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DOE OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.

Gu, Shouzhen [Yale U.]↗

DOE OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Gu, Shouzhen [Yale U.]↗

DOE OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Gu, Shouzhen [Yale U.]↗

DOE OSTI2024

Sound propagation in realistic interactive 3D scenes with parameterized sources using deep neural operators

We address the challenge of acoustic simulations in three-dimensional (3D) virtual rooms with parametric source positions, which have applications in virtual/augmented reality, game audio, and spatial computing. The wave equation can fully describe wave phenomena such as diffraction and interference. However, conventional numerical discretization methods are computationally expensive when simulating hundreds of source and receiver positions, making simulations with parametric source positions impractical. To overcome this limitation, we propose using deep operator networks to approximate linear wave-equation operators. This enables the rapid prediction of sound propagation in realistic 3D acoustic scenes with parametric source positions, achieving millisecond-scale computations. By learning a compact surrogate model, we avoid the offline calculation and storage of impulse responses for all relevant source/listener pairs. Our experiments, including various complex scene geometries, show good agreement with reference solutions, with root mean squared errors ranging from 0.02 to 0.10 Pa. Notably, our method signifies a paradigm shift as—to our knowledge—no prior machine learning approach has achieved precise predictions of complete wave fields within realistic domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2016

Application of X-Ray Pulsar Navigation: A Characterization of the Earth Orbit Trade Space

The potential for pulsars as a navigation source has been studied since their discovery in 1967. X-ray pulsar navigation (XNAV) is a celestial navigation system that uses the consistent timing nature of x-ray photons from milli-second pulsars (MSP) to perform space navigation. By comparing the detected arrival of x-ray photons to a reference database of expected pulsar lightcurve timing models, one can infer a range and range rate measurement based on light time delay. Much of the challenge of XNAV comes from the faint signal, availability, and distant nature of pulsars. This is a study of potential pulsar XNAV measurements to measure extended Kalman filter (EKF) tracking performance with a wide trade space of bounded Earth orbits, using a simulation of existing x-ray detector space hardware. An example of an x-ray detector for XNAV is the NASA Station Explorer for X-ray Timing and Navigation (SEXTANT) mission, a technology demonstration of XNAV set to perform on the International Space Station (ISS) in late 2016early 2017. XNAV hardware implementation is driven by trajectory and environmental influences which add noise to the x-ray pulse signal. In a closed Earth orbit, the radiation environment can exponentially increase the signal noise from x-ray pulsar sources, decreasing the quality and frequency of measurements. The SEXTANT mission in particular improves on the signal to noise ratio by focusing an array of 56 x-ray silicon drift detectors at one pulsar target at a time. This reduces timing glitches and other timing noise contributions from ambient x-ray sources to within a 100 nanosecond resolution. This study also considers the SEXTANT scheduling challenges inherent in a single target observation. Finally, as the navigation sources are now relatively inertial targets, XNAV measurements are also subject to periods of occultation from various celestial bodies. This study focuses on the characterization of these drivers in closed Earth orbits and is not a tuning analysis of the EKF. The study shows that the closed Earth orbit for XNAV performance is reliant on the orbit semi-major axis and eccentricity as well as orbit inclination. These parameters are the primary drivers of pulsar measurement availability and significantly influence the natural spacecraft orbit dynamics. Sensitivity to initial orbit determination error growth due to the scarcity of XNAV measurements within an orbital period require appropriate timing of initial XNAV measurements. The orbit angles of argument of perigee and right ascension of the ascending node, alongside the other orbit parameters, complete the initial cadence of XNAV measurements. The performance of initial XNAV measurements then propagates throughout the experimental period. The study provides a basis to missions who wish to consider XNAV as a potential navigation source in a closed Earth orbit design. It provides a family of orbit trajectories as well as other modeling considerations needed to effectively evaluate if XNAV is an effective navigation source for a potential mission. As an EKF is sensitive to a linearized estimated state, this study has a direct benefit of providing effective XNAV measurements to maintain spacecraft tracking, independent of other navigation sources. In the particular use case of the SEXTANT mission, it also provides a novel scheduling algorithm which addresses the need to prioritize and manage pulsar observations for effective navigation.

