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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 703 records · Page 39

A Study of Synchronization Techniques for Optical Communication Systems

The study of synchronization techniques and related topics in the design of high data rate, deep space, optical communication systems was reported. Data cover: (1) effects of timing errors in narrow pulsed digital optical systems, (2) accuracy of microwave timing systems operating in low powered optical systems, (3) development of improved tracking systems for the optical channel and determination of their tracking performance, (4) development of usable photodetector mathematical models for application to analysis and performance design in communication receivers, and (5) study application of multi-level block encoding to optical transmission of digital data.

Gagliardi, R. M.↗

Low-Speed Pressure Sensitive Paint Studies

A series of low speed (M less than 0.2) experiments using University of Washington Fib-07 Pressure Sensitive Paint (PSP) have been conducted at NASA Ames on a NACA 0012 airfoil. Significant improvements in results have been shown: PSP calibration errors of the improved data (with pressure taps as a reference) now agree with theoretical error limits. Additional measurements on the 0012 airfoil using Temperature Sensitive Paint have been made. These TSP measurements now fully quantify the impact of temporal temperature changes on model surfaces on PSP measurements. Finally, simultaneous PSP - TSP measurements have been performed, allowing in-situ temperature correction of PSP data with good results.

Owen, Brown↗

Errors in retarding potential analyzers caused by nonuniformity of the grid-plane potential.

One aspect of the degradation in performance of retarding potential analyzers caused by potential depressions in the retarding grid is quantitatively estimated from laboratory measurements and theoretical calculations. A simple expression is obtained that permits the use of laboratory measurements of grid properties to make first-order corrections to flight data. Systematic positive errors in ion temperature of approximately 16% for the Ogo 4 instrument and 3% for the Ogo 6 instrument are deduced. The effects of the transverse electric fields arising from the grid potential depressions are not treated.

Hanson, W. B.↗

One way and two way VHF ranging system performance for tracking and data relay applications

The trajectory of an orbiting spacecraft is determined from an orbit determination program. Two inputs to this program, among others, are the range and range rate relative to some known location. The arithmetic and measurement errors in the determinations of the range, range rate, and range differences were identified and evaluated. These uncertainties are tabulated for one way and two way systems. A comparison of the measurement error contributions illustrate the predominance of thermal noise effects under low power budget conditions, with the other error sources becoming relevent for the high power budget case. The evaluated uncertainties are summarized as root sum squared noise and bias errors.

Bryan, J. W.↗

Baseflow Identification via Explainable AI With Kolmogorov‐Arnold Networks

Abstract Hydrological models often involve constitutive laws that may not be optimal in every application. We propose to replace such laws with the Kolmogorov‐Arnold networks (KANs), a class of neural networks designed to identify symbolic expressions. We demonstrate KAN's potential on the problem of baseflow identification, a notoriously challenging task plagued by significant uncertainty. KAN‐derived functional dependencies of the baseflow components on the aridity index outperform their original counterparts; they demonstrate that water availability, rather than potential evapotranspiration, drives baseflow by constraining actual evapotranspiration under arid conditions. On a test set, they increase the Nash‐Sutcliffe efficiency (NSE) by 65%, decrease the root mean squared error by 29%, and increase the Kling‐Gupta efficiency by 34%. This superior performance is achieved while reducing the number of fitting parameters from three to two. Next, we use data from 378 catchments across the continental United States to refine the water‐balance equation at the mean‐annual scale. The KAN‐derived equations based on the refined water balance outperform both the current aridity index model, with up to a 105% increase in NSE, and the KAN‐derived equations based on the original water balance. While the performance of our model and tree‐based machine learning methods is similar, KANs offer the advantage of simplicity and transparency and require no specific software or computational tools. This case study focuses on the aridity index formulation, but the approach is flexible and transferable to other hydrological processes. Plain Language Summary Equations used in hydrologic model are often suboptimal, resulting in reduced prediction accuracy and efficiency. We implemented Kolmogorov‐Arnold networks (KAN), a machine learning algorithm for deriving symbolic formulations, to estimate groundwater recharge and showed that it outperforms an existing state‐of‐the‐art semi‐empirical formulation. In hydrology, Nash‐Sutcliffe efficiency (NSE), root mean squared error (RMSE), and Kling‐Gupta efficiency (KGE) are commonly used to evaluate model performance. Higher NSE and KGE values indicate better performance, while lower RMSE values are preferable. Our results show that NSE increased by 71%, RMSE decreased by 32%, and KGE improved by 25%. In addition, KAN identifies an optimal functional form and can be used to derive new analytical formulas using the prior knowledge. The KAN‐inspired equation outperformed the original formulation and reduced the fitting parameters. Furthermore, we refined the water‐balance equation at the mean‐annual scale and showed that, based on the new water‐balance equation, KAN can derive new formulations that are superior to the original aridity index formulations (up to 105% increase in NSE) and KAN‐derived equations based on the original water balance. These findings highlight the significant potential of KAN to advance the scientific understanding of a wide range of hydrologic processes. Key Points Kolmogorov‐Arnold networks (KANs) enhance interpretability of machine‐learned hydrological models KAN‐derived symbolic formulations outperform state‐of‐the‐art semi‐empirical aridity indices KAN‐identified functional form yields an analytical index with fewer fitting parameters and improved performance

