Search results for "error detection"
showing 10 items of 39 documents
Overview of Other Results and Open Problems
2014
This chapter presents an overview of results related to error control methods, which were not considered in previous chapters. In the first part, we discuss possible extensions of the theory exposed in Chaps. 3 and 4 to nonconforming approximations and certain classes of nonlinear problems. Also, we shortly discuss some results related to explicit evaluation of modeling errors. The remaining part of the chapter is devoted to a posteriori estimates of errors in iteration methods. Certainly, the overview is not complete. A posteriori error estimation methods are far from having been fully explored and this subject contains many unsolved problems and open questions, some of which we formulate …
Data Compression with ENO Schemes: A Case Study
2001
Abstract We study the compresion properties of ENO-type nonlinear multiresolution transformations on digital images. Specific error control algorithms are used to ensure a prescribed accuracy. The numerical results reveal that these methods strongly outperform the more classical wavelet decompositions in the case of piecewise smooth geometric images.
An optimal code for patient identifiers.
2004
How to distinguish 1 billion individuals by an identifier consisting of eight characters, allowing a reasonable amount of error detection or even error correction? Our solution of this problem is an optimal code over a 32-character alphabet that detects up to two errors and corrects one error as well as a transposition of two adjacent characters. The corresponding encoding and error checking algorithms are available for free; they are also embedded as components of the pseudonymisation service that is used in the TMF-the German telematics platform for health research networks.
Syntax Error Handling
1990
In the previous chapters we have seen that the various parsers discussed, at least whenever they are deterministic, detect an error in any nonsentence. This means, that on any nonsentence there is a computation ending with an error configuration. For practical parsers, mere error detection is not enough; the parser should also emit a meaningful error message and recover from the error. A recovery means that the error configuration is transformed into a non-error configuration at which normal parsing can be resumed. Moreover, the transformation should be done so that as few input symbols as possible will be discarded. The goal of the error recovery is to maximize the amount of input text tha…
Neutron-induced soft errors in advanced Flash memories
2008
Atmospheric neutrons are a known source of Soft Errors (SE), in static and dynamic CMOS memories. This paper shows for the first time that atmospheric neutrons are able to induce SE in Flash memories as well. Detailed experimental results provide an explanation linking the Floating Gate (FG) cell SE rate to the physics of the neutron-matter interaction. The neutron sensitivity is expected to increase with the number of bits per cell and the reduction of the feature size, but the SE issue is within the limit of current ECC capabilities and will remain so in the foreseeable future.
Approximate quantum error correction for generalized amplitude damping errors
2014
We present analytic estimates of the performances of various approximate quantum error correction schemes for the generalized amplitude damping (GAD) qubit channel. Specifically, we consider both stabilizer and nonadditive quantum codes. The performance of such error-correcting schemes is quantified by means of the entanglement fidelity as a function of the damping probability and the non-zero environmental temperature. The recovery scheme employed throughout our work applies, in principle, to arbitrary quantum codes and is the analogue of the perfect Knill-Laflamme recovery scheme adapted to the approximate quantum error correction framework for the GAD error model. We also analytically re…
Entanglement production by quantum error correction in the presence of correlated environment
2003
We analyze the effect of a quantum error correcting code on the entanglement of encoded logical qubits in the presence of a dephasing interaction with a correlated environment. Such correlated reservoir introduces entanglement between physical qubits. We show that for short times the quantum error correction interprets such entanglement as errors and suppresses it. However for longer time, although quantum error correction is no longer able to correct errors, it enhances the rate of entanglement production due to the interaction with the environment.
A Perturbative Approach to Continuous-Time Quantum Error Correction
2014
We present a novel discussion of the continuous-time quantum error correction introduced by Paz and Zurek in 1998 [Paz and Zurek, Proc. R. Soc. A 454, 355 (1998)]. We study the general Lindbladian which describes the effects of both noise and error correction in the weak-noise (or strong-correction) regime through a perturbative expansion. We use this tool to derive quantitative aspects of the continuous-time dynamics both in general and through two illustrative examples: the 3-qubit and the 5-qubit stabilizer codes, which can be independently solved by analytical and numerical methods and then used as benchmarks for the perturbative approach. The perturbatively accessible time frame featur…
On strongly tactical codes
1986
We study perfect error correcting codes in which the codewords are protected by Hamming spheres of distinct protective radii. These codes have been introduced by Cohen, Montaron and Frankl [3, 4, 10].
CARE: context-aware sequencing read error correction.
2020
Abstract Motivation Error correction is a fundamental pre-processing step in many Next-Generation Sequencing (NGS) pipelines, in particular for de novo genome assembly. However, existing error correction methods either suffer from high false-positive rates since they break reads into independent k-mers or do not scale efficiently to large amounts of sequencing reads and complex genomes. Results We present CARE—an alignment-based scalable error correction algorithm for Illumina data using the concept of minhashing. Minhashing allows for efficient similarity search within large sequencing read collections which enables fast computation of high-quality multiple alignments. Sequencing errors ar…