Error Correction Techniques Research Articles

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.

A deep convolutional neural network for Blind element Error Correction of Spatial Heterodyne Spectrometer using line selective convolutional blocks

The "GF Special Project" is a massive remote sensing technology initiative including a number of satellites and various observation platforms. GF-5 is the satellite with the most payloads, the highest spectral resolution, and the most difficulty in development, and it can monitor a variety of environmental elements using spatial heterodyne spectroscopy (SHS) technology, including atmospheric aerosols, carbon dioxide, methane, terrestrial vegetation, straw burning, and urban heat islands. In this study, a novel blind element error correction technique based on deep learning network is investigated and developed for spatial heterodyne interferograms, as well as the formation mechanism and distribution characteristics of the SHS interferometric data. LSConv-Net, a new CNN model, was created and trained to denoise in the presence of high-density and ultra-high-density blind element errors. We do this by introducing a new line-selective convolutional (LSConv) block. Simultaneously, experimental validation of blind element error correction utilizing laboratory water vapor interferometric data and atmospheric CO2 absorption interferometric data from GF-5, and the change in FWHM before and after the experiment was tested using potassium lamp interferograms. Experiments show that the Deep neural networks trained with this model may successfully suppress the effect of blind element noise on spectra, recover spectra that have been overwhelmed by high-density blind element noise without any effect on other non-blind pixels, and surpass all similar techniques in terms of spectral recovery.

Macroeconomic stability and economic growth: Evidence from Bangladesh

This paper investigates the link and causal relationship between macroeconomic stability and economic growth in Bangladesh for the period 1971 through 2023. Cointegration, vector error correction technique, and the Granger causality test are applied for this purpose. The paper finds sufficient evidence that macroeconomic stability and economic growth are positively related with each other in the long run. Like the long-run relationship, government consumption and investment proxy are significant in the short-run among all the factors of stability while only government consumption and inflation show some causal relationship with growth. Thus, the results are suggestive of the fact that it is better to comment about factors of stability separately rather than macroeconomic stability as a whole. The results also emphasize evaluation of both the long-run and the short-run effects of macroeconomic stability separately for effective policymaking.

Integrating error correction and detection techniques in RISC-V processor microarchitecture for enhanced reliability

An essential consideration in processor design is ensuring reliability, particularly in demanding environments such as outer space and nuclear plants. To mitigate the effects of errors and enable error recovery, processors need to incorporate fault tolerance techniques. One common type of error is SEU (Single Event Upset), which affects various microelectronic devices including microprocessors, microcontrollers, and semiconductor memory devices. While error mitigation techniques have been developed for processors based on architectures like ARM (Advanced RISC Machine) and MIPS (Million Instructions Per Second), there is a gap in research for open-source ISAs (Instruction Set Architecture) like RISC-V, which this paper aims to address. This paper focuses on designing a fault-tolerant microarchitecture for a RISC-V processor that can correct one-bit errors, detect up to two-bit errors, and integrate lockstep and pipeline rollback features at a lower LUTs (Look Up Tables) consumption by re-using the same hardware pipeline for error mitigation and recovery through instruction mimicking. By incorporating these features, the proposed approach enhances the system’s fault tolerance by detecting and correcting errors caused by transient events and achieves a lower effective die size upon realization compared to contemporary works. The proposed microarchitecture design was simulated and synthesized using the Vivado Design Suite 2023.1 and implemented on a Zynq 7000 SoC ZC702 Evaluation Kit.

Correction‐enabled reversible data hiding with pixel repetition for high embedding rate and quality preservation

AbstractA novel correction‐enabled Pixel Repetition (PR)‐based Reversible Data Hiding (RDH) framework, featuring a new embedding scheme is presented. The proposed RDH scheme uses contextually redundant block pixels, generated via PR, in a two‐phase adaptive embedding process, enhancing both image quality and data embedding rates. Specifically, each block encodes 4 bits of data using new mapping conditions that facilitate seed pixel reconstruction from remaining block pixels and provide additional embedding opportunities. Additionally, an innovative post‐embedding error correction technique, based on ‐bit error‐correction, minimises post‐embedding distortion, further improving image quality. This error correction approach augments data embedding robustness, vital for applications like medical imaging, telemedicine, and digital watermarking that requires high embedding capacity with minimum possible distortion. The proposed scheme surpasses existing state‐of‐the‐art methods in embedding rate‐distortion performance, validated through subjective and objective analyses. Furthermore, statistical analysis, including histogram and fragility testing, confirms the scheme's potential for image authentication across diverse multimedia applications. The correction‐enabled RDH with PR offers enhanced embedding capacity and image quality preservation, making it particularly advantageous for applications requiring robust data hiding while maintaining visual fidelity.