baseflow↗

Modelling above-ground biomass stock over Norway using national forest inventory data with ArcticDEM and Sentinel-2 data

Boreal forests constitute a large portion of the global forest area, yet they are undersampled through field surveys, and only a few remotely sensed data sources provide structural information wall-to-wall throughout the boreal domain. ArcticDEM is a collection of high-resolution (2 m) space-borne stereogrammetric digital surface models (DSM) covering the entire land area north of 60° of latitude. The free-availability of ArcticDEM data offers new possibilities for aboveground biomass mapping (AGB) across boreal forests, and thus it is necessary to evaluate the potential for these data to map AGB over alternative open-data sources (i.e., Sentinel-2). This study was performed over the entire land area of Norway north of 60° of latitude, and the Norwegian national forest inventory (NFI) was used as a source of field data composed of accurately geolocated field plots (n=7710) systematically distributed across the study area. Separate random forest models were fitted using NFI data, and corresponding remotely sensed data consisting of either: i) a canopy height model (ArcticCHM) obtained by subtracting a high-quality digital terrain model (DTM) from the ArcticDEM DSM height values, ii) Sentinel-2 (S2), or iii) a combination of the two (ArcticCHM+S2). Furthermore, we assessed the effect of the forest- and terrain-specific factors on the models’ predictive accuracy. The best model (,i.e., ArcticCHM+S2) explained nearly 60% of the variance of the training set, which translated in the largest accuracy in terms of root mean square error (RMSE=41.4 t/ha). This result highlights the synergy between 3D and multispectral data in AGB modelling. Furthermore, this study showed that despite the importance of ArcticCHM variables, the S2 model performed slightly better than ArcticCHM model. This finding highlights some of the limitations of ArcticDEM, which, despite the unprecedented spatial resolution, is highly heterogeneous due to the blending of multiple acquisitions across different years and seasons. We found that both forest- and terrain-specific characteristics affected the uncertainty of the ArcticCHM+S2 model and concluded that the combined use of ArcticCHM and Sentinel-2 represents a viable solution for AGB mapping across boreal forests. The synergy between the two data sources allowed for a reduction of the saturation effects typical of multispectral data while ensuring the spatial consistency in the output predictions due to the removal of artifacts and data voids present in ArcticCHM data. While the main contribution of this study is to provide the first evidence of the best-case-scenario (i.e., availability of accurate terrain models) that ArcticDEM data can provide for large-scale AGB modelling, it remains critically important for other studies to investigate how ArcticDEM may be used in areas where no DTMs are available as is the case for large portions of the boreal zone.

