Lower bounds to error probability for coding on discrete memoryless channels. I.
Lower bounds to minimum error probability using block coding on noisy discrete memoryless communication channels
ERROR DETECTING CODE↗
SEARCH · Engineering Papers
Results for “discretization error”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Lower bounds to error probability for coding on discrete memoryless channels. II.
Lower bounds to minimum error probability for block coding on noisy discrete memoryless channels
CHANNEL CAPACITY↗
Notes on Accuracy of Finite-Volume Discretization Schemes on Irregular Grids
Truncation-error analysis is a reliable tool in predicting convergence rates of discretization errors on regular smooth grids. However, it is often misleading in application to finite-volume discretization schemes on irregular (e.g., unstructured) grids. Convergence of truncation errors severely degrades on general irregular grids; a design-order convergence can be achieved only on grids with a certain degree of geometric regularity. Such degradation of truncation-error convergence does not necessarily imply a lower-order convergence of discretization errors. In these notes, irregular-grid computations demonstrate that the design-order discretization-error convergence can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all.
Diskin, Boris↗
An error bound for a discrete reduced order model of a linear multivariable system
The design of feasible controllers for high dimension multivariable systems can be greatly aided by a method of model reduction. In order for the design based on the order reduction to include a guarantee of stability, it is sufficient to have a bound on the model error. Previous work has provided such a bound for continuous-time systems for algorithms based on balancing. In this note an L-infinity bound is derived for model error for a method of order reduction of discrete linear multivariable systems based on balancing.
Al-Saggaf, Ubaid M.↗
Discreteness noise versus force errors in N-body simulations
A low accuracy in the force calculation per time step of a few percent for each particle pair is sufficient for collisionless N-body simulations. Higher accuracy is made meaningless by the dominant discreteness noise in the form of two-body relaxation, which can be reduced only by increasing the number of particles. Since an N-body simulation is a Monte Carlo procedure in which each particle-particle force is essentially random, i.e., carries an error of about 1000 percent, the only requirement is a systematic averaging-out of these intrinsic errors. We illustrate these assertions with two specific examples in which individual pairwise forces are deliberately allowed to carry significant errors: tree-codes on supercomputers and algorithms on special-purpose machines with low-precision hardware.
Hernquist, Lars↗
A variational framework for residual-based adaptivity in neural PDE solvers and operator learning
Residual-based adaptive strategies are widely used in scientific machine learning yet remain largely heuristic. We introduce a variational framework that formalizes these methods through convex transformations of the residual, where different transformations correspond to distinct objective functionals. For instance, exponential weights target uniform error minimization, while linear weights recover quadratic error minimization. This perspective reveals adaptive weighting as a means of selecting sampling distributions that optimize a primal objective, directly linking discretization choices to error metrics. This principled approach yields three key benefits: it enables systematic design of adaptive schemes, reduces discretization error by lowering estimator variance, and enhances learning dynamics by improving gradient signal-to-noise ratio. Extending the framework to operator learning, we demonstrate substantial performance gains across diverse optimizers and architectures. Our results provide a theoretical perspective for residual-based adaptivity and establish a foundation for principled discretization and training.
97 MATHEMATICS AND COMPUTING↗
Refinement and validation of two digital Microwave Landing System (MLS) theoretical models
Two digital microwave landing system theoretical models are considered which are generic models for the Doppler and scanning-beam frequency reference versions of the MLS. These models represent errors resulting from both system noise and discrete multipath. The data used for the validation effort were obtained from the Texas Instrument conventional scanning beam and the Hazeltine Doppler feasibility hardware versions of the MLS. Topics discussed include tape read software, time history plots, computation of power spectral density, smoothed power spectra, best-fit models, different equations for digital simulation, and discrete multipath errors.
Duff, W. G.↗
Discrete Goal-Oriented Error Estimation and Mesh Adaptation for Finite Deformation Elastoplasticity
Explore the source record for details and available documents.
Granzow, Brian Neal [Sandia National Laboratories ↗
Towards as assessment of fault-tolerant design principles for software
Several topics related to the assessment of fault-tolerant design principles for software are presented in outline form. A coincident errors model, discrete intensity distribution and the effects of coincident errors are discussed.