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.

English grammar intelligent error correction technology based on the n-gram language model

Abstract With the development of the Internet, the number of electronic texts has increased rapidly. Automatic grammar error correction technology is an effective safeguard measure for the quality of electronic texts. To improve the quality of electronic text, this study introduces a moving window algorithm and linear interpolation smoothing algorithm to build a Cn-gram language model. On this basis, a syntactic analysis strategy is introduced to construct a syntactic error correction model integrating Cn-gram and syntactic analysis, and English grammar intelligent error correction is carried out through the model. The results show that compared with the Bi-gram and Tri-gram, the precision of the Cn-gram model is 0.85 and 0.91% higher, and the F1 value is 0.97 and 1.14% higher, respectively. Compared with the results of test set Long, the Cn-gram model has better performance on verb error correction of the Short test set, and the precision rate, recall rate, and F1 value are increased by 0.86, 3.94, and 1.87%, respectively. The comparison of the precision, recall rate, and F1 value of the proposed grammar error correction model on the complete test set shows that the precision of the study is 19.10 and 5.41% higher for subject–verb agreement errors. The recall rate is 9.55 and 10.77% higher, respectively; F1 values are higher by 12.65 and 10.59%, respectively. The above results show that the error-correcting technique of the research design has excellent error-correcting performance. It is hoped that this experiment can provide a reference for the relevant research of automatic error correction technology of electronic text.

Improved defect-correction algorithms for the Navier–Stokes equations at small viscosity

In this article, based on finite element discretization, we propose some improved defect-correction algorithms for solving the stationary Navier–Stokes equations with small viscosity. The proposed algorithms are mainly inspired by the idea of the grad-div stabilized method and error correction technique. Maintaining the benefit of the usual defect-correction method, the proposed algorithms further improve the ability to solve problems with small viscosity and have a fast convergence rate. Moreover, stability analysis and error estimation of these algorithms are provided under the uniqueness requirement. Finally, some numerical experiments are tested to illustrate the effectiveness of the presented algorithms for small viscosity problem.

Fault-Tolerant Operation of Bosonic Qubits with Discrete-Variable Ancillae

Fault-tolerant quantum computation with bosonic qubits often necessitates the use of noisy discrete-variable ancillae. In this work, we establish a comprehensive and practical fault-tolerance framework for such a hybrid system and synthesize it with fault-tolerant protocols by combining bosonic quantum error correction (QEC) and advanced quantum control techniques. We introduce essential building blocks of error-corrected gadgets by leveraging ancilla-assisted bosonic operations using a generalized variant of path-independent quantum control. Using these building blocks, we construct a universal set of error-corrected gadgets that tolerate a single-photon loss and an arbitrary ancilla fault for four-legged cat qubits. Notably, our construction requires only dispersive coupling between bosonic modes and ancillae, as well as beam-splitter coupling between bosonic modes, both of which have been experimentally demonstrated with strong strengths and high accuracy. Moreover, each error-corrected bosonic qubit is comprised of only a single bosonic mode and a three-level ancilla, featuring the hardware efficiency of bosonic QEC in the full fault-tolerant setting. We numerically demonstrate the feasibility of our schemes using current experimental parameters in the circuit-QED platform. Finally, we present a hardware-efficient architecture for fault-tolerant quantum computing by concatenating the four-legged cat qubits with an outer qubit code utilizing only beam-splitter couplings. Our estimates suggest that the overall noise threshold can be reached using existing hardware. These developed fault-tolerant schemes extend beyond their applicability to four-legged cat qubits and can be adapted for other rotation-symmetrical codes, offering a promising avenue toward scalable and robust quantum computation with bosonic qubits. Published by the American Physical Society 2024

A Hierarchical Priority Based Multi-Bit Error Tolerant Design for FPGA Configuration Memory

The reconfigurability of a field-programmable gate array (FPGA), which is utilized in many applications, permits changes to be made to an existing design. In hostile environments such as space, where radiation and ionizing particles increase the risk for failure and human maintenance is either impossible or time-consuming, this reconfigurable capability becomes even more important. Single event upsets (SEUs) and multi-bit upsets (MBUs) on configuration memory can cause soft errors and circuit malfunctions in SRAM-based field programmable gate arrays (FPGAs). The ever-increasing quantity of configuration bits in contemporary FPGAs makes it more difficult for traditional scrubbing to identify faults in a timely manner, leading to a mismatch between scrubbing performance and MBU sensitivity.A hierarchical multi-bit error correcting method fully utilizes the MBU sensitivity at various configuration frame locations. It employs distinct techniques for varying priorities and differentiates across configuration frames with multiple priorities. They divided code words into several sections and used distinct error-correction techniques in each section. In high radiation conditions, the suggested integrated error correction technique enhances FPGA configuration memory protection by substituting memory scrubbing. The suggested approach lowers total TTD and enables priority-based asynchronous MBU detection and correction. Index Terms—FPGA,MBU,Sensitivity,Configuration memory

