Local Error Detection Research Articles

Locally Testable and Locally Correctable Codes approaching the Gilbert-Varshamov Bound

One of the most important open problems in the theory of error-correcting codes is to determine the tradeoff between the rate $R$ and minimum distance $\delta $ of a binary code. The best known tradeoff is the Gilbert–Varshamov bound, and says that for every $\delta \in (0, 1/2)$ , there are codes with minimum distance $\delta $ and rate $R = {R_{\mathsf {GV}}}(\delta) > 0$ (for a certain simple function ${R_{\mathsf {GV}}}(\cdot)$ ). In this paper, we show that the Gilbert–Varshamov bound can be achieved by codes, which support local error-detection and error-correction algorithms. Specifically, we show the following results. 1) Local testing: for all $\delta \in (0,1/2)$ and all $R , there exist codes with length $n$ , rate $R$ , and minimum distance $\delta $ that are locally testable with $\mathsf {quasipolylog}(n)$ query complexity. 2) Local correction: for all $\epsilon > 0$ , for all $\delta sufficiently large, and all $R , there exist codes with length $n$ , rate $R$ , and minimum distance $\delta $ that are locally correctable from $({\delta }/{2}) - o(1)$ fraction errors with $O(n^{\epsilon })$ query complexity. Furthermore, these codes have an efficient randomized construction, and the local testing and local correction algorithms can be made to run in time polynomial in the query complexity. Our results on locally correctable codes also immediately give locally decodable codes with the same parameters. Our local testing result is obtained by combining Thommesen’s random concatenation technique and the best known locally testable codes by Kopparty et al. Our local correction result, which is significantly more involved, also uses random concatenation, along with a number of further ideas: the Guruswami–Sudan–Indyk list decoding strategy for concatenated codes, Alon–Edmonds–Luby distance amplification, and the local list-decodability, local list-recoverability, and local testability of Reed–Muller codes. Curiously, our final local correction algorithms go via local list-decoding and local testing algorithms; this seems to be the first time local testability is used in the construction of a locally correctable code.

Accurate template‐based modeling in CASP12 using the IntFOLD4‐TS, ModFOLD6, and ReFOLD methods

Our aim in CASP12 was to improve our Template-Based Modeling (TBM) methods through better model selection, accuracy self-estimate (ASE) scores and refinement. To meet this aim, we developed two new automated methods, which we used to score, rank, and improve upon the provided server models. Firstly, the ModFOLD6_rank method, for improved global Quality Assessment (QA), model ranking and the detection of local errors. Secondly, the ReFOLD method for fixing errors through iterative QA guided refinement. For our automated predictions we developed the IntFOLD4-TS protocol, which integrates the ModFOLD6_rank method for scoring the multiple-template models that were generated using a number of alternative sequence-structure alignments. Overall, our selection of top models and ASE scores using ModFOLD6_rank was an improvement on our previous approaches. In addition, it was worthwhile attempting to repair the detected errors in the top selected models using ReFOLD, which gave us an overall gain in performance. According to the assessors' formula, the IntFOLD4 server ranked 3rd/5th (average Z-score > 0.0/-2.0) on the server only targets, and our manual predictions (McGuffin group) ranked 1st/2nd (average Z-score > -2.0/0.0) compared to all other groups.

Timing Error Tolerance in Small Core Designs for SoC Applications

Timing errors are an increasing reliability concern in nanometer technology, high complexity and multi-voltage\frequency integrated circuits. A local error detection and correction technique is presented in this work that is based on a new bit flipping flip-flop. Whenever a timing error is detected, it is corrected by complementing the output of the corresponding flip-flop. The proposed solution is characterized by very low silicon area and power requirements compared to previous design schemes in the open literature. To validate its efficiency, it has been applied in the design of a MIPS microprocessor core in a 90 nm technology, while a demonstration version of the same core in an FPGA platform is presented.

Using Multicriteria Plan Quality Metrics to Perform an Objective, Retrospective Analysis of Complex Head and Neck Plan Quality Differences Between Different VMAT Vendors

Purpose/Objective(s): To determine if x-ray projection radiation therapy setup images could be used to perform patient identification and detect gross errors in patient setup using a computer algorithm. Materials/Methods: Three patient cohorts treated using a commercially available image guided radiation therapy (IGRT) system were retrospectively analyzed: a group of 100 cranial radiation therapy patients, a group of 100 prostate cancer patients, and a group of 83 patients treated for spinal lesions. In the prostate and cranial patient groups, localizations using image registration were performed between computed tomography (CT) images from radiation therapy planning and setup x-ray images both corresponding to the same patient, and corresponding to different patients. For the group of spinal patients, localizations were performed to the correct vertebral body, and to vertebral bodies off by one from the correct body, using planning CTs and setup x-rays from the same patient. An image similarity measure used by the image registration algorithm of the IGRT system was recorded from the log files of the IGRT system and evaluated as a discriminant for error detection. Results: A threshold value of the similarity measure could be chosen to separate correct and incorrect patient matches and correct and incorrect vertebral body localizations with excellent accuracy for these patient cohorts. A 10-fold cross-validation using linear discriminant analysis yielded misclassification probabilities of 0.000, 0.0045, and 0.014 for the cranial, prostate, and spinal cases respectively. Conclusions: An automated measure of the image similarity between x-ray setup images and corresponding planning CT images could be used to perform automated patient identification and detection of localization errors in radiation therapy treatments. Author Disclosure: J.M. Lamb: None. N. Agazaryan: None. D.A. Low: None.

