Numerical tests and properties of waves in radiating fluids

We discuss the properties of an analytical solution for waves in radiating fluids, with a view towards its implementation as a quantitative test of radiation hydrodynamics codes. A homogeneous radiating fluid in local thermodynamic equilibrium is periodically driven at the boundary of a one-dimensional domain, and the solution describes the propagation of the waves thus excited. Two modes are excited for a given driving frequency, generally referred to as a radiative acoustic wave and a radiative diffusion wave. While the analytical solution is well known, several features are highlighted here that require care during its numerical implementation. We compare the solution in a wide range of parameter space to a numerical integration with a Lagrangian radiation hydrodynamics code. Our most significant observation is that flux-limited diffusion does not preserve causality for waves on a homogeneous background.     

A Construction of Quantum Error-Locating Codes

We present the construction of quantum error-locating(QEL) codes based on classical error-locating(EL)codes. Similar to classical EL codes, QEL codes lie midway between quantum error-correcting codes and quantum errordetecting codes. Then QEL codes can locate qubit errors within one sub-block of the received qubit symbols but do not need to determine the exact locations of the erroneous qubits. We show that, an e-error-locating code derived from an arbitrary binary cyclic code with generator polynomial g(x), can lead to a QEL code with e error-locating abilities, only if g(x) does not contain the(1 + x)-factor.     

Robust quantum error correction via convex optimization

We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the encoding, recovery, or both, and is amenable to approximations that significantly improve computational cost while retaining fidelity. We illustrate our theory numerically for optimized 5-qubit codes, using the standard [5,1,3] code as a benchmark. Our optimized encoding and recovery yields fidelities that are uniformly higher by 1-2 orders of magnitude against random unitary weight-2 errors compared to the [5,1,3] code with standard recovery.     

An iterative improvement algorithm for coherent codes

Coherent codes (arrays of 1 and -1 whose aperiodic autocorrelation approximateds the delta function) are of interest for several imaging applications. Analytic techniques of code generation have not had much impact on this class of codes. In practice, useful codes are found by hill-climbing searches accomplishing either code generation or improvement. One such improvement algorithm is described.     

Application of the mutual-interaction method to a class of two-scatterer systems: II. Scatterer near an interface

Abstract

This paper applies the methodology developed in Part I to the problem of a separable scatterer near a dielectric (penetrable) or perfectly conducting (impenetrable) interface. For a penetrable interface, the scatterer may be on either side of the interface (exposed or embedded). As in Part I, the scatterer may also be an active element. Thus, our solutions extend the classic treatments of dipoles radiating near a planar dielectric interface. The mutual-interaction method accommodates a uniform half-space as an equivalent scattering plate of zero thickness that preserves amplitudes and phases of the transmitted and reflected waves. Because this scattering function necessarily includes a Dirac delta function, exact analytic solutions are possible for the class of separable scatterers, which include isotropic scatterers and electric or magnetic dipoles. The results can be interpreted within the context of image theory. Integrals similar to those derived by Sommerfeld must be evaluated to calculate the spatial fields for dielectric media; however, for highly conducting media good approximations are readily obtained.     

Application of the mutual-interaction method to a class of two-scatterer systems: II. Scatterer near an interface

This paper applies the methodology developed in Part I to the problem of a separable scatterer near a dielectric (penetrable) or perfectly conducting (impenetrable) interface. For a penetrable interface, the scatterer may be on either side of the interface (exposed or embedded). As in Part I, the scatterer may also be an active element. Thus, our solutions extend the classic treatments of dipoles radiating near a planar dielectric interface. The mutual-interaction method accommodates a uniform half-space as an equivalent scattering plate of zero thickness that preserves amplitudes and phases of the transmitted and reflected waves. Because this scattering function necessarily includes a Dirac delta function, exact analytic solutions are possible for the class of separable scatterers, which include isotropic scatterers and electric or magnetic dipoles. The results can be interpreted within the context of image theory. Integrals similar to those derived by Sommerfeld must be evaluated to calculate the spatial fields for dielectric media; however, for highly conducting media good approximations are readily obtained.     

On approximations involved in the theory of charged particletransport in gases in electric and magnetic fields at arbitrary angles

Various approximations and computer codes for the calculation of charged particle transport in gases in electric and magnetic fields have found their may into mainstream applications of various types. Some of these codes/approximations avoid the mathematical complexity associated with an accurate solution of Boltzmann's equation, but because of assumptions of symmetry and/or near isotropy in velocity space they may be incorrect. Using an accurate multiterm solution of Boltzmann's equation for electric and magnetic fields oriented at arbitrary angles with respect to each other, we highlight the inadequacies of such assumptions. In addition we explore the validity of Tonks' theorem and the effective field approximation as applied to the more general case of arbitrary orientation angles     

Fully self-consistent ion-drag-force calculations for dust in collisional plasmas with an external electric field

The ion drag force on a spherical dust particle immersed in a flowing plasma with an external electric field is self-consistently calculated using the particle-in-cell code SCEPTIC in the entire range of charge-exchange collisionality. Our results, not based on questionable approximations, extend prior analytic calculations valid only in a few limiting regimes. Particular attention is given to the force direction, shown never to be directed opposite to the flow except in the continuum limit, where other forces are of a much stronger magnitude.     