PULSAR↗

NASA NTRS2016

Application of X-Ray Pulsar Navigation: A Characterization of the Earth Orbit Trade Space

The potential for pulsars as a navigation source has been studied since their discovery in 1967. X-ray pulsar navigation (XNAV) is a celestial navigation system that uses the consistent timing nature of x-ray photons from millisecond pulsars (MSP) to perform space navigation. By comparing the detected arrival of x-ray photons to a reference database of expected pulsar light-curve timing models, one can infer a range and range rate measurement based on light time delay. Much of the challenge of XNAV comes from the faint signal, availability, and distant nature of pulsars. This is a study of potential pulsar XNAV measurements to measure extended Kalman filter (EKF) tracking performance with a wide trade space of bounded Earth orbits, using a simulation of existing x-ray detector space hardware. An example of an x-ray detector for XNAV is the NASA Station Explorer for X-ray Timing and Navigation (SEXTANT) mission, a technology demonstration of XNAV set to perform on the International Space Station (ISS) in late 2016early 2017. XNAV hardware implementation is driven by trajectory and environmental influences which add noise to the x-ray pulse signal. In a closed Earth orbit, the radiation environment can exponentially increase the signal noise from x-ray pulsar sources, decreasing the quality and frequency of measurements. The SEXTANT mission in particular improves on the signal to noise ratio by focusing an array of 56 x-ray silicon drift detectors at one pulsar target at a time. This reduces timing glitches and other timing noise contributions from ambient x-ray sources to within a 100 nanosecond resolution. This study also considers the SEXTANT scheduling challenges inherent in a single target observation. Finally, as the navigation sources are now relatively inertial targets, XNAV measurements are also subject to periods of occultation from various celestial bodies. This study focuses on the characterization of these drivers in closed Earth orbits and is not a tuning analysis of the EKF. The study shows that the closed Earth orbit for XNAV performance is reliant on the orbit semi-major axis and eccentricity as well as orbit inclination. These parameters are the primary drivers of pulsar measurement availability and significantly influence the natural spacecraft orbit dynamics. Sensitivity to initial orbit determination error growth due to the scarcity of XNAV measurements within an orbital period require appropriate timing of initial XNAV measurements. The orbit angles of argument of perigee and right ascension of the ascending node, alongside the other orbit parameters, complete the initial cadence of XNAV measurements. The performance of initial XNAV measurements then propagates throughout the experimental period. The study provides a basis to missions who wish to consider XNAV as a potential navigation source in a closed Earth orbit design. It provides a family of orbit trajectories as well as other modeling considerations needed to effectively evaluate if XNAV is an effective navigation source for a potential mission. As an EKF is sensitive to a linearized estimated state, this study has a direct benefit of providing effective XNAV measurements to maintain spacecraft tracking, independent of other navigation sources. In the particular use case of the SEXTANT mission, it also provides a novel scheduling algorithm which addresses the need to prioritize and manage pulsar observations for effective navigation.

x-ray↗

NASA NTRSDate not supplied

Mitigating Grazing Flow Impedance Eduction Errors in Additively Manufactured Porous Liners

Additively manufactured porous metamaterials, including triply periodic minimal surface (TPMS) cores, are promising candidates for aeroengine liners but often behave as extended-reacting treatments under grazing flow. Standard impedance eduction procedures assume locally-reacting behavior and can yield physically inconsistent results for such materials. This study evaluates internal partitions (thin solid walls inserted at regular intervals along the liner’s streamwise extent) as a means of suppressing internal streamwise propagation to improve eduction consistency. Six TPMS configurations were tested in the NASA Langley Grazing Flow Impedance Tube (GFIT) at partition spacings of 4′′, 2′′, and 1′′, as well as unpartitioned, and at Mach numbers up to 0.3. For most geometries, 2′′ partition spacing eliminated impedance discontinuities and substantially improved Prony correlation, though effectiveness varied with core topology. Partitions also altered the acoustic response of the liners: resistance increased, resonance frequencies shifted downward, and peak attenuation decreased while bandwidth broadened in some cases. Because partitions modify the liner itself, the educed impedance characterizes the partitioned system rather than the original unpartitioned core. These results establish partitioning as a practical pathway toward liners that are more compatible with standard eduction methods, while demonstrating that the intervention is itself an acoustic design change.

