Error Detection and Error Correction

2009 ◽  
pp. 699-743
Keyword(s):  
Error Correction ◽  
Error Detection

scholarly journals Artificial Neural Network Assisted Error Correction for MLC NAND Flash Memory

Micromachines ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 879
Author(s):  
Ruiquan He ◽  
Haihua Hu ◽  
Chunru Xiong ◽  
Guojun Han
Keyword(s):  
Neural Network ◽  
Error Correction ◽  
Error Detection ◽  
Flash Memory ◽  
Nand Flash ◽  
Data Reliability ◽  
Nand Flash Memory ◽  
Process Technology ◽  
Noise Mitigation ◽  
Memory Channel

The multilevel per cell technology and continued scaling down process technology significantly improves the storage density of NAND flash memory but also brings about a challenge in that data reliability degrades due to the serious noise. To ensure the data reliability, many noise mitigation technologies have been proposed. However, they only mitigate one of the noises of the NAND flash memory channel. In this paper, we consider all the main noises and present a novel neural network-assisted error correction (ANNAEC) scheme to increase the reliability of multi-level cell (MLC) NAND flash memory. To avoid using retention time as an input parameter of the neural network, we propose a relative log-likelihood ratio (LLR) to estimate the actual LLR. Then, we transform the bit detection into a clustering problem and propose to employ a neural network to learn the error characteristics of the NAND flash memory channel. Therefore, the trained neural network has optimized performances of bit error detection. Simulation results show that our proposed scheme can significantly improve the performance of the bit error detection and increase the endurance of NAND flash memory.

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 Lookup Table Algorithm for Error Correction in Color Images

2018 ◽  
Vol 2 (2) ◽  
pp. 63
Author(s):  
Ruaa Alaadeen Abdulsattar ◽  
Nada Hussein M. Ali
Keyword(s):  
Error Correction ◽  
Error Detection ◽  
Color Image ◽  
Color Images ◽  
Lookup Table ◽  
Hamming Code ◽  
Detection Techniques ◽  
Error Ratio ◽  
Error Detection And Correction ◽  
Large Burst

Error correction and error detection techniques are often used in wireless transmission systems. A color image of type BMP is considered as an application of developed lookup table algorithms to detect and correct errors in these images. Decimal Matrix Code (DMC) and Hamming code (HC) techniques were integrated to compose Hybrid Matrix Code (HMC) to maximize the error detection and correction. The results obtained from HMC still have some error not corrected because the redundant bits added by Hamming codes to the data are considered inadequate, and it is suitable when the error rate is low for detection and correction processes. Besides, a Hamming code could not detect large burst error period, in addition, the have same values sometimes which lead to not detect the error and consequently increase the error ratio. The proposed algorithm LUT_CORR is presented to detect and correct errors in color images over noisy channels, the proposed algorithm depends on the parallel Cyclic Redundancy Code (CRC) method that's based on two algorithms: Sarwate and slicing By N algorithms. The LUT-CORR and the aforementioned algorithms were merged to correct errors in color images, the output results correct the corrupted images with a 100 % ratio almost. The above high correction ratio due to some unique values that the LUT-CORR algorithm have. The HMC and the proposed algorithm applied to different BMP images, the obtained results from LUT-CORR are compared to HMC for both Mean Square Error (MSE) and correction ratio.  The outcome from the proposed algorithm shows a good performance and has a high correction ratio to retrieve the source BMP image.

scholarly journals Proposal of an Adaptive Fault Tolerance Mechanism to Tolerate Intermittent Faults in RAM

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2074
Author(s):  
J.-Carlos Baraza-Calvo ◽  
Joaquín Gracia-Morán ◽  
Luis-J. Saiz-Adalid ◽  
Daniel Gil-Tomás ◽  
Pedro-J. Gil-Vicente
Keyword(s):  
Fault Tolerance ◽  
Error Correction ◽  
Error Detection ◽  
Fault Injection ◽  
Error Correction Codes ◽  
Transient Faults ◽  
Tolerance Mechanism ◽  
Intermittent Faults ◽  
Risc Processor ◽  
Simulation Based

Due to transistor shrinking, intermittent faults are a major concern in current digital systems. This work presents an adaptive fault tolerance mechanism based on error correction codes (ECC), able to modify its behavior when the error conditions change without increasing the redundancy. As a case example, we have designed a mechanism that can detect intermittent faults and swap from an initial generic ECC to a specific ECC capable of tolerating one intermittent fault. We have inserted the mechanism in the memory system of a 32-bit RISC processor and validated it by using VHDL simulation-based fault injection. We have used two (39, 32) codes: a single error correction–double error detection (SEC–DED) and a code developed by our research group, called EPB3932, capable of correcting single errors and double and triple adjacent errors that include a bit previously tagged as error-prone. The results of injecting transient, intermittent, and combinations of intermittent and transient faults show that the proposed mechanism works properly. As an example, the percentage of failures and latent errors is 0% when injecting a triple adjacent fault after an intermittent stuck-at fault. We have synthesized the adaptive fault tolerance mechanism proposed in two types of FPGAs: non-reconfigurable and partially reconfigurable. In both cases, the overhead introduced is affordable in terms of hardware, time and power consumption.

scholarly journals Error Detection and Correction On-Board Nanosatellites Using Hamming Codes

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Caleb Hillier ◽  
Vipin Balyan
Keyword(s):  
Error Correction ◽  
Error Detection ◽  
Simulation Software ◽  
Hamming Code ◽  
Single Event ◽  
Hamming Codes ◽  
Single Event Effects ◽  
Effective Version ◽  
Fast Speed ◽  
Error Detection And Correction

The field of nanosatellites is constantly evolving and growing at a very fast speed. This creates a growing demand for more advanced and reliable EDAC systems that are capable of protecting all memory aspects of satellites. The Hamming code was identified as a suitable EDAC scheme for the prevention of single event effects on-board a nanosatellite in LEO. In this paper, three variations of Hamming codes are tested both in Matlab and VHDL. The most effective version was Hamming [16, 11, 4]2. This code guarantees single-error correction and double-error detection. All developed Hamming codes are suited for FPGA implementation, for which they are tested thoroughly using simulation software and optimized.

Ultrafast Error Correction Codes for Double Error Detection/Correction

2016 ◽  
Author(s):  
Luis-J. Saiz-Adalid ◽  
Pedro Gil ◽  
Juan-Carlos Ruiz ◽  
Joaquin Gracia-Moran ◽  
Daniel Gil-Tomas ◽  
...  
Keyword(s):  
Error Correction ◽  
Error Detection ◽  
Error Correction Codes
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