Automated Patient Identification and Localization Error Detection Using 2-Dimensional to 3-Dimensional Registration of Kilovoltage X-Ray Setup Images

To determine whether kilovoltage x-ray projection radiation therapy setup images could be used to perform patient identification and detect gross errors in patient setup using a computer algorithm. Three patient cohorts treated using a commercially available image guided radiation therapy (IGRT) system that uses 2-dimensional to 3-dimensional (2D-3D) image registration were retrospectively analyzed: a group of 100 cranial radiation therapy patients, a group of 100 prostate cancer patients, and a group of 83 patients treated for spinal lesions. The setup images were acquired using fixed in-room kilovoltage imaging systems. In the prostate and cranial patient groups, localizations using image registration were performed between computed tomography (CT) simulation images from radiation therapy planning and setup x-ray images corresponding both to the same patient and to different patients. For the spinal patients, localizations were performed to the correct vertebral body, and to an adjacent vertebral body, using planning CTs and setup x-ray images from the same patient. An image similarity measure used by the IGRT system image registration algorithm was extracted from the IGRT system log files and evaluated as a discriminant for error detection. A threshold value of the similarity measure could be chosen to separate correct and incorrect patient matches and correct and incorrect vertebral body localizations with excellent accuracy for these patient cohorts. A 10-fold cross-validation using linear discriminant analysis yielded misclassification probabilities of 0.000, 0.0045, and 0.014 for the cranial, prostate, and spinal cases, respectively. An automated measure of the image similarity between x-ray setup images and corresponding planning CT images could be used to perform automated patient identification and detection of localization errors in radiation therapy treatments.

Construction of explicit runge-kutta pairs with stiffness detection

Explicit Runge-Kutta schemes are the methods of choice for solving nonstiff systems of ordinary differential equations at low to medium tolerances. The construction of optimal formulae has been the subject of much research. In this article, it will be shown how to construct some low order formula pairs using tools from computer algebra. Our focus will be on methods that are equipped with local error detection (for adaptivity in the step size) and with the ability to detect stiffness. It will be demonstrated how criteria governing ‘optimal’ tuning of free parameters and matching of the embedded method can be accomplished by forming a constrained optimization problem. In contrast to standard numerical optimization processes our approach finds an exact (infinite precision) global minimum. Quantitative measures will be given comparing our new methods with some established formula pairs.

Is it necessary to repeat quality control procedures for head and neck patients?

Using serial verification films for detection of localization errors and in vivo measurements of the delivered dose, a comparison was made of the information obtained from a single check on the first treatment session or from repeated checks in subsequent irradiations, leading to an assessment of the predictive value of a single check. A total number of 215 films and 261 entrance dose measurements have been performed on 34 fields for 10 head and neck patients. The patients are immobilized with individual plastic masks fixed on the couch and treated on a 6 MV linac, supplied with an automatic verification system excluding the couch parameters. The global results show Gaussian frequency distributions with standard deviations of 4 mm for port film measurements and 3.4% for the dose measurements. Large errors (> 5 mm displacement and > 4 % deviation from the expected dose) have been detected in 16% in the cranio-caudal direction and 24% in the antero-posterior direction with port films and in 15 % of the in vivo measurements. In order to identify the nature of the errors, which can be random or systematic, the first measurement is taken as the reference value and shows that consecutive measurements on the same field were reproducible with standard deviations of respectively 2.5 mm and 1.8 %. This means that a large part of the spread of the global results can be explained by systematic errors in the treatment preparation chain. With the first check, 6 out of 10 systematic localization errors and 7 out of 7 systematic errors leading to erroneous dose delivery have been detected. Therefore, most of the systematic errors, which affect the overall quality of the treatment, can be identified with the first check. The four systematic localization errors, missed with the first film, were of rather limited size: only one of them showed a mean displacement larger than 7 mm. Because the first measurement is an acceptable indication of the overall quality of the treatment delivery, the authors propose a code of practice for checking the treatment quality at the patient level.

Weekly verification films and the detection of localization errors

Weekly verification films and the detection of localization errors

Localization error in the radiotherapy of Hodgkin's disease and malignant lymphoma with extended mantle fields.

In a review of 902 treatment verification films for 99 lymphoma patients receiving radiation therapy with extended mantle fields, 330 localization errors were detected. We found that 50% of the localization errors occurred in the axillae and that the axillae were the sites of most frequent clustering and recurrence. These facts suggest that localization errors caused sufficient reduction in dose to explain the recurrence of lymphoma in the axillae of several patients. Technical modifications of the blocks in relation to the axillae are discussed. Of 10 patients with local recurrence of Hodgkin's disease or malignant lymphoma, 2 had enough documented localization errors at the site of recurrence to account for a dose reduction sufficient to explain the recurrence. For the remaining 8 cases, we lacked sufficient films to determine the incidence of localization errors and thus to make estimates of reductions in dose. We observed a reduction of localization errors from 55% to 29% over the last 2 years of the study. This gratifying result is best explained by technical refinements and by the increased use of treatment verification films. On the basis of the data gathered in this study, we feel that treatment verification films are invaluable in the detection of localization errors in the treatment of lymphoma, and that they can lead to a reduction in localization errors if they are used regularly.