liners↗

NASA NTRS1973

Investigation into the propagation of Omega very low frequency signals and techniques for improvement of navigation accuracy including differential and composite omega

An analysis of Very Low Frequency propagation in the atmosphere in the 10-14 kHz range leads to a discussion of some of the more significant causes of phase perturbation. The method of generating sky-wave corrections to predict the Omega phase is discussed. Composite Omega is considered as a means of lane identification and of reducing Omega navigation error. A simple technique for generating trapezoidal model (T-model) phase prediction is presented and compared with the Navy predictions and actual phase measurements. The T-model prediction analysis illustrates the ability to account for the major phase shift created by the diurnal effects on the lower ionosphere. An analysis of the Navy sky-wave correction table is used to provide information about spatial and temporal correlation of phase correction relative to the differential mode of operation.

Source record↗

NASA NTRS1994

Computer modeling the fatigue crack growth rate behavior of metals in corrosive environments

The objective of this task was to develop a method to digitize FCP (fatigue crack propagation) kinetics data, generally presented in terms of extensive da/dN-Delta K pairs, to produce a file for subsequent linear superposition or curve-fitting analysis. The method that was developed is specific to the Numonics 2400 Digitablet and is comparable to commercially available software products as Digimatic(sup TM 4). Experiments demonstrated that the errors introduced by the photocopying of literature data, and digitization, are small compared to those inherent in laboratory methods to characterize FCP in benign and aggressive environments. The digitizing procedure was employed to obtain fifteen crack growth rate data sets for several aerospace alloys in aggressive environments.

Richey, Edward, III↗

NASA NTRS2012

Mars Relay Lander and Orbiter Overflight Profile Estimation

This software allows science and mission operations to view graphs of geometric overflights of satellites and landers within the Mars (or other planetary) networks. It improves on the MaROS Web interface within any modern Web browser, in that it adds new capabilities to the MaROS suite. The profile for an overflight is an important element for selecting communication/ overflight opportunities between the landers and orbiters within the Mars network. Unfortunately, determining these estimates is very computationally expensive and difficult to compute by hand. This software allows the user to select different overflights (via the existing MaROS Web interface) and specify the smoothness of the estimation. Estimates for the geometric relationship between a lander and an orbiter are determined based upon the orbital conditions of the orbiter at the moment the orbiter rises above the horizon from the perspective of the lander. It utilizes 2-body orbital equations to propagate the trajectory through the duration of the view period, and returns profiles that represent the range between the two vehicles, and the elevation and azimuth angles of the orbiter as measured from the lander s position. The algorithms assume a 2-body relationship with an ideal, spherical planetary body, so therefore can see errors less than 2% at polar landing sites on Mars. These algorithms are being implemented to provide rough estimates rapidly for the geometry of a geometric view period where more complete data is unavailable, such as for planning purposes. While other software for this task exists, each at the time of this reporting has been contained within a much more complicated package. This tool allows science and mission operations to view the estimates with a few clicks of the mouse.

Wallick, Michael N.↗

NASA NTRS2019

Efficient On-Orbit Singularity-Free Geopotential Estimation

The complexity of the geopotential model can heavily impact the navigation error in satellites and spacecraft. Geopotential models of the accuracy needed for spaceflight are too complicated for flight computers to run at the rate needed by the navigation system. There are methods to make the geopotential model more efficient while maintaining the needed accuracy, which include: using an efficient method for the full model, propagating to avoid singularities, and running the full model at a low rate and propagating to the needed rate. These methods can decrease the computational requirement enough to be run by the flight computer at the rate required of the navigation system.

