A new code construction with zero cross correlation based on BIBD

This paper presents a newly constructed zero cross correlation code (ZCC) which is based on BIBD (balanced incomplete block design) code. The ZCC (C, w) code is a family of binary sequences of length C and constant Hamming-weight w. Such codes find applications in spectral amplitude-coding optical code division multiple access (SAC-OCDMA). The constructing ZCC codes have a size of C ? N ÿ w + 1, where N is the number of users and C is any prime number. The proposed construction method is not complicated compared to the existing ones.     

New design of spectral amplitude coding in OCDMA with zero cross-correlation

A zero cross-correlation (ZCC) code is proposed to reduce the impact of system impairment and multiple access interference (MAI) in spectral amplitude coding optical code division multiple access (SAC-OCDMA) system. Bit-error-rate (BER) performance is derived taking into account the effect of some noises. The key to an effective OCDMA system is the choice of efficient address codes with good or almost zero correlation properties for encoding the source. The use of ZCC code can eradicate phase induced intensity noise (PIIN) which will contribute to better BER. Thus, we demonstrate, theoretically, the performance of optical ZCC code. It is shown that optical ZCC code can accommodate more users simultaneously for the typical error rate of optical communication system of 10⁻⁹. The result indicates that the established system not only preserves the capability of suppressing MAI, but also improves bit-error-rate performance as compared to the conventional coders.     

Minimizing correlation effect using zero cross correlation code in spectral amplitude coding optical code division multiple access

The use of minimal multiple access interference (MAI) in code design is investigated. Applying a projection and mapping techniques, a code that has a zero cross correlation (ZCC) between users in optical code division multiple access (OCDMA) is presented in this paper. The system is based on an incoherent light source—LED, spectral amplitude coding (SAC), and direct detection techniques at the receiver. Using power spectral density (PSD) function and Gaussian approximation, we obtain the signal-to-noise ratio (SNR) and the bit-error rate (BER) to measure the code performance. Making a comparison with other existing codes, e.g., Hadamard, MFH and MDW codes, we show that our code performs better at BER 10⁻⁹ in terms of number of simultaneous users. We also demonstrate the comparison between the theoretical and simulation analyses, where the results are close to one another.     

Performance evaluation of Fi-Wi network based on SCM–optical code division multiple access architecture

This paper investigates the performance of a spectral amplitude coding (SAC)–OCDMA system design utilizing subcarrier multiplexing techniques for use in the popular fiber-wireless (Fi-Wi) technology. Zero cross correlation code is employed because of its ability to eliminate phase induced intensity noise (PIIN) and the simplicity of using a direct detection technique at the receiving end. The performances are evaluated theoretically to derive the signal-to-noise ratio and results are presented in terms of bit error rates (BER). Results are analyzed to investigate the effect of code weight and variable data rates on the system performance. To validate the results, simulative analysis is also done using Optisys version 6.0. We demonstrated that the ZCC code performed better compared to other code for a BER floor of 10⁻⁹ with larger cardinality of subscribers. Results obviously indicate that system performance can be improved with larger code weight. In addition, the choice of lower bit rate is observed to perform better and more suitable for application in this hybrid Fi-Wi network.     

PIN versus Avalanche photodiode gain optimization in zero cross correlation optical code division multiple access system

In this paper, we show details of zero cross correlation (ZCC) code development and investigate performance by measuring bit-error-rates compared to other optical code division multiple access (OCDMA) codes using Avalanche photodiode (APD) and PIN photodetector. We present a configuration to determine how optical OCDMA systems can be applied with PIN and APD photodetector. Analysis of Avalanche photodiode gain optimization is discussed in ZCC code system. We also present analytical and numerical theoretical results for data transmission of spectrally encoded incoherent OCDMA signal and how signal-noise is being affected by using these two photodetectors.     

Design and performance analysis of various one dimensional codes using different data formats for OCDMA system

In this paper, the design, implementation and performance analysis of various one dimensional codes in an OCDMA system for different data formats is presented. A number of different codes are used with optical CDMA to improve its error performance. Here, three such codes, optical orthogonal codes (OOC), Walsh Hadamard codes and zero cross-correlation (ZCC) codes have been compared using different data formats, NRZ raised cosine, NRZ rectangular, RZ raised cosine and RZ rectangular. It is found that NRZ raised cosine has the best system performance for all the codes used. After that, the three codes have been compared in terms of the BER, eye diagrams and received optical power using NRZ raised cosine modulation format. It is analyzed that ZCC codes have zero cross-correlation property. The simulation results revealed that ZCC codes can provide a better BER compared to the OOC and Walsh Hadamard codes and it is most suitable to be employed in the OCDMA systems.     