space-borne imagery↗

Deep Space Atomic Clock Technology Demonstration Mission Results

The Deep Space Atomic Clock (DSAC), a NASA Technology Demonstration Mission, was launched into low-Earth orbit on June 25, 2019 as a hosted payload aboard General Atomics’ Orbital Test Bed (OTB) spacecraft. The DSAC mission has been conducting a two-year demonstration of a mercury ion atomic clock to characterize its space-based performance and to validate its utility for deep space navigation and radio science. Analysis of the collected data using JPL’s GIPSY-OASIS software has shown DSAC’s AD at one-day to be near 310-15; much better than required AD of 210-14. Such low spacecraft clock errors will enable one-way radiometric tracking data with precision equivalent to or better than current-day two way tracking data, allowing a shift to a more efficient and flexible one-way deep space navigation architecture. To verify this, an analog deep space navigation experiment was performed using JPL’s operational navigation software (Monte). The experiment recovered orbit solutions with reduced data sets and geometric variations that are more representative of deep space missions, and showed that orbit determination using DSAC derived data is on par with more traditional two-way datatypes. As a technology demonstrator, DSAC’s development focus has been on maturing the mercury ion trap clock technology rather than achieving the smallest size, weight, and power (SWaP). Over the course of DSAC’s development the project has identified numerous improvements that could be made to significantly reduce SWaP for DSAC’s next version. Indeed, DSAC-2 was recently selected by NASA for further demonstration on the VERITAS mission to Venus. This work will review the DSAC technology, mission, and results from its two-year mission.

Wang, Rabi↗

Estimating the Contributions to Human Error Probability from the Convolution of the Distribution of Time Available and Time Required

As part of their duties, Human Reliability Analysis must often evaluate if crews in nuclear power plants (NPPs) can complete tasks associated with a human-failure event within time limits. For example, the time required in NPP scenarios is determined by systematic and structured walkthroughs, feasibility studies, recorded times from training exercises, and interviews with experienced operators and experts. Typically, a point estimate is derived for the estimate (mean, maximum, or 95th percentile of time required). Using point-estimate values can mask the risk associated with variability among crews, plant conditions and set-up, environmental conditions, and other impact factors under which these actions are executed. While point estimates for time required and time available have served the industry well, without considering the uncertainty they could lead to biased understanding about the risk. The Integrated Human Event Analysis System - General Methodology (IDHEAS-G) model (developed by the US Nuclear Regulatory Commission, NRC) for human error probability calculates human error probability by summing two probabilities: insufficient time and cognitive error. As such, the model takes a more holistic approach by considering the full distributions for time required and time available to calculate the human error probability because the time available to complete the task is insufficient. In this study, we expand on the work of the NRC and discuss methods for estimating these time considerations. For example, for the time required, the impact of Performance Influencing Factors (PIFs) on the distribution was divided into impacts that are aleatory in nature, such as crew-to-crew variability, and those that are epistemic (i.e., the PIFs). Starting with the factors that introduce aleatory uncertainty, a first-order distribution was developed from a large set of time required (i.e., NPP task completion times) data for the range of operator actions that occur in the NPP control room under simulated accident conditions. The first-order distribution can then be adjusted to account for epistemic uncertainty using research associated with the impact of applicable PIFs on the time required. We also develop guidance for analysts to address the probability distributions for the time available. The guidance we developed on how to estimate time required and time available distributions is based on the identification of pertinent research and data, data analyses, and expert knowledge elicitation.

human error probability, human performance, time e↗

Evaluation of lens distortion errors using an underwater camera system for video-based motion analysis

Video-based motion analysis systems are widely employed to study human movement, using computers to capture, store, process, and analyze video data. This data can be collected in any environment where cameras can be located. One of the NASA facilities where human performance research is conducted is the Weightless Environment Training Facility (WETF), a pool of water which simulates zero-gravity with neutral buoyance. Underwater video collection in the WETF poses some unique problems. This project evaluates the error caused by the lens distortion of the WETF cameras. A grid of points of known dimensions was constructed and videotaped using a video vault underwater system. Recorded images were played back on a VCR and a personal computer grabbed and stored the images on disk. These images were then digitized to give calculated coordinates for the grid points. Errors were calculated as the distance from the known coordinates of the points to the calculated coordinates. It was demonstrated that errors from lens distortion could be as high as 8 percent. By avoiding the outermost regions of a wide-angle lens, the error can be kept smaller.

Poliner, Jeffrey↗

The effects of transmitter/receiver clock time base instability on coherent communication system performance

The purpose of this paper is to present a model and associated analysis of the deleterious effects which both transmitter and receiver data clock time-base instability have on bit error probability. The types of time-base instability modeled and analyzed include bit jitter (epoch jitter), bit jitter rate (time interval jitter) and data asymmetry. The bit error probability is determined as a function of the statistical characteristics of the time-base instability, the data transition density, the signal-to-noise ratio in the bit rate bandwidth and the mechanizations of both the data bit detector and bit synchronizer. Numerical results are provided.

