Parity-check Research Articles

Transmission system with adaptive LDPC-Coded OFDM modulation implemented in GNU Radio

Real-time testing in wireless channel conditions of Forward Error Correction (FEC) coding techniques, Modulation and Coding Scheme (MCS) selection algorithms is a complex and challenging task. GNU Radio and Software Defined Radio (SDR) concept allow a wide range of practical and low-cost solutions to perform the testing operations mentioned above. The paper proposes a duplex transmission system with adaptive LDPC (Low Density Parity Check) coding and OFDM (Orthogonal Frequency Division Multiplexing) modulation implemented in GNU Radio. The frame structure, design principles, system architecture, and mechanisms controlling the transmission process are presented. The system’s modular architecture provides the framework for testing various LDPC coding and MCS selection techniques. The system’s design allows us to maximize the transmission’s efficiency, the encapsulation of various data structures, i.e., frame and transport block, using reduced overheads and the necessity of padding operations is minimized.

Orbital moiré and quadrupolar triple-q physics in a triangular lattice

We numerically study orders of planer type (xy,x2−y2) quadrupoles on a triangular lattice with nearest-neighbor isotropic J and anisotropic K interactions. This type of quadrupole possesses unique single-ion anisotropy proportional to a third order of the quadrupole moments. This provides an unconventional mechanism of triple-q orders which does not exist for the degrees of freedom with odd parity under time-reversal operation such as magnetic dipoles. In addition to several single-q orders, we find various orders including incommensurate triple-q quasi-long-range orders with orbital moiré and a four-sublattice triple-q partial order. Our Monte Carlo simulations demonstrate that the phase transition to the latter triple-q state belongs to the universality class of the critical line of the Ashkin-Teller model in two dimensions close to the four-state Potts class. These results indicate a possibility of realizing unique quadrupole textures in simple triangular systems. Published by the American Physical Society 2024

Mirror resonances in Be9 and B9 within an α+α+N model

Using an α+α+N three-body model, we describe the ground and excited unbound states above the three-body threshold of A=9 mirror nuclei. We investigate the energy levels of low-lying and highly excited resonances below ≈10MeV excitation energy of Be9 and B9 mirror nuclei with the complex-scaling method. The same number of solutions are found for both mirror nuclei, namely, thirteen resonances, 3/21−4−, 5/21−3−, 1/21−3−, 7/21,2−, and 9/2−, including the ground state for odd parity states, and eight resonances 5/21,2+, 3/21,2+, 7/21,2+, and 9/21,2+, for even-parity states with the exception of the low-lying 1/2+ state. These results are compared with experimentally observed and other theoretically calculated results. The band structures of odd and even parity states for both Be9 and B9 mirror nuclei are discussed in relation to the effect of the Coulomb energy difference. Published by the American Physical Society 2024

Exploring the role of adamantane core in the mesophase formation of trimers

ABSTRACT We report the synthesis and phase behaviour of liquid crystalline trimers containing a 1,3-adamantane unit in the central core with 4-n-hexylbiphenyl and 4-cyanobiphenyl as wing mesogens. These materials with even parity spacers form hexagonal smectic phases (B and E). As shown by conformational simulation using a simple graphical user interface tool, their liquid crystal behaviour appears to be primarily driven by their molecular shape. The presence 1,3-adamantane unit in the central core of these trimers leads to narrow distribution of possible conformers with domination of elongated forms that drive the formation of hexagonal smectic phases. The odd parity trimers have a broad distribution of possible conformers that govern the formation of nematic phase or prevent liquid crystalline behaviour.

Emulation of Optical Binary to Gray Code Converter and Even/Odd Parity Checker Circuit Using Electro-optic Effect-Based Directional Couplers

Emulation of Optical Binary to Gray Code Converter and Even/Odd Parity Checker Circuit Using Electro-optic Effect-Based Directional Couplers

Hyperfine structure of Lu I transition at 642 nm and its application to explore new odd parity autoionization resonances

Resonance ionization mass spectroscopy using three-step photoionization (PI) schemes was employed to study the 642 nm transition of Lu I. Multimode tunable dye lasers were used in these studies to confirm the transition and further characterization of its hitherto unreported hyperfine structure. The hyperfine features of less abundant isotope 176Lu and hyperfine A constant of upper level of 642 nm line and its transition isotope shift were determined for the first time. New autoionization resonances of odd parity connecting from the upper level of this transition were explored in the range 48315 – 50940 cm−1.