Rate compatible reconciliation for continuous-variable quantum key distribution using Raptor-like LDPC codes

In the practical continuous-variable quantum key distribution(CV-QKD) system, the postprocessing process, particularly the error correction part, significantly impacts the system performance. Multi-edge type low-density parity-check(MET-LDPC) codes are suitable for CV-QKD systems because of their Shannon-limit-approaching performance at a low signal-to-noise ratio(SNR).However, the process of designing a low-rate MET-LDPC code with good performance is extremely complicated. Thus, we introduce Raptor-like LDPC(RL-LDPC) codes into the CV-QKD system, exhibiting both the rate compatible property of the Raptor code and capacity-approaching performance of MET-LDPC codes. Moreover, this technique can significantly reduce the cost of constructing a new matrix. We design the RL-LDPC matrix with a code rate of 0.02 and easily and effectively adjust this rate from 0.016 to 0.034. Simulation results show that we can achieve more than 98% reconciliation efficiency in a range of code rate variation using only one RL-LDPC code that can support high-speed decoding with an SNR less than-16.45 d B. This code allows the system to maintain a high key extraction rate under various SNRs, paving the way for practical applications of CV-QKD systems with different transmission distances.     

The near edge structure of cubic boron nitride

We compare the near edge structure (NES) of cubic boron nitride (cBN) measured using both electron energy loss spectroscopy (EELS) and X-ray absorption spectroscopy (XAS) with that calculated using three commonly used theoretical approaches. The boron and nitrogen K-edges collected using EELS and XAS from cBN powder were found to be nearly identical. These experimental edges were compared to calculations obtained using an all-electron density functional theory code (WIEN2k), a pseudopotential density functional theory code (CASTEP) and a multiple scattering code (FEFF). All three codes were found to reproduce the major features in the NES for both ionisation edges when a core-hole was included in the calculations. A partial core hole (1/2 of a 1s electron) was found to be essential for correctly reproducing features near the edge threshold in the nitrogen K-edge and to correctly obtain the positions of all main peaks. CASTEP and WIEN2k were found to give almost identical results. These codes were also found to produce NES which most closely matched experiment based on χ² calculations used to qualitatively compare theory and experiment. This work demonstrated that a combined experimental and theoretical approach to the study of NES is a powerful way of investigating bonding and electronic structure in boron nitride and related materials.     

Simple family of nonadditive quantum codes

Most known quantum codes are additive, meaning the code can be described as the simultaneous eigenspace of an Abelian subgroup of the Pauli group. While in some scenarios such codes are strictly suboptimal, very little is understood about how to construct nonadditive codes with good performance. Here we present a family of distance 2 nonadditive quantum codes for all odd block lengths n, that has a particularly simple form. Our codes detect single qubit errors (or correct single qubit erasures) while encoding a higher dimensional space than is possible with an additive code or, for n> or =11, any previous codes. We exhibit the encoding circuits and automorphism group for our codes as well.     

一种严格最佳(ν,k,1)光正交码的设计方法

介绍了严格最佳和准最佳(ν,k,1)光正交码的定义，阐述了它们与(ν,k,1)循环差集族的关系。基于Wilson均匀分布差引理和初等数论的基本理论，提出一种最佳(ν,k,1)循环差集族的构造方法，即构造定义在ν阶有限域上满足特定约束条件的k元集合。将该方法用于光正交码的设计中，可以有效地设计一些严格最佳(ν,k,1)光正交码，其中，码长ν为素数，码重k的取值为4、5和6。最后结合具体实例，给出严格最佳(ν,k,1)光正交码的计算机辅助设计方法。同其他设计方法相比，该设计方法既简单又实用，尤其对严格最佳（ν,k,1）光正交码而言，设计效率较高；随着码重k的增加，码的设计效率逐渐降低。     

Degenerate quantum codes for Pauli channels

A striking feature of quantum error correcting codes is that they can sometimes be used to correct more errors than they can uniquely identify. Such degenerate codes have long been known, but have remained poorly understood. We provide a heuristic for designing degenerate quantum codes for high noise rates, which is applied to generate codes that can be used to communicate over almost any Pauli channel at rates that are impossible for a nondegenerate code. The gap between nondegenerate and degenerate code performance is quite large, in contrast to the tiny magnitude of the only previous demonstration of this effect. We also identify a channel for which none of our codes outperform the best nondegenerate code and show that it is nevertheless quite unlike any channel for which nondegenerate codes are known to be optimal.     

Homological stabilizer codes

In this paper we define homological stabilizer codes on qubits which encompass codes such as Kitaev’s toric code and the topological color codes. These codes are defined solely by the graphs they reside on. This feature allows us to use properties of topological graph theory to determine the graphs which are suitable as homological stabilizer codes. We then show that all toric codes are equivalent to homological stabilizer codes on 4-valent graphs. We show that the topological color codes and toric codes correspond to two distinct classes of graphs. We define the notion of label set equivalencies and show that under a small set of constraints the only homological stabilizer codes without local logical operators are equivalent to Kitaev’s toric code or to the topological color codes.     