Advancing cancer MRD monitoring through tumor whole-genome informed, duplex ctDNA sequencing.

e15044 Background: Circulating tumor DNA (ctDNA), a cell-free DNA (cfDNA) present in the plasma of cancer patients, originates from cancer cells and serves as a crucial biomarker during cancer treatment. Despite its importance, the current limit of detection (LoD) of conventional ctDNA assays is suboptimal (0.01%; 10-4) for detecting ctDNA from microscopic residual and recurrent cancer tissues. To address this, we integrated two cutting-edge techniques: whole-genome sequencing (WGS) of primary cancer tissue (a mutation capture step) and duplex DNA sequencing-based cfDNA sequencing (mutation recapture steps). Methods: Thirteen colorectal cancer patients participated in this study. Primary tumor tissues and matched normal blood tissues were collected for WGS in the mutation capture step, while plasma samples for cfDNA sequencing in the mutation recapture steps were obtained just prior to colorectal cancer surgery and 1-month post-surgery follow-up. Tumor DNA and germline DNA were analyzed using CancerVision, a CLIA-certified clinical-grade cancer WGS platform, in the mutation capture step. In the mutation recapture steps, somatically acquired mutations from the previous step were tracked in cfDNA samples using the Concatenating Original Duplex for Error Correction (CODEC) technique, a duplex DNA sequencing technique that examines both Watson and Crick strands of double-stranded DNA molecules to discern true mutations from sequencing noise. Results: The median WGS depth of tumor and germline tissues was 40x and 20x, respectively. The mean depth of cfDNA WGS with CODEC was 25x, with a median duplex sequencing rate of 70%. Overall, 4,828-301,434 somatic base substitutions (SBSs) per sample were discovered in the capture step. Four of the thirteen tumors exhibited hypermutator characteristics with microsatellite instability features. The CODEC technique demonstrated excellent capability in tracing cancer-specific mutations in cfDNA sequencing with a technical sequencing error rate of 4 x 10-7, defining the maximum technical LoD, which is 250-fold lower errors than conventional sequencing. In our sample cohort, tumor fractions in cfDNA sequencing were robustly estimated from 0.001% (10-5), below the LoD of conventional MRD methods. Conclusions: Our integration of tumor-WGS-informed duplex cfDNA sequencing methods significantly enhances the sensitivity of sequencing-based MRD assays, achieving a technical LoD limit of 10-7 for detecting ctDNA in cancer patients. These approaches represent a breakthrough in monitoring MRD in real-world cancer patients.

Hadamard Error-Correcting Codes and Their Application in Digital Watermarking.

In communication technologies such as digital watermarking, wireless sensor networks (WSNs), and visual light communication (VLC), error-correcting codes are crucial. The Enhanced Hadamard Error-Correcting Code (EHC), which is based on 2D Hadamard Basis Images, is a novel error correction technique that is presented in this study. This technique is used to evaluate the effectiveness of the video watermarking scheme. Even with highly sophisticated embedding techniques, watermarks usually fail to resist such comprehensive attacks because of the extraordinarily high compression rate of approximately 1:200 that is frequently employed in video dissemination. It can only be used in conjunction with a sufficient error-correcting coding method. This study compares the efficacy of the well-known Reed-Solomon Code with this novel technique, the Enhanced Hadamard Error-Correcting Code (EHC), in maintaining watermarks in embedded videos. The main idea behind this newly created multidimensional Enhanced Hadamard Error-Correcting Code is to use a 1D Hadamard decoding approach on the 2D base pictures after they have been transformed into a collection of one-dimensional rows. Following that, the image is rebuilt, allowing for a more effective 2D decoding procedure. Using this technique, it is possible to exceed the theoretical error-correcting capacity threshold of ⌊dmin-12⌋ bits, where dmin is the Hamming distance. It may be possible to achieve better results by converting the 2D EHC into a 3D format. The new Enhanced Hadamard Code is used in a video watermarking coding scheme to show its viability and efficacy. The original video is broken down using a multi-level interframe wavelet transform during the video watermarking embedding process. Low-pass filtering is applied to the video stream in order to extract a certain frequency range. The watermark is subsequently incorporated using this filtered section. Either the Reed-Solomon Correcting Code or the Enhanced Hadamard Code is used to protect the watermarks. The experimental results show that EHC far outperforms the RS Code and is very resilient against severe MPEG compression.