Eckhardt, Dave E., Jr.↗
Machine learning for continuous quantum error correction on superconducting qubits
Abstract Continuous quantum error correction has been found to have certain advantages over discrete quantum error correction, such as a reduction in hardware resources and the elimination of error mechanisms introduced by having entangling gates and ancilla qubits. We propose a machine learning algorithm for continuous quantum error correction that is based on the use of a recurrent neural network to identify bit-flip errors from continuous noisy syndrome measurements. The algorithm is designed to operate on measurement signals deviating from the ideal behavior in which the mean value corresponds to a code syndrome value and the measurement has white noise. We analyze continuous measurements taken from a superconducting architecture using three transmon qubits to identify three significant practical examples of non-ideal behavior, namely auto-correlation at temporal short lags, transient syndrome dynamics after each bit-flip, and drift in the steady-state syndrome values over the course of many experiments. Based on these real-world imperfections, we generate synthetic measurement signals from which to train the recurrent neural network, and then test its proficiency when implementing active error correction, comparing this with a traditional double threshold scheme and a discrete Bayesian classifier. The results show that our machine learning protocol is able to outperform the double threshold protocol across all tests, achieving a final state fidelity comparable to the discrete Bayesian classifier.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Rotational wind indicator enhances control of rotated displays
Rotation by 108 deg of the spatial mapping between a visual display and a manual input device produces large spatial errors in a discrete aiming task. These errors are not easily corrected by voluntary mental effort, but the central nervous system does adapt gradually to the new mapping. Bernotat (1970) showed that adding true hand position to a 90 deg rotated display improved performance of a compensatory tracking task, but tracking error rose again upon removal of the explicit cue. This suggests that the explicit error signal did not induce changes in the neural mapping, but rather allowed the operator to reduce tracking error using a higher mental strategy. In this report, we describe an explicit visual display enhancement applied to a 108 deg rotated discrete aiming task. A 'wind indicator' corresponding to the effect of the mapping rotation is displayed on the operator-controlled cursor. The human operator is instructed to oppose the virtual force represented by the indicator, as one would do if flying an airplane in a crosswind. This enhancement reduces spatial aiming error in the first 10 minutes of practice by an average of 70 percent when compared to a no enhancement control condition. Moreover, it produces adaptation aftereffect, which is evidence of learning by neural adaptation rather than by mental strategy. Finally, aiming error does not rise upon removal of the explicit cue.
Cunningham, H. A.↗
An improved upper bound on the block coding error exponent for binary input discrete memoryless channels
For coded telemetry systems it is important to know the tradeoff between the error probability and the complexity of implementation. For systems using block codes, the block coding error exponent is a good way to estimate this tradeoff. The new upper bounds on the minimum distance of binary codes result in improved upper bounds on the coding error exponents for binary input memoryless channels.
Mceliece, R. J.↗
Choice of method for discretization of continuous systems
The paper discusses and compares several common methods of discretizing the transfer function of a continuous control system so that a digital computer can be used. The discretization effect on the frequency response attenuation of the simple transfer function G(s) = 1/(s + 1) is illustrated for the Tusting, Boxer-Thaler, Madwed, linear segment approximation, and stair-step with half period advanced methods. The input frequency must be significantly lower than one-half the sampling error to have negligible discretization error. Phase differences due to discretization are also plotted, and it is seen that the zero-order hold contributes much more phase shift than that due to discretization. In situations where zero-order hold must follow a computer, the method of discretization of a continuous system is not a major factor if phase shift is important.
Mcvey, E. S.↗
Discrete model reference adaptive control with an augmented error signal
A method for designing discrete model reference adaptive control systems when one has access to only the plant's input and output signals is given. Controllers for single-input, single-output, nonlinear, nonautonomous plants are developed via Liapunov's second method. Anticipative values of the plant output are not required, but are replaced by signals easily obtained from a low-pass filter operating on the plant's output. The augmented error signal method is employed, ensuring finally that the normally used error signal also approaches zero asymptotically.
Ionescu, T.↗
Error analysis and correction of discrete solutions from finite element codes
Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of finite element results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.
Thurston, G. A.↗
Code verification for practically singular equations
We report the method-of-moments implementation of the electric-field integral equation (EFIE) yields many code-verification challenges due to the various sources of numerical error and their possible interactions. Matters are further complicated by singular integrals, which arise from the presence of a Green's function. To address these singular integrals, an approach is presented in wherein both the solution and Green's function are manufactured. Because the arising equations are poorly conditioned, they are reformulated as a set of constraints for an optimization problem that selects the solution closest to the manufactured solution. In this paper, we demonstrate how, for such practically singular systems of equations, computing the truncation error by inserting the exact solution into the discretized equations cannot detect certain orders of coding errors. On the other hand, the discretization error from the optimal solution is a more sensitive metric that can detect orders less than those of the expected convergence rate.
97 MATHEMATICS AND COMPUTING↗
Modeling error analysis of stationary linear discrete-time filters
The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a design can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices is available.
Patel, R.↗
DESC: A stellarator equilibrium solver
In this paper, the new code DESC is presented to solve for fixed-boundary ideal magnetohydrodynamic equilibria in stellarators. The approach directly solves the equilibrium force balance as a system of nonlinear equations in the form f(x) = 0. The independent variables x represent nested magnetic flux surfaces expressed in the inverse representation with toroidal flux coordinates, and the equations f(x) quantify equilibrium force balance errors at discrete points in real space. Discretizing with global Fourier–Zernike basis functions properly treats the magnetic axis and minimizes the number of coefficients needed to describe the flux surfaces. The pseudospectral method provides great flexibility in where the errors are evaluated, and the system of equations is efficiently solved with a Newton–Raphson iteration. Equilibria are computed and compared against VMEC for both axisymmetric and non-axisymmetric examples. The results show fast convergence rates and solutions with low errors throughout the plasma volume.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