Standard form of qudit stabilizer groups

We investigate stabilizer codes with carrier qudits of equal dimension D, an arbitrary integer greater than 1. We prove that there is a direct relation between the dimension of a qudit stabilizer code and the size of its corresponding stabilizer, and this implies that the code and its stabilizer are dual to each other. We also show that any qudit stabilizer can be put in a canonical, or standard, form using a series of Clifford gates, and we provide an explicit efficient algorithm for doing this. Our work generalizes known results that were valid only for prime dimensional systems and may be useful in constructing efficient encoding/decoding quantum circuits for qudit stabilizer codes and better qudit quantum error correcting codes.     

Evaluation of coherent homodyne and heterodyne optical CDMA structures

This paper evaluates the coherent optical code-division multiple-access (OCDMA) techniques and examines the overall system performance in terms of signal-to-noise ratio (SNR) penalty as a function of simultaneous users accommodated to maintain an appropriate value of the bit-error rate (BER) for homodyne and heterodyne detections. As spreading codes, the proposed structures are utilizing a recently introduced prime code family hereby referred to as double-padded modified prime code (DPMPC). As a coherent modulation, binary phase-shift keying (BPSK) format is deployed. In homodyne detection, two different phase modulations are studied including either an external phase-modulator or injection-locking methods. The phase limitation and the performance for two methods plus multiple-access interferences (MAI) and receiver noise in a shot-noise limited regime are investigated. In heterodyne detection, BER analysis of the system based on only external phase modulator is examined. It is found that by maintaining BER = 10⁻⁹, this system can accommodate an increased number of simultaneous users to compare with systems which employ conventional bipolar codes.     

Performance of concatenated codes over an APD-based optical system with estimated channel-state information

In this paper, we investigate the efficiency of serially concatenated codes using a BCH (32400, 32208) inner code and an LDPC (64800, 32400) outer code over a free-space optical communication (FSOC) system with APD detectors. Based on the experimental optical signals recorded from a FSO (free-space optical) link with the distance z = 11.8 km, the bit error rate (BER) performance of the concatenated codes is evaluated from the aspect of simulation under weak turbulence conditions (for which the scintillation index σ _I ² = 0.18) and strong turbulence conditions (for which σ _I ² = 1.49). The results indicate that the fade level P _T can be set much lower for the FSOC system using the concatenated codes, leading to shorter fade length and interleavers in smaller size. The concatenated codes are shown to even outperform the (4, 1, 7) convolutional code in both cases. In addition, we analyze the BER performance of these concatenated codes on the basis of pilot-aided channel estimation with different numbers of pilot symbols.     

Public-Key Cryptosystems and Bounded Distance Decoding of Linear Codes

Error-correcting codes form an important topic in information theory. They are used to correct errors that occur during transmission on a noisy channel. An important method for correcting errors is bounded distance decoding. The public-key cryptosystem is a cryptographic protocol that has two different keys. One of them is a public-key that can be known by everyone, and the other is the private-key only known to the user of the system. The data encrypted with the public-key of a given user can only be decrypted by this user with his or her private-key. In this paper, we propose a public-key cryptosystem based on the error-correcting codes. The decryption is performed by using the bounded distance decoding of the code. For a given code length, dimension, and error-correcting capacity, the new system allows dealing with larger plaintext than other code based public-key cryptosystems.     

适用于同步光码分多址通信系统的同步光码及其全光可调编/解码器

异步光码分多址通信系统,要求用户地址码具有好的循环自相关和互相关特性,因此,系统中的用户数受到很大的限制;而对同步光码分多址通信系统,只要求光地址码是非循环相关意义下的准正交,从而可实现较大的用户数,因此具有广阔的应用前景.实现同步光码分多址的关键之一是同步光码的设计和可调光编/解码器的实现.本文介绍了同步光码的构造方法,给出了同步光码的构造过程,分析了码的容量,提出了全光可调同步光码编/解码器的实现方法.     

辐射式核电磁脉冲模拟器TEM喇叭天线

针对辐射式核电磁脉冲模拟器采用TEM喇叭天线作为辐射天线时低频辐射能力有限的问题,对板型和线型两种基本形式的TEM喇叭天线进行了分析。在采用线型TEM喇叭天线以减轻模拟器重量的基础上,在天线末端采用螺旋线结构,并增加屏蔽板回路,构造了一种新型TEM喇叭天线。结果表明:与普通线型TEM喇叭天线相比,该新型天线较大地提高了低频辐射性能,可使近场波形脉宽提高7ns左右,峰值场强提高了1kV/m左右;通过增大螺旋线半径和提高螺旋线密度可以提高峰值场强,增加近场波形脉宽;通过屏蔽板回路可以降低反射波纹的波峰从而改善近场波形。