Creation of a Corneal Flap for Laser In Situ Keratomileusis Using a Three-Dimensional Femtosecond Laser Cut: Clinical and Optical Coherence Tomography Features

Laser in situ keratomileusis (LASIK) is the most frequently used technique for the surgical correction of refractive errors on the cornea. It entails the creation of a superficial hinged corneal flap using a femtosecond laser, ablation of the underlying stromal bed using an excimer laser, and repositioning of the flap. A corneal flap with an angled side cut reduces the risk of flap dislocation and infiltration of epithelial cells and confers unique biomechanical properties to the cornea. A new laser software creating three-dimensional (3D) flaps using a custom angle side cut was retrospectively evaluated, comparing optical coherence tomography 3D (with intended 90° side cut) and 2D flaps (with tapered side cuts) as well as respective intra- and early postoperative complications. Four hundred consecutive eyes were included, two hundred for each group. In the 3D group, the mean edge angle was 92°, and the procedure was on average 5.2 s slower (p = 0). Non-visually significant flap folds were found in thirteen eyes of the 2D group and in seven eyes of the 3D group (p = 0.17). In conclusion, the creation of a LASIK flap using a 3D femtosecond laser cut, although slightly slower, was safe and effective. The side cut angle was predictable and accurate.

Cointegration analysis of US space activity and its environmental impact

Space activities are known for releasing different kinds of pollutants into the atmosphere. This study employs cointegration and error-correction techniques to explore the environmental impacts of U.S. space activity over both short and long terms. The findings reveal a long-run relationship between space activity and the environment. In the short run, except for biocapacity, space activity shows no significant impact on the environment according to the error-correction model analysis. In the long run, noteworthy relationships emerge, such as the launch of objects correlating with an increased ecological footprint and a decline in ozone concentration, and both objects and space debris contributing to reduced ozone concentration. Specifically, the estimates indicate that a one-percent increase in launches increases footprint by 0.07%, whereas a one-percent increase in object launches and space debris reduces the ozone concentration by 2.231% and 0.499%, respectively. The impulse response functions analysis affirms a predominantly permanent negative impact of space activity on the environment, jeopardizing environmental sustainability. Additionally, two crucial breakeven points are identified: space debris initially increases (i.e. deteriorates) the ecological footprint for the first 9 years before permanently improving footprint, while it initially enhances the ozone concentration for about 6 years before causing a lasting detrimental effect on the ozone layer.

Adjustable random linear network coding (ARLNC): a solution for data transmission in dynamic IoT computational environments

In mobile computing environments, most IoT devices connected to networks experience variable error rates and possess limited bandwidth. The conventional method of retransmitting lost information during transmission, commonly used in data transmission protocols, increases transmission delay and consumes excessive bandwidth. To overcome this issue, forward error correction techniques, e.g., Random Linear Network Coding (RLNC) can be used in data transmission. The primary challenge in RLNC-based methodologies is sustaining a consistent coding ratio during data transmission, leading to notable bandwidth usage and transmission delay in dynamic network conditions. Therefore, this study proposes a new block-based RLNC strategy known as Adjustable RLNC (ARLNC), which dynamically adjusts the coding ratio and transmission window during runtime based on the estimated network error rate calculated via receiver feedback. The calculations in this approach are performed using a Galois field with the order of 256. Furthermore, we assessed ARLNC's performance by subjecting it to various error models such as Gilbert Elliott, exponential, and constant rates and compared it with the standard RLNC. The results show that dynamically adjusting the coding ratio and transmission window size based on network conditions significantly enhances network throughput and reduces total transmission delay in most scenarios. In contrast to the conventional RLNC method employing a fixed coding ratio, the presented approach has demonstrated significant enhancements, resulting in a 73% decrease in transmission delay and a 4 times augmentation in throughput. However, in dynamic computational environments, ARLNC generally incurs higher computational costs than the standard RLNC but excels in high-performance networks.