Chie, C. M.↗

Decomposition of the Mean Squared Error and NSE Performance Criteria: Implications for Improving Hydrological Modelling

The mean squared error (MSE) and the related normalization, the Nash-Sutcliffe efficiency (NSE), are the two criteria most widely used for calibration and evaluation of hydrological models with observed data. Here, we present a diagnostically interesting decomposition of NSE (and hence MSE), which facilitates analysis of the relative importance of its different components in the context of hydrological modelling, and show how model calibration problems can arise due to interactions among these components. The analysis is illustrated by calibrating a simple conceptual precipitation-runoff model to daily data for a number of Austrian basins having a broad range of hydro-meteorological characteristics. Evaluation of the results clearly demonstrates the problems that can be associated with any calibration based on the NSE (or MSE) criterion. While we propose and test an alternative criterion that can help to reduce model calibration problems, the primary purpose of this study is not to present an improved measure of model performance. Instead, we seek to show that there are systematic problems inherent with any optimization based on formulations related to the MSE. The analysis and results have implications to the manner in which we calibrate and evaluate environmental models; we discuss these and suggest possible ways forward that may move us towards an improved and diagnostically meaningful approach to model performance evaluation and identification.

Gupta, Hoshin V.↗

Use Computer-Aided Tools to Parallelize Large CFD Applications

Porting applications to high performance parallel computers is always a challenging task. It is time consuming and costly. With rapid progressing in hardware architectures and increasing complexity of real applications in recent years, the problem becomes even more sever. Today, scalability and high performance are mostly involving handwritten parallel programs using message-passing libraries (e.g. MPI). However, this process is very difficult and often error-prone. The recent reemergence of shared memory parallel (SMP) architectures, such as the cache coherent Non-Uniform Memory Access (ccNUMA) architecture used in the SGI Origin 2000, show good prospects for scaling beyond hundreds of processors. Programming on an SMP is simplified by working in a globally accessible address space. The user can supply compiler directives, such as OpenMP, to parallelize the code. As an industry standard for portable implementation of parallel programs for SMPs, OpenMP is a set of compiler directives and callable runtime library routines that extend Fortran, C and C++ to express shared memory parallelism. It promises an incremental path for parallel conversion of existing software, as well as scalability and performance for a complete rewrite or an entirely new development. Perhaps the main disadvantage of programming with directives is that inserted directives may not necessarily enhance performance. In the worst cases, it can create erroneous results. While vendors have provided tools to perform error-checking and profiling, automation in directive insertion is very limited and often failed on large programs, primarily due to the lack of a thorough enough data dependence analysis. To overcome the deficiency, we have developed a toolkit, CAPO, to automatically insert OpenMP directives in Fortran programs and apply certain degrees of optimization. CAPO is aimed at taking advantage of detailed inter-procedural dependence analysis provided by CAPTools, developed by the University of Greenwich, to reduce potential errors made by users. Earlier tests on NAS Benchmarks and ARC3D have demonstrated good success of this tool. In this study, we have applied CAPO to parallelize three large applications in the area of computational fluid dynamics (CFD): OVERFLOW, TLNS3D and INS3D. These codes are widely used for solving Navier-Stokes equations with complicated boundary conditions and turbulence model in multiple zones. Each one comprises of from 50K to 1,00k lines of FORTRAN77. As an example, CAPO took 77 hours to complete the data dependence analysis of OVERFLOW on a workstation (SGI, 175MHz, R10K processor). A fair amount of effort was spent on correcting false dependencies due to lack of necessary knowledge during the analysis. Even so, CAPO provides an easy way for user to interact with the parallelization process. The OpenMP version was generated within a day after the analysis was completed. Due to sequential algorithms involved, code sections in TLNS3D and INS3D need to be restructured by hand to produce more efficient parallel codes. An included figure shows preliminary test results of the generated OVERFLOW with several test cases in single zone. The MPI data points for the small test case were taken from a handcoded MPI version. As we can see, CAPO's version has achieved 18 fold speed up on 32 nodes of the SGI O2K. For the small test case, it outperformed the MPI version. These results are very encouraging, but further work is needed. For example, although CAPO attempts to place directives on the outer- most parallel loops in an interprocedural framework, it does not insert directives based on the best manual strategy. In particular, it lacks the support of parallelization at the multi-zone level. Future work will emphasize on the development of methodology to work in a multi-zone level and with a hybrid approach. Development of tools to perform more complicated code transformation is also needed.