Amert, Joel↗

NASA NTRSDate not supplied

Comparison of Inlet Broadband Acoustic Liner Predictions to Quiet Technology Demonstrator 3 Flight Data

Companion acoustic liner attenuation predictions and flight data representative of certification conditions are analyzed to determine the validation quality and gain an understanding of current prediction shortcomings. These comparisons are limited to the inlet broadband component of fan noise. Two prediction methods are assessed: a traditional, semiempirical model, and a computational approach with a parabolic duct propagation code coupled with a Ffowcs Williams-Hawkings solver for free-field propagation. The semiempirical method is widely used for aircraft system noise predictions, but does not explicitly account for several physical parameters important for sound attenuation. The computational approach includes these effects, but requires a significant increase in cycle time. For the three-degree-of-freedom (3DOF) liner tested, both methods have a bias error less than 0.5 dB for cutback and takeoff power settings, and a much larger 3–4 dB bias for approach power setting. The standard deviation of each method varies between 1–2 dB for different conditions. The similar performance of both approaches illustrates that, in this instance, the additional complexity of the computational approach does not provide a clear improvement over the semiempirical method. Planned improvements to the numerical grid and source assumptions may result in reevaluation of this conclusion in later work.

aircraft system noise↗

NASA NTRSDate not supplied

Sonic Boom Ground Noise Minimization Via the Adjoint Method

A multidisciplinary design optimization methodology to directly minimize the ground-level noise generated by the sonic boom of a high altitude supersonic body is presented. A Cartesian Euler flow solver is coupled with an atmospheric propagation tool to create a ground-noise analysis capability for supersonic bodies. Adjoint formulations for both the flow solver and propagation tool are also coupled to compute sensitivities of shape variations in the body in a highly efficient manner. A gradient-based optimizer is then introduced to forge a valuable design capability. Output-based mesh adaptation that is driven directly by ground-level noise is employed to increase accuracy and provide error estimation. The design method is demonstrated first on a simple axisymmetric body with few design variables to evaluate the efficacy of the optimization scheme. Guided by the results of this initial case, the problem is then repeated with somewhat different design variables to further demonstrate the capabilities of the design method. Finally, the method is applied to a real-world problem by optimizing control surface deflection settings of a low-boom aircraft to minimize ground noise while maintaining trimmed, level flight.

ARMD↗

NASA NTRS1988

An analysis of the Kalman filter in the Gamma Ray Observatory (GRO) onboard attitude determination subsystem

The Gamma Ray Observatory (GRO) spacecraft needs a highly accurate attitude knowledge to achieve its mission objectives. Utilizing the fixed-head star trackers (FHSTs) for observations and gyroscopes for attitude propagation, the discrete Kalman Filter processes the attitude data to obtain an onboard accuracy of 86 arc seconds (3 sigma). A combination of linear analysis and simulations using the GRO Software Simulator (GROSS) are employed to investigate the Kalman filter for stability and the effects of corrupted observations (misalignment, noise), incomplete dynamic modeling, and nonlinear errors on Kalman filter. In the simulations, on-board attitude is compared with true attitude, the sensitivity of attitude error to model errors is graphed, and a statistical analysis is performed on the residuals of the Kalman Filter. In this paper, the modeling and sensor errors that degrade the Kalman filter solution beyond mission requirements are studied, and methods are offered to identify the source of these errors.

Snow, Frank↗

NASA NTRS1993

Unstructured adaptive mesh computations of rotorcraft high-speed impulsive noise

A new method is developed for modeling helicopter high-speed impulsive (HSI) noise. The aerodynamics and acoustics near the rotor blade tip are computed by solving the Euler equations on an unstructured grid. A stationary Kirchhoff surface integral is then used to propagate these acoustic signals to the far field. The near-field Euler solver uses a solution-adaptive grid scheme to improve the resolution of the acoustic signal. Grid points are locally added and/or deleted from the mesh at each adaptive step. An important part of this procedure is the choice of an appropriate error indicator. The error indicator is computed from the flow field solution and determines the regions for mesh coarsening and refinement. Computed results for HSI noise compare favorably with experimental data for three different hovering rotor cases.