Variable cross-correlation code construction for spectral amplitude coding optical CDMA networks

We present, for the first time, several aspects of incoherent optical code-division multiple access (OCDMA) codes, focusing on the flexible variable cross-correlation code allocation and its potential for future optical networks. We briefly present a new version of the Random Diagonal (RD) codes for Spectral-Amplitude Coding (SAC) OCDMA approaches. We then concentrate on the properties specific to such schemes allowing for its increased scalability and flexibility. The main coding properties are reviewed. The RD codes provide simple matrix constructions compared to the other SAC-OCDMA codes such as Hadamard, MQC and MFH codes. This code possesses such a numerous advantages, including the efficient and easy code construction, simple encoder/decoder design, existence for every natural number n, and variable in-phase cross-correlation and easy to implement using Fiber Bragg Gratings (FBGs). Finally, a new detection scheme called “NAND” detection is developed for the variable cross-correlation RD code.     

How to utilize a Grover search in general programming

It is widely believed that quantum computers (if realized) will be more powerful than today’s computers from the viewpoint of computational complexity. However, it is not obvious how to utilize quantum computers in practical situations. For practical purposes, a Grover search may be one of the most promising quantum algorithms known so far. Thus, in this paper, we propose an efficient framework where we can use Grover search for general programming. Our framework has the following steps. (1) A programmer writes a program by using standard C++ programming language. (2) Some if expressions within for loops in the C++ source code are chosen as candidates to be performed as a Grover search on a quantum computer. (3) The framework automatically generates a corresponding quantum circuit for each Grover search chosen in (2). Unlike the existing quantum circuit design methods, we can treat large problems in our quantum circuit design. (4) By evaluating the number of primitive quantum gates in the quantum circuit generated in (3), the framework determines whether the processing time of the quantum circuit is faster than the processing time of the corresponding if expression on a classical computer. If the framework determines that the quantum circuit is faster, it generates some interface source codes for a classical computer. Thus, in our framework, a programmer can use a Grover search with almost no effort.     

Implementation of Fault-Tolerant Encoding Circuit Based on Stabilizer Implementation and “Flag” Bits in Steane Code

Quantum error correction (QEC) is an effective way to overcome quantum noise and de-coherence, meanwhile the fault tolerance of the encoding circuit, syndrome measurement circuit, and logical gate realization circuit must be ensured so as to achieve reliable quantum computing. Steane code is one of the most famous codes, proposed in 1996, however, the classical encoding circuit based on stabilizer implementation is not fault-tolerant. In this paper, we propose a method to design a fault-tolerant encoding circuit for Calderbank-Shor-Steane (CSS) code based on stabilizer implementation and “flag” bits. We use the Steane code as an example to depict in detail the fault-tolerant encoding circuit design process including the logical operation implementation, the stabilizer implementation, and the “flag” qubits design. The simulation results show that assuming only one quantum gate will be wrong with a certain probability p, the classical encoding circuit will have logic errors proportional to p; our proposed circuit is fault-tolerant as with the help of the “flag” bits, all types of errors in the encoding process can be accurately and uniquely determined, the errors can be fixed. If all the gates will be wrong with a certain probability p, which is the actual situation, the proposed encoding circuit will also be wrong with a certain probability, but its error rate has been reduced greatly from p to p2 compared with the original circuit. This encoding circuit design process can be extended to other CSS codes to improve the correctness of the encoding circuit.     

Repetition versus noiseless quantum codes for correlated errors

We study the performance of simple quantum error correcting codes with respect to correlated noise errors characterized by a finite correlation strength μ. Specifically, we consider bit flip (phase flip) noisy quantum memory channels and use repetition and noiseless quantum codes. We characterize the performance of the codes by means of the entanglement fidelity F(μ,p) as function of the error probability p and degree of memory μ. Finally, comparing the entanglement fidelities of repetition and noiseless quantum codes, we find a threshold μ^*(p) for the correlation strength that allows to select the code with better performance.     