Jin, H.↗

Light Water Reactor Sustainability Program: Use of Time Distributions to Predict Operator Procedure Performance in Dynamic Human Reliability Analysis

The Human Unimodel for Nuclear Technology to Enhance Reliability (HUNTER) framework affords software capable of conducting human reliability analysis (HRA) using a dynamic approach built around operating procedures (OPs) from nuclear power plants (NPPs). Previous HUNTER reports document the development of this software tool, the coupling of HUNTER to the simulator code, the collection of operator performance data by using simulators to calibrate HUNTER models, and linking HUNTER to probabilistic risk assessment (PRA) software. The present report largely addresses two topics. The first is a new function in HUNTER called the HUNTER Procedure Performance Predictor (P3). HUNTER P3 uses HUNTER’s built in Monte Carlo tools featuring human performance variability to identify potential error traps in procedures. The second topic is time distribution analysis to generate time inputs for dynamic HRA. The current analysis was performed to investigate time distributions for task primitives, which are the minimum task unit of analysis used in dynamic HRA modeling. Using the time distribution data, the elapsed time for human actions in an extended loss of AC power (ELAP) scenario is then investigated. Time data and prediction are essential for modeling procedure performance.

99 GENERAL AND MISCELLANEOUS↗

Coupled Data Assimilation for Integrated Earth System Analysis and Prediction: Goals, Challenges, and Recommendations

The purpose of this report is to identify fundamental issues for coupled data assimilation (CDA), such as gaps in science and limitations in forecasting systems, in order to provide guidance to the World Meteorological Organization (WMO) on how to facilitate more rapid progress internationally. Coupled Earth system modeling provides the opportunity to extend skillful atmospheric forecasts beyond the traditional two-week barrier by extracting skill from low-frequency state components such as the land, ocean, and sea ice. More generally, coupled models are needed to support seamless prediction systems that span timescales from weather, subseasonal to seasonal (S2S), multiyear, and decadal. Therefore, initialization methods are needed for coupled Earth system models, either applied to each individual component (called Weakly Coupled Data Assimilation - WCDA) or applied the coupled Earth system model as a whole (called Strongly Coupled Data Assimilation - SCDA). Using CDA, in which model forecasts and potentially the state estimation are performed jointly, each model domain benefits from observations in other domains either directly using error covariance information known at the time of the analysis (SCDA), or indirectly through flux interactions at the model boundaries (WCDA). Because the non-atmospheric domains are generally under-observed compared to the atmosphere, CDA provides a significant advantage over single-domain analyses. Next, we provide a synopsis of goals, challenges, and recommendations to advance CDA: Goals: (a) Extend predictive skill beyond the current capability of NWP (e.g. as demonstrated by improving forecast skill scores), (b) produce physically consistent initial conditions for coupled numerical prediction systems and reanalyses (including consistent fluxes at the domain interfaces), (c) make best use of existing observations by allowing observations from each domain to influence and improve the full earth system analysis, (d) develop a robust observation-based identification and understanding of mechanisms that determine the variability of weather and climate, (e) identify critical weaknesses in coupled models and the earth observing system, (f) generate full-field estimates of unobserved or sparsely observed variables, (g) improve the estimation of the external forcings causing changes to climate, (h) transition successes from idealized CDA experiments to real-world applications. Challenges: (a) Modeling at the interfaces between interacting components of coupled Earth system models may be inadequate for estimating uncertainty or error covariances between domains, (b) current data assimilation methods may be insufficient to simultaneously analyze domains containing multiple spatiotemporal scales of interest, (c) there is no standardization of observation data or their delivery systems across domains, (d) the size and complexity of many large-scale coupled Earth system models makes it is difficult to accurately represent uncertainty due to model parameters and coupling parameters, (e) model errors lead to local biases that can transfer between the different Earth system components and lead to coupled model biases and long-term model drift, (e) information propagation across model components with different spatiotemporal scales is extremely complicated, and must be improved in current coupled modeling frameworks, (h) there is insufficient knowledge on how to represent evolving errors in non-atmospheric model components (e.g. as sea ice, land and ocean) on the timescales of NWP.