Manifestation of a1(1260) meson in the process e+e−→π+π−π0

The charge asymmetry in the process e+e−→π+π−π0 is studied taking into account a longitudinal polarization of electrons (positrons). The asymmetry arises due to interference of amplitudes corresponding to production of pions in states with charge parity odd and charge parity even. It is a manifestation of a1(1260) meson in the intermediate state. Polarization leads to additional correlations in the differential cross section, which simplifies the experimental study of the process. It is shown that the charge asymmetry can reach several percent. Published by the American Physical Society 2024

Implementation of EXOR and Subsequent Modular Circuits for Application at Nanoscale Level

Evolving as an outperforming nanotechnology, quantum-dot cellular automata (QCA) is being efficiently used for the design and development of digital modules. This paper presents a novel design for an ultra-efficient exclusive-OR (EXOR) gate in QCA nanotechnology using the cell translation technique. The analysis for fault tolerance and power dissipation of the proposed design is also assessed. To establish the effectiveness of the proposed design, an extensive comparison with the existing designs is provided. As a test bench implementation, the proposed EXOR gate is available as a module for the development of a parity checker, a full subtractor, and a 4-input binary to gray (B2G) code converter in QCA. The cell count for the proposed design of the EXOR gate, full subtractor, parity checker, and 4-input B2G converter is 8, 35, 24, and 24, and the total area (µm2) is 0.0039, 0.0259, 0.01749, and 0.0129, respectively. The proposed EXOR gate design outclasses the hitherto prevailing designs both in terms of the operational parameters and the dissipation of energy. The design simulations have been performed in QCA Designer 2.0.3, and the energy dissipation analysis has been executed in QCA Designer-E and QCAPro.

Higgs-portal spin-1 dark matter with parity-violating interaction

We introduce the spin-1 U(1)X gauged field X with Z2 odd dark parity to evade the current strong constraints on kinetic mixing. Then, X becomes stable and a candidate for the dark matter. The lowest mass dimension of interaction is six, and the type is the Higgs portal. Two types of dim-6 operators are introduced. We consider the freeze-out dark matter scenario. With the limit of null momentum transfer, a parity odd operator is free from the direct detection constraints. Accordingly, the strong constraints on a parity even operator indicate turning on this parity odd operator to realize the dark matter relic density of the Universe. With the 1 TeV cut-off scale, our dark matter of around 400 GeV mass can explain the dark matter relic density and is allowed from the LUX-ZEPLIN experiment of the direct detection.

Two-Phase Globally Coupled Low-Density Parity Check Decoding Aided with Early Termination and Forced Convergence.

To enhance the decoding efficiency of Globally Coupled (GC) LDPC codes, we incorporated Early Termination (ET) and Forced Convergence (FC) into the local/global two-phase decoding algorithm to expedite the decoding process. The two-phase decoding scheme integrates the ET technique to halt unnecessary iterations in the local decoding phase while employing the FC technique to accelerate convergence in the global phase decoding. The application of ET technology in the local decoding of GC-LDPC codes will not cause performance loss as in traditional block codes and will cause considerable complexity gains. For a longer code length and larger convergence differences between nodes' global codes, the FC technique operates more efficiently in global code than local code. Two variants are proposed for the ET scheme in the local decoding, namely ET-1 and ET-2. The initial variant, ET-1, predicts whether local decoding can be successful according to data characteristics and stop the local decoding iteration that is not expected to be successful in time. In the case of ET-2, the saved local iterations are transformed to global decoding equally. The results show that ET-1 saves considerable decoding time complexity and ET-2 improves the performance of the GC-LDPC code with the same decoding time complexity. The combined approach of ET-1 with FC reduces the decoding time complexity up to 42% at a low Signal Noise Rate region while maintaining its performance; ET-2-FC two-phase decoding saves approximately 25% decoding time complexity while improving the BER by about 0.18 dB and FER by about 0.23 dB.

Realization of 4-Bit Parity Checker Circuit Using XPM Technique-Based Phase-Shifted Fiber Bragg Grating Scheme

Realization of 4-Bit Parity Checker Circuit Using XPM Technique-Based Phase-Shifted Fiber Bragg Grating Scheme

Multi-bit error detection and correction technique using HVDK (Horizontal-Vertical-Diagonal-Knight) parity

In a data stream, errors are quite likely to occur and sometimes this is much more terrible. So, data safety is very important in digital systems, especially in critical and real-time systems, microprocessors, embedded systems, computer memory, and data communication. The probability of soft error increases with the exponential rate of increasing transistor per chip, operational voltage, particle strike, condensation of bit-cell area, etc. To ensure data integrity, safety, and system reliability, error detection, and correction are fundamental components of data transmission and storage systems. Existing error correction techniques can solve several bits of error. However, these existing methods are not fully efficient, as some consume a lot of time, space, and bit overhead. An ideal approach will have the potential to minimize all of these parameters. This research paper proposes a novel error correction approach with horizontal, vertical, diagonal, and knight (HVDK) parity bits. This approach has been taken to correct 5-bit errors in 64 bits of data word using the parity-based technique with less bit overhead. Our research advances the knowledge of error correction methods and sheds light on how to pick and use parity bit schemes that are appropriate for different applications.