FPGA-Implemented Fractal Decoder with Forward Error Correction in Short-Reach Optical Interconnects

Forward error correction (FEC) codes combined with high-order modulator formats, i.e., coded modulation (CM), are essential in optical communication networks to achieve highly efficient and reliable communication. The task of providing additional error control in the design of CM systems with high-performance requirements remains urgent. As an additional control of CM systems, we propose to use indivisible error detection codes based on a positional number system. In this work, we evaluated the indivisible code using the average probability method (APM) for the binary symmetric channel (BSC), which has the simplicity, versatility and reliability of the estimate, which is close to reality. The APM allows for evaluation and compares indivisible codes according to parameters of correct transmission, and detectable and undetectable errors. Indivisible codes allow for the end-to-end (E2E) control of the transmission and processing of information in digital systems and design devices with a regular structure and high speed. This study researched a fractal decoder device for additional error control, implemented in field-programmable gate array (FPGA) software with FEC for short-reach optical interconnects with multilevel pulse amplitude (PAM-M) modulated with Gray code mapping. Indivisible codes with natural redundancy require far fewer hardware costs to develop and implement encoding and decoding devices with a sufficiently high error detection efficiency. We achieved a reduction in hardware costs for a fractal decoder by using the fractal property of the indivisible code from 10% to 30% for different n while receiving the reciprocal of the golden ratio.     

Influence of Fringle Fields in Quadrupole Lenses on the Dynamics of Particles in the NICA Collider

A study of the NICA collider dynamical aperture (DA) using the MADX code has shown that, in the chosen working point (Q_x,Q_y ～ 9,43), the DA sharply decreases when taking into account the fringe fields of the quadrupole lenses and dipole magnets. An analytical theory is developed to calculating the strength of resonances generated by the fringe fields of the quadrupole lenses in a circular machine. It is shown that the formulae derived for these parameters have a general character and do not depend on the lens design. The codes for a numerical calculation of the anharmonicity coefficients and resonance strength in the NICA collider are written. The method is developed to estimate the resonance strength by using the numerical simulation of the trajectories with the help of the MADX code. For the NICA collider structure, the results of the analytical calculation of the resonance strength for a chosen resonance coincide with the results obtained using the MADX code with a satisfactory accuracy.     

General coding method of address code for optical code division multiple access passive optical network – (F,K, λa, λc) optical orthogonal code

Since the importance of address code of OCDMA passive optical network (PON) diversity and lacking of general coding method until now, in this paper, we present a general coding method of (F, K, λ_a, λ_c) optical orthogonal code (OOC) based on block design. Through the discussion of block, difference sets and cyclic permutation of perfect distance (CPPD), cyclic permutation of imperfect distance (CPID) is defined and applied to realize the coding method. Simulations results demonstrated that it is possible to construct (F, K, λ_a, λ_c) OOCs with arbitrary code length, code weight, auto-correlation constraints and co-correlation constraints based on the same general coding method.     

Magnetic phases of amorphous transition metal-metalloid alloys

Hysteresis loop and ac susceptibility measurements were performed on three series of amorphous alloys: (A_wB_1-w)₇₅P₁₆B₆Al₃, where (A, B) are (Fe, Ni), (Co, Ni) and (Fe, Mn). Upon cooling, low w alloys undergo paramagne t to spin glass transitions. Alloys with higher w first experience a Curie transition to a ferromagnetic state, and then a spin freezing transition to a spin glass state. the T dependence of the width of the ac hysteresis loop is used to determine the spin freezing transition temperature. A magnetic phase diagram is presented for each alloy series and the value of w required for ferromagnetism, w_C, is determined. When measured in the presence of small constant fields, the ac susceptibility of alloys with w just above w_C has maxima near both transition temperatures. The field and temperature dependences of the peaks are explained by scaling arguments, used to determine the critical exponent δ for the Curie transition, and suggest that a similar scaling law holds for the ferromagnet to spin glass transition.     

Determination of the physical network of entanglements and the molecular mobility in linear flexible polymers by the NMR method

In the present paper, a theory of free induction decay in linear flexible chain polymers is developed. Theoretical and experimental dependences of the spin-spin relaxation time T ₂ on the average molecular weight M _w and temperature are compared. It is shown that, with increasing M _w , the topological structure of linear polymers changes, and at M _w > 10⁵, a physical network entanglements (quasi-network) is formed. A correlation function of molecular motions is obtained, which indicates whether the quasi-network is formed in polymer melts.     