CDA↗

Effects of low sampling rate in the digital data-transition tracking loop

This article describes the performance of the all-digital data-transition tracking loop (DTTL) with coherent and noncoherent sampling using nonlinear theory. The effects of few samples per symbol and of noncommensurate sampling and symbol rates are addressed and analyzed. Their impact on the probability density and variance of the phase error are quantified through computer simulations. It is shown that the performance of the all-digital DTTL approaches its analog counterpart when the sampling and symbol rates are noncommensurate (i.e., the number of samples per symbol is an irrational number). The loop signal-to-noise ratio (SNR) (inverse of phase error variance) degrades when the number of samples per symbol is an odd integer but degrades even further for even integers.

Mileant, A.↗

Remote sensing of Pu in uranyl nitrate crystals using reflectance spectroscopy and chemometrics

Remote quantification of Pu(VI) (0–5 mol%) co-crystallized with U in uranyl nitrate hexahydrate (UNH) crystals was achieved in a glove box using reflectance spectroscopy coupled with chemometric modeling. Reflectance spectra were also acquired for Pu(IV) and Np(VI) (0–5 mol%) crystallized with UNH; revealing spectral features consistent with their solution-phase analogs. Principal component analysis revealed Pu(IV/VI) and Np(VI) concentrations as the primary source of variation in the data, informing the development of a supervised partial least squares regression model for Pu(VI). The resulting calibration demonstrated robust performance, with replicate root mean square errors near 10% and quantifiable limits near 0.2 mol% Pu(VI) relative to U. The Pu(VI) remained stable in the crystalline UNH matrix for at least one week with minimal reduction to Pu(IV). Notably, Pu(VI) and Np(VI) incorporation in UNH quenched U(VI) fluorescence while Pu(IV) did not. This study presents a noninvasive, spectroscopic approach for solid-state Pu quantification, with direct implications for material accountability and nuclear nonproliferation monitoring.

Sadergaski, Luke R. [Oak Ridge National Laboratory↗

Reinforcement Learning for Anomaly Detection in Nuclear Power Plant Operation and Maintenance

In nuclear power plants (NPPs), timely identification of sensor and human errors is critical to ensure safe and efficient plant operations. Anomaly detection models can be employed for this task. However, traditional anomaly detection approaches may have high dependency on labeled datasets and struggle with adaptability in complex, dynamic environments. Reinforcement learning (RL) has demonstrated significant potential in fault diagnosis and anomaly detection; however, its application to anomaly detection in NPPs remains a relatively underexplored research direction. Hence, to address this gap, in this study, we present a novel physics-informed reinforcement learning model, PIRL-AD: Physics-Informed Reinforcement Learning for Anomaly Detection, that integrates domain knowledge from calorimetric equations into the RL framework for enhanced sensor and human error anomaly detection. We evaluate the performance of PIRL-AD against a non-physics informed RL benchmark and a support vector machine (SVM) on data collected from a forced flow loop testbed. Experimental results suggest that PIRL-AD outperforms other baselines on a range of anomalous datasets that include both sensor and human-induced anomalies across key performance metrics, statistically outperforming the RL and SVM benchmarks with respect to geometric mean (respectively, 92.96% vs. 91.06% vs. 83.01%) and F1-score (respectively, 89.23% vs. 86.98% vs. 77.01%). Furthermore, the findings suggest the potential of physics-integrated reinforcement learning models for enhanced anomaly detection performance in NPPs.

Reinforcement learning↗

Performance results for a hybrid coding system.

Results of computer simulation studies of the hybrid pull-up bootstrap decoding algorithm, using a constraint length 24, nonsystematic, rate 1/2 convolutional code for the symmetric channel with both binary and eight-level quantized outputs. Computational performance was used to measure the effect of several decoder parameters and determine practical operating constraints. Results reveal that the track length may be reduced to 500 information bits with small degradation in performance. The optimum number of tracks per block was found to be in the range from 7 to 11. An effective technique was devised to efficiently allocate computational effort and identify reliably decoded data sections. Long simulations indicate that a practical bootstrap decoding configuration has a computational performance about 1.0 dB better than sequential decoding and an output bit error rate about .0000025 near the R sub comp point.

Hoffman, L. B.↗