary and a surrounding circumbinary (CB) disk could account for the observed orbital decay. Read More

We study the propagation of comparative ideas in social network. A full characterization for submodularity in the comparative independent cascade (Com-IC) model of two-idea cascade is given, for competing ideas and complementary ideas respectively. We further introduce One-Shot model where agents show less patience toward ideas, and show that in One-Shot model, only the stronger idea spreads with submodularity. Read More

In the animal world, the competition between individuals belonging to different species for a resource often requires the cooperation of several individuals in groups. This paper proposes a generalization of the Hawk-Dove Game for an arbitrary number of agents: the N-person Hawk-Dove Game. In this model, doves exemplify the cooperative behavior without intraspecies conflict, while hawks represent the aggressive behavior. Read More

It is generally thought that an ultracompact X-ray binary is composed with a neutron star and a helium white dwarf donor star. As one of the most compact binaries, 4U 1820-303 in globular cluster NGC 6624 was predicted an orbital-period derivative at a rate of $\dot{P}/P\sim1.1\times10^{-7}$ ${\rm yr^{-1}}$ if the mass transfer is fully driven by gravitational radiation. Read More

Round-robin-differential-phase (RRDPS) quantum key distribution (QKD) protocol has attracted intensive studies due to its distinct security characteristic, e.g., information leakage in RRDPS can be bounded without learning error rate of key bits. Read More

The standard design method for conventional straight dipole magnets is improved in this paper. The good field region is not symmetric with respect to the magnet mechanical center, and its width is not enlarged to include the beam sagitta. The integrated field quality is obtained by integrating the field along nominal beam paths. Read More

In this letter, we experimentally report an achromatic metalens (AML) operating over a continuous bandwidth in the visible. This is accomplished via dispersion engineering of dielectric phase shifters: titanium dioxide nanopillars tiled on a dielectric spacer layer above a metallic mirror. The AML works in reflection mode with a focal length independent of wavelength from wavelength of 490 nm to 550 nm. Read More

In this paper, we consider the problem of polar coding for block fading channels, with emphasis on those with instantaneous channel state information (CSI) at neither the transmitter nor the receiver. Our approach is to decompose a block fading channel of $T_c$ symbols per coherent interval into $T_c$ binary-input sub-channels in a capacity-preserving way, and design a polar code for each of them. For the case when instantaneous CSI is available at the receiver, a random interleaver can be used to enable joint encoding and decoding of all sub-channels so as to enhance the finite length performance. Read More