Universal quantum operations and ancilla-based read-out for tweezer clocks

Enhancing the precision of measurements by harnessing entanglement is a long-sought goal in quantum metrology1,2. Yet attaining the best sensitivity allowed by quantum theory in the presence of noise is an outstanding challenge, requiring optimal probe-state generation and read-out strategies3–7. Neutral-atom optical clocks8, which are the leading systems for measuring time, have shown recent progress in terms of entanglement generation9–11 but at present lack the control capabilities for realizing such schemes. Here we show universal quantum operations and ancilla-based read-out for ultranarrow optical transitions of neutral atoms. Our demonstration in a tweezer clock platform9,12–16 enables a circuit-based approach to quantum metrology with neutral-atom optical clocks. To this end, we demonstrate two-qubit entangling gates with 99.62(3)% fidelity—averaged over symmetric input states—through Rydberg interactions15,17,18 and dynamical connectivity19 for optical clock qubits, which we combine with local addressing16 to implement universally programmable quantum circuits. Using this approach, we generate a near-optimal entangled probe state1,4, a cascade of Greenberger–Horne–Zeilinger states of different sizes, and perform a dual-quadrature5 Greenberger–Horne–Zeilinger read-out. We also show repeated fast phase detection with non-destructive conditional reset of clock qubits and minimal dead time between repetitions by implementing ancilla-based quantum logic spectroscopy20 for neutral atoms. Finally, we extend this to multi-qubit parity checks and measurement-based, heralded, Bell-state preparation21–24. Our work lays the foundation for hybrid processor–clock devices with neutral atoms and more generally points to a future of practical applications for quantum processors linked with quantum sensors25.

Joint Decoding Technique for Collision Resolution in Non-orthogonal Multiple Access Environment

Multiple access technologies have grown hand in hand from the first generation to the 5th Generation (5G) with both performance and quality improvement. Non-Orthogonal Multiple Access (NOMA) is the recent multiple access technology adopted in the 5G communication technology. Capacity requirements of wireless networks have grown to a large extent with the penetration of ultra-high-definition video transmission, Internet of Things (IoT), and virtual reality applications taking ground in the recent future. This paper develops the Physical Layer Network Coding (PNC) for collision resolution in a NOMA environment with two users. Traditionally NOMA uses Successive Interference Cancellation (SIC) for collision resolution. While additionally a decoding algorithm is added along with SIC to improve the performance of the collision resolution. MATLAB-based simulation is developed on the NOMA environment with two users using Viterbi coding, Low-Density Parity Check (LDPC), and Turbo coding. Performance parameters of Bit Error Rate (BER) and throughput are compared for these three algorithms. It is observed that the Turbo coding performed better among these three algorithms both in the BER and throughput. The BER obtained from the SIC- Turbo is found to be performing well with an increase of about 14% from the ordinary SIC implementation. The performance of the collision resolution has increased by 13% to 14% when joint decoding techniques are used and thus increasing the throughput of the NOMA paradigm.

A New Class of Braided Block Codes Constructed by Convolutional Interleavers

Parallel Concatenated Block (PCB) codes are conventionally represented as high-rate codes with low error correcting capability. To form a reliable and outstanding code, this paper presents a modification on the structure of PCB codes, which is accomplished by encoding some parity bits of one of their component codes. For the newly proposed code, named as the braided code, non-stuff bit-based convolutional interleavers are applied, aiming to minimize the design complexity while ensuring the proper permutations of the original message and selected parity bits. To precisely determine the error correcting capability, a tight bound for the minimum weight of braided code is presented. Additionally, further analyses are provided, which verify iterative decoding performance and the complexity of the constructed code. It is concluded that an outstanding braided code is formed by utilizing a reasonable number of iterations applied at its decoding processes, while maintaining its design complexity at a level similar to other well-known codes. The significant performance of short and long-length-based braided codes is evident in both waterfall and error floor regions.

Weight-Reduced Stabilizer Codes with Lower Overhead

Stabilizer codes are the most widely studied class of quantum error-correcting codes and form the basis of most proposals for a fault-tolerant quantum computer. A stabilizer code is defined by a set of parity-check operators, which are measured in order to infer information about errors that may have occurred. In typical settings, measuring these operators is itself a noisy process and the noise strength scales with the number of qubits involved in a given parity check, or its weight. Hastings has proposed a method for reducing the weights of the parity checks of a stabilizer code, though it has previously only been studied in the asymptotic regime. Here, we instead focus on the regime of small to medium-size codes suitable for quantum computing hardware. We both provide a fully explicit description of Hastings’s method and propose a substantially simplified weight-reduction method that is applicable to the class of quantum product codes. Our simplified method allows us to reduce the check weights of hypergraph- and lifted-product codes to at most six, while preserving the number of logical qubits and at least retaining (in fact, often increasing) the code distance. The price we pay is an increase in the number of physical qubits by a constant factor but we find that our method is much more efficient than Hastings’s method in this regard. We benchmark the performance of our codes on a simulated photonic quantum computing architecture based on Gottesman-Kitaev-Preskill qubits and passive linear optics, finding that our weight-reduction method substantially improves code performance. Published by the American Physical Society 2024

Pressure-Tuned Quantum Criticality in the Locally Noncentrosymmetric Superconductor CeRh_{2}As_{2}.