Strawn, Roger↗

NASA NTRS1992

The effect of temperature on attenuation-correction schemes in rain using polarization propagation differential phase shift

The study elucidates and quantifies differences in the response of the rate of change of polarization propagation differential phase shift Phi, the rate of attenuation for a horizontally/vertically polarized wave A(H,V), and the rate of polarization differential attenuation A(H-V) to temperature. It is shown that if the effects of temperature when estimating A(H) and A(H-V) from Phi are neglected, the average fractional standard error increases only slightly at 9 GHz but significantly at 5 and 3 GHz. Errors at 5 and 3 GHz are about two to three times those at 9 GHz. The performance of Phi-based schemes of attenuation correction at these lower frequencies is much more significantly degraded by temperature uncertainty than at 9 GHz. It is concluded that it is best to use Phi to correct for attenuation at the least-attenuating frequencies.

Jameson, A. R.↗

NASA NTRS2003

Doppler Global Velocimetry at NASA Glenn Research Center: System Discussion and Results

A ruggedized Doppler Global Velocimetry system has been built and tested at NASA Glenn Research Center. One component of planar velocity measurements of subsonic and supersonic flows from an under-expanded free jet are reported, which agree well with predicted values. An error analysis evaluates geometric and spectral error terms, and characterizes speckle noise in isotropic data. A multimode, fused fiber optic bundle is demonstrated to couple up to 650 mJ/pulse of laser light without burning or fiber ablation, and without evidence of Stimulated Brillouin Scattering or other spectral-broadening problems. Comparisons are made between spinning wheel data using illumination by freespace beam propagation and fiber optic beam delivery. The fiber bundle illumination is found to provide more spatially even and stable illumination than is typically available from pulsed Nd:YAG laser beams. The fiber bundle beam delivery is also a step toward making remote measurements and automatic real-time plume sectioning feasible in wind tunnel environments.

Lant, Christian T.↗

NASA NTRS2009

Constructing LDPC Codes from Loop-Free Encoding Modules

A method of constructing certain low-density parity-check (LDPC) codes by use of relatively simple loop-free coding modules has been developed. The subclasses of LDPC codes to which the method applies includes accumulate-repeat-accumulate (ARA) codes, accumulate-repeat-check-accumulate codes, and the codes described in Accumulate-Repeat-Accumulate-Accumulate Codes (NPO-41305), NASA Tech Briefs, Vol. 31, No. 9 (September 2007), page 90. All of the affected codes can be characterized as serial/parallel (hybrid) concatenations of such relatively simple modules as accumulators, repetition codes, differentiators, and punctured single-parity check codes. These are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. These codes can also be characterized as hybrid turbolike codes that have projected graph or protograph representations (for example see figure); these characteristics make it possible to design high-speed iterative decoders that utilize belief-propagation algorithms. The present method comprises two related submethods for constructing LDPC codes from simple loop-free modules with circulant permutations. The first submethod is an iterative encoding method based on the erasure-decoding algorithm. The computations required by this method are well organized because they involve a parity-check matrix having a block-circulant structure. The second submethod involves the use of block-circulant generator matrices. The encoders of this method are very similar to those of recursive convolutional codes. Some encoders according to this second submethod have been implemented in a small field-programmable gate array that operates at a speed of 100 megasymbols per second. By use of density evolution (a computational- simulation technique for analyzing performances of LDPC codes), it has been shown through some examples that as the block size goes to infinity, low iterative decoding thresholds close to channel capacity limits can be achieved for the codes of the type in question having low maximum variable node degrees. The decoding thresholds in these examples are lower than those of the best-known unstructured irregular LDPC codes constrained to have the same maximum node degrees. Furthermore, the present method enables the construction of codes of any desired rate with thresholds that stay uniformly close to their respective channel capacity thresholds.

Divsalar, Dariush↗