scholarly journals TWO-DIMENSIONAL ERROR CONTROL BASED ON MODULAR CORRECTIVE CODES

2015 ◽  
pp. 208-215
Author(s):  
Jürgen Sieck ◽  
Vasyl Yatskiv ◽  
Anatoly Sachenko ◽  
Taras Tsavolyk
Keyword(s):  
Error Correction ◽  
Error Control ◽  
Data Matrix ◽  
Two Dimensional ◽  
Dimensional Error ◽  
Matrix Coefficients ◽  
Quartus Ii

The paper presents a method of detecting and correcting packet errors in the block of data based on the modular corrective codes. Check symbols are calculated separately in rows and columns of the data matrix. Herewith, the same data matrix coefficients are used for calculating the check symbols in rows and columns. This allows the detection and correction of errors packets that are in the same row or column. When two or more distorted information symbols are in the same row (assuming that there is only one error in the column) then errors can be corrected through the analysis of the column syndrome. The possible cases of the distorted symbols placement in a block of data and ways of their fixing are considered. The algorithm for detecting and correcting errors packets is elaborated. In the general case the offered method of error correction, based on modular correcting code, provides a correction of: n errors, which are in the same row or column of the data matrix of n size; 2*n-1 errors that are in the same row and column. The proposed method of encoding / decoding is designed in Verilog and implemented on FPGA in the Quartus II of Altera company.

scholarly journals Exponential suppression of bit or phase errors with cyclic error correction

Nature ◽  
2021 ◽  
Vol 595 (7867) ◽  
pp. 383-387
Author(s):  
◽  
Zijun Chen ◽  
Kevin J. Satzinger ◽  
Juan Atalaya ◽  
Alexander N. Korotkov ◽  
...  
Keyword(s):  
Error Correction ◽  
Error Detection ◽  
Fault Tolerant ◽  
Error Rates ◽  
Quantum Error Correction ◽  
Superconducting Qubits ◽  
Two Dimensional ◽  
Logical Error ◽  
Quantum Error ◽  
Logical Qubit

AbstractRealizing the potential of quantum computing requires sufficiently low logical error rates1. Many applications call for error rates as low as 10−15 (refs. 2–9), but state-of-the-art quantum platforms typically have physical error rates near 10−3 (refs. 10–14). Quantum error correction15–17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device18,19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits.

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

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 122
Author(s):  
Svitlana Matsenko ◽  
Oleksiy Borysenko ◽  
Sandis Spolitis ◽  
Aleksejs Udalcovs ◽  
Lilita Gegere ◽  
...  
Keyword(s):  
Error Correction ◽  
Error Detection ◽  
Optical Interconnects ◽  
Error Control ◽  
Forward Error Correction ◽  
Golden Ratio ◽  
Probability Method ◽  
Additional Error ◽  
Hardware Costs ◽  
Forward Error

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.

scholarly journals Dual weighted residual error estimation for the finite cell method

2019 ◽  
Vol 27 (2) ◽  
pp. 101-122 ◽  
Author(s):  
Paolo Di Stolfo ◽  
Andreas Rademacher ◽  
Andreas Schröder
Keyword(s):  
Error Estimation ◽  
Error Control ◽  
Combined Treatment ◽  
Adaptive Strategy ◽  
Two Dimensional ◽  
Weighted Residual Method ◽  
Finite Cell Method ◽  
Cell Method ◽  
Quadrature Error ◽  
Finite Cell

Abstract The paper presents a goal-oriented error control based on the dual weighted residual method (DWR) for the finite cell method (FCM), which is characterized by an enclosing domain covering the domain of the problem. The error identity derived by the DWR method allows for a combined treatment of the discretization and quadrature error introduced by the FCM. We present an adaptive strategy with the aim to balance these two error contributions. Its performance is demonstrated for several two-dimensional examples.

TWO-DIMENSIONAL VISUALIZATION OF THE PROPAGATION SPEED OF CORTICAL SPREADING DEPRESSION IN RAT CORTEX

2010 ◽  
Vol 03 (01) ◽  
pp. 75-80
Author(s):  
TINGTING XU ◽  
PENGCHENG LI ◽  
SHANGBIN CHEN ◽  
WEIHUA LUO
Keyword(s):  
Cortical Spreading Depression ◽  
Spreading Depression ◽  
Time Lag ◽  
Polar Angle ◽  
Propagation Speed ◽  
Least Square ◽  
Data Matrix ◽  
Radial Coordinate ◽  
Two Dimensional ◽  
Polar Coordinate

Cortical spreading depression (CSD), which is a significant pathological phenomenon that correlates with migraines and cerebral ischemia, has been characterized by a wave of depolarization among neuronal cells and propagates across the cortex at a rate of 2–5 mm/min. Although the propagation pattern of CSD was well-investigated using high-resolution optical imaging technique, the variation of propagation speed of CSD across different regions of cortex was not well-concerned, partially because of the lack of ideal approach to visualize two-dimensional distribution of propagation speed of CSD over the whole imaged cortex. Here, we have presented a method to compute automatically the propagation speed of CSD throughout every spots in the imaged cortex. In this method, temporal clustering analysis (TCA) and least square estimation (LSE) were first used to detect origin site where CSD was induced. Taking the origin site of CSD as the origin of coordinates, the data matrix of each image was transformed into the corresponding points based on the polar-coordinate representation. Then, two fixed-distance regions of interest (ROIs) are sliding along with the radial coordinate at each polar angle within the image for calculating the time lag with correlating algorithm. Finally, we could draw a two-dimensional image, in which the value of each pixel represented the velocity of CSD when it spread through the corresponding area of the imaged cortex. The results demonstrated that the method can reveal the heterogeneity of propagation speed of CSD in the imaged cortex with high fidelity and intuition.

Practical Dimensional Error Control and Surface Roughness Inspection in Turning

2002 ◽  
Author(s):  
M. Shiraishi ◽  
T. Yamagiwa ◽  
A. Ito
Keyword(s):  
Surface Roughness ◽  
Optical Method ◽  
Machine Tools ◽  
Error Control ◽  
Manufacturing Processes ◽  
Dimensional Error ◽  
Final Output

Monitoring of machine tools and optimization of manufacturing processes require accurate values of in process measured quantities such as dimensional error, force, and surface roughness. The measurement as workpiece is in particular important because the final output in machining is evaluated as the quality machined workpiece itself. A new hybrid sensor using pneumatic and optical method has been developed which can monitor the dimensional error and surface roughness in turning. Satisfactory results were obtained through several experiments.

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