Advanced Secure Communication: Exploring Quantum Key Distribution, the BB84 Method

One promising way to use quantum information to secure everyday communication is through the distribution of quantum keys. By exchanging a secret key, the Quantum Key Distribution (QKD) approach allows two parties to communicate securely.BB84 protocol is among the most well-known QKD protocols. In this protocol, qubits are exchanged via a quantum channel between the sender and the receiver. This enables them to produce a shared key that is impenetrable to eavesdroppers and illustrate the fundamental ideas of QKD using current simulations and implementations. The results of this study demonstrate that the BB84 protocol is a highly secure QKD technique that has been investigated in great detail and used in a variety of contexts. Additionally, over the enhancements made to the BB84 protocol such as the use of advanced error correction techniques and decoy states to increase its security and usability is discussed. With an emphasis on the BB84 protocol in secure communication technologies, this study offers an extensive analysis of QKD systems overall.

The Influence of Nigeria's Level of Public Debt on the Country's Ability to Sustain Fiscal Stability

This research investigates the impact of public debt exposure on Nigeria's fiscal sustainability through an ex post facto research design. The study utilizes quarterly data from 1986 to 2021, comprising 36 data points sourced from the Central Bank of Nigeria (CBN) and World Bank databases. Employing descriptive statistics, unit root analysis, Johansen cointegration, and Vector Error Correction techniques, the analysis maintains a significance level of 5%. The model exhibits a satisfactory fit with an R-squared value of 0.67 and an Adjusted R-squared value of 0.65. Key factors, including the domestic debt to GDP ratio, external debt to GDP ratio, debt servicing to GDP ratio, economic growth, exchange rate, and interest rate, undergo evaluation for their impact on Nigeria's current account balance and budget deficit/surplus. The findings highlight the external debt to GDP ratio, debt servicing to GDP ratio, economic growth, exchange rate, and interest rate as primary determinants of Nigeria's fiscal responsibility. The study recommends several measures based on these findings. These include managing external debt effectively, prioritizing debt servicing, promoting economic growth, monitoring exchange rates and interest rates, strengthening debt management practices, diversifying revenue sources, enhancing budget discipline, and improving governance.

New quantum LDPC codes based on Euclidean Geometry

With the advancements in quantum error correction technique, quantum low density parity check (QLDPC) codes have emerged as a promising area in the field of quantum error correction. This paper focuses on the requirement of QLDPC codes based on points excluding the origin, and lines that do not pass through the origin of Euclidean Geometry. It also explores QLDPC codes based on all the points and lines. Finally, a series of simulation analyses are presented.

Physics-inspired and data-driven two-stage deep learning approach for wind field reconstruction with experimental validation

Accurate and reliable wind forecasts for urban blocks play a pivotal role in the construction of zero-energy communities by guiding the selection and placement of wind turbines and the aerodynamic design optimization of ducted openings. While relatively accurate wind fields are available based on numerical methods, their heavy computational cost and discontinuity make it necessary to explore an interactive and end-to-end method. In this study, we develop a physics-inspired and data-driven two-stage deep learning approach that can reconstruct complex wind fields precisely. The proposed method integrates a physical feature extraction model of the flow field with a sparse measurement data-driven error correction approach. In particular, a well-designed and well-trained flow field feature extraction model (original model) can preserve salient features of CFD modelling, while data-driven error correction techniques may harvest the uncertainty features and fill the remaining gaps between the original model predictions and the measured data. The proposed method is verified by a measured dataset from a community in Beijing. Experimental validation illustrates that the proposed algorithm successfully accomplishes wind field reconstruction in complex terrains using sparse datasets. We show that the proposed two-stage strategy exhibits significantly improved prediction results over the purely original method, with an average accuracy improvement of 47.17% and a maximum accuracy improvement of 72.59%. Overall, the proposed method delivers the potential in accurate wind field construction and urban wind energy forecasting.

Efficient VLSI Implementation of Hybrid LDPC-STBC Codes for Enhanced Satellite Communication Systems

Satellite communication systems play a pivotal role in facilitating global connectivity, necessitating the development of robust error correction codes to ensure reliable data transmission. In contemporary communication systems, the demand for higher data rates and improved spectral efficiency has led to the integration of advanced error correction techniques. However, existing systems often face challenges in striking a balance between complexity, power consumption, and performance. This work addresses the limitations of current systems by proposing a hybrid approach that combines the advantages of LDPC (Low-Density Parity-Check) codes and STBC (Space-Time Block Coding) techniques. The hybrid LDPC-STBC codes aim to enhance the error correction capabilities of satellite communication systems, ensuring robust data transmission in the presence of channel impairments. Despite the advancements in error correction coding, current systems encounter drawbacks such as increased computational complexity, higher power consumption, and potential performance degradation under adverse channel conditions. The proposed hybrid LDPC-STBC codes mitigate these issues by leveraging the strengths of both coding schemes, achieving a synergistic balance between error correction performance and computational efficiency.