A new coding scheme of QC-LDPC codes for optical transmission systems

Based on Galois Field (GF(q)) multiplicative group, a new coding scheme for Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes is proposed, and the new coding scheme has some advantages such as the simpler construction, the easier implementation encoding, the lower complexity of the encoding and decoding, the more flexible adjustment of the code length as well as the code rate and so forth. Under the condition of considering the characteristics of optical transmission systems, an irregular QC-LDPC (3843,3603) code to be suitable for optical transmission systems is constructed by applying the proposed new coding scheme. The simulation result shows that the net coding gain (NCG) of the irregular QC-LDPC (3843,3603) code is respectively improved 2.14 dB, 1.19 dB, 0.24 dB and 0.14 dB more than those of the classic RS (255,239) code in ITU-T G.975, the LDPC (32640,30592) code in ITU-T G.975.1, the regular SCG-LDPC (3969,3720) code constructed by the Systematically Constructed Gallager (SCG) coding scheme and the regular QC-LDPC (4221,3956) code at the bit error rate (BER) of 10-8. Furthermore, all the five codes have the same code rate of 93.7%. Therefore, the irregular QC-LDPC (3843,3603) code constructed by the proposed new coding scheme has the more excellent error-correction performance and can be better suitable for optical transmission systems.     

Three-dimensional simulation of triode-type MIG for 1 MW, 120 GHz gyrotron for ECRH applications

In this paper, the three-dimensional simulation of triode-type magnetron injection gun (MIG) for 120 GHz, 1 MW gyrotron is presented. The operating voltages of the modulating anode and the accelerating anode are 57 kV and 80 kV respectively. The high order TE_22,6 mode is selected as the operating mode and the electron beam is launched at the first radial maxima for the fundamental beam-mode operation. The initial design is obtained by using the in-house developed code MIGSYN. The numerical simulation is performed by using the commercially available code CST-Particle Studio (PS). The simulated results of MIG obtained by using CST-PS are validated with other simulation codes EGUN and TRAK, respectively. The results on the design output parameters obtained by using these three codes are found to be in close agreement.     

Abnormal blood-brain barrier water exchange in chronic multiple sclerosis lesions: A preliminary study

Relapsing-remitting multiple sclerosis (RRMS) is associated with persistent blood-brain barrier (BBB) dysfunction. The impact of this persistent dysfunction in both active and chronic MS lesions has yet to be investigated due to technological challenges associated with invasive assessment of BBB water transportation (e.g. ¹⁵O-PET). The purpose of this study was to test if persistent BBB dysfunction in RRMS manifests as lower BBB water exchange in chronic lesions using a recently developed noninvasive MRI paradigm. Patients with relapsing-remitting MS and healthy subjects were recruited for this prospective study. The novel Intrinsic Diffusivity Encoding of Arterial Labeled Spins (IDEALS) MRI method was used to map BBB water extraction fraction (E_w) and water permeability surface area product (PS_w), as well as cerebral blood flow (CBF). Regional differences in BBB water exchange were evaluated between MS patients (normal appearing white matter [NAWM] and normal appearing gray matter [NAGM]) and healthy subjects (white matter [WM] and gray matter [GM]) and within MS subjects in non gadolinium-based contrast-agent (GBCA) enhancing chronic lesions, perilesional areas, and NAWM. Significantly lower PS_w and E_w were observed in NAWM compared to WM (ΔPS_w: −11.9 mL/100 g/min, p < .05; ΔE_w: −4.3%, p < .01). Significantly lower E_w was observed in NAGM compared to GM (ΔE_w: −12.1%, p < .01). Significantly lower PS_w and CBF were observed in non-GBCA contrast enhancing lesions compared to NAWM (ΔPS_w = −11.5 mL/100 g/min, p < .05; ΔCBF = −8.1 mL/100 g/min, p < .05). E_w was significantly higher in non-GBCA enhancing chronic MS lesions compared to NAWM (ΔE_w = 1.6%, p < .05). The lower BBB water exchange in chronic MS lesions is consistent with previously reported observations and may demonstrate metabolic changes associated with MS.     

Pareto–Zipf law in growing systems with multiplicative interactions

Numerical simulations of multiplicatively interacting stochastic processes with weighted selections were conducted. A feedback mechanism to control the weight w of selections was proposed. It becomes evident that when w is moderately controlled around 0, such systems spontaneously exhibit the Pareto–Zipf distribution. The simulation results are universal in the sense that microscopic details, such as parameter values and the type of control and weight, are irrelevant. The central ingredient of the Pareto–Zipf law is argued to be the mild control of interactions.