The unconventional superconductor CeRh_{2}As_{2} (critical temperature T_{c}≈0.4 K) displays an exceptionally rare magnetic-field-induced transition between two distinct superconducting (SC) phases, proposed to be states of even and odd parity of the SC order parameter, which are enabled by a locally noncentrosymmetric structure. The superconductivity is preceded by a phase transition of unknown origin at T_{0}=0.5 K. Electronic low-temperature properties of CeRh_{2}As_{2} show pronounced non-Fermi-liquid behavior, indicative of a proximity to a quantum critical point (QCP). The role of quantum fluctuations and normal state orders for the superconductivity in a system with staggered Rashba interaction is currently an open question, pertinent to explaining the occurrence of the two-phase superconductivity. In this work, using measurements of resistivity and specific heat under hydrostatic pressure, we show that the T_{0} order vanishes completely at a modest pressure of P_{0}≈0.5 GPa, revealing a QCP. In line with the quantum criticality picture, the linear temperature dependence of the resistivity at P_{0} evolves into a Fermi-liquid quadratic dependence as quantum critical fluctuations are suppressed by increasing pressure. Furthermore, the domelike behavior of T_{c} around P_{0} implies that the fluctuations of the T_{0} order are involved in the SC pairing mechanism.

Enhancing Quantum Key Distribution Protocols for Extended Range and Reduced Error

Abstract this paper proposes an optimized Quantum Key Distribution (QKD) protocol using entanglement swapping techniques to extend transmission range and improve error correction. Additionally, integrates an advanced error correction technique which is Low Density Parity Check (LDPC) and multi-hop quantum repeaters for more enhancement of the protocol performance. Hybrid Quantum Classical Error Correction Methods is applied ensuring compatibility and optimal performance and to manage the increased complexity. Simulations prove that 25% improvement in transmission distance with entanglement swapping. 50% improvement with advanced error correction and a 100% improvement with multi-hop quantum repeaters compared to existing protocols. These discoveries are supported by both theoretical analysis and simulation results, indicating significant decreases in error rates and extensions in maximum transmission distances. Comparative analysis made with existing protocols and that demonstrated the superiority of proposed approach in terms of extended secure communication distance, higher key generation rate and improved resilience to attacks.

Comparing structures of two-dimensional error correction codes

Advances in integrated circuit production technologies have reduced device sizes, leading to corresponding scaling in electrical characteristics, such as threshold voltage. This scaling has increased the susceptibility of devices to electromagnetic radiation, raising the bitflip probability. Systems requiring a certain level of fault tolerance employ techniques like Error Correction Codes (ECC), providing a degree of reliability in mitigating this issue. The error correction and detection efficacies and ECC scalability vary based on the encoding and codestruct employed. This study employs four Hamming and parity code organizations for performing four Two-Dimensional (2D)-ECCs (N × 4p, N × ExHam, N × Ham_p, and N × Ham2_2p). We investigated the scalability, synthesis results, and correction and detection rates employing the same number of check and data bits for the four 2D-ECCs. The results point to the advantages for ECCs that employ cross-checking using radiation-hardened memories for checkbits, especially when ECCs scale to large codestructs.

Spin-Degeneracy Breaking and Parity Transitions in Three-Terminal Josephson Junctions

Hybrid Josephson junctions (JJs) realized in superconductor-semiconductor heterostructures host fermionic modes known as Andreev bound states (ABSs). In these structures, a promising and yet unexplored avenue for harnessing spin and parity degrees of freedom is offered by JJs with three or more superconducting terminals, where phase-induced spin polarization and transitions of the ground state to an odd parity were predicted to arise. Here we spectroscopically probe the two-dimensional band structure of ABSs in a phase-controlled InAs/Al three-terminal JJ. Andreev bands show signatures of spin-degeneracy breaking, with level splitting in excess of ∼9 GHz, and zero-energy crossings associated to ground state fermion parity transitions. Spin splitting and parity transitions are enabled and controlled by locally applied magnetic fluxes, in the absence of Zeeman effect or Coulomb blockade. Our results underscore the potential of multiterminal hybrid devices for phase engineering ABSs, with significant implications for spin- and parity-based quantum devices. Published by the American Physical Society 2024