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NASA NTRS1984

Fast decoding techniques for extended single-and-double-error-correcting Reed Solomon codes

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. For example, some 256K-bit dynamic random access memories are organized as 32K x 8 bit-bytes. Byte-oriented codes such as Reed Solomon (RS) codes provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special high speed decoding techniques for extended single and double error correcting RS codes. These techniques are designed to find the error locations and the error values directly from the syndrome without having to form the error locator polynomial and solve for its roots.

Costello, D. J., Jr.↗

NASA NTRS1984

Reed Solomon codes for error control in byte organized computer memory systems

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. In LSI and VLSI technology, memories are often organized on a multiple bit (or byte) per chip basis. For example, some 256K-bit DRAM's are organized in 32Kx8 bit-bytes. Byte oriented codes such as Reed Solomon (RS) codes can provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special decoding techniques for extended single-and-double-error-correcting RS codes which are capable of high speed operation are presented. These techniques are designed to find the error locations and the error values directly from the syndrome without having to use the iterative algorithm to find the error locator polynomial.

Lin, S.↗

NASA NTRS1983

Model error estimation for distributed systems described by elliptic equations

A function space approach is used to develop a theory for estimation of the errors inherent in an elliptic partial differential equation model for a distributed parameter system. By establishing knowledge of the inevitable deficiencies in the model, the error estimates provide a foundation for updating the model. The function space solution leads to a specification of a method for computation of the model error estimates and development of model error analysis techniques for comparison between actual and estimated errors. The paper summarizes the model error estimation approach as well as an application arising in the area of modeling for static shape determination of large flexible systems.

Rodriguez, G.↗

NASA NTRS1983

The effect of earth orientation errors in baseline determination

Baselines estimated from certain space techniques are susceptible to systematic errors affecting the relative coordinates. The set of parameters that describes the continuously changing relative orientation of the conventional terrestrial (CTS) and inertial (CIS) reference frames is one source of error. As a result of these errors, the coordinates of each terminal station may actually refer to a slightly different coordinate system and therefore errors will result when these coordinates are used to compute the length between the stations. The present paper examines the expected magnitudes of these errors and their possible presence in current solutions. To test for the presence of such errors, some of the NASA/GSFC preliminary SL5 monthly baseline variations during 1979-1981 were analyzed. It is found that the present level of accuracy and stability of the available parameters linking the CTS and CIS is unsatisfactory for centimeter level baseline length determinations. It is noted that the available options are either the use of strictly simultaneous SLR data sets or the improvement of the parameters linking the CTS and CIS.

Pavlis, E. C.↗

NASA NTRS1983

Analysis of the impact of error detection on computer performance

Conventionally, reliability analyses either assume that a fault/error is detected immediately following its occurrence, or neglect damages caused by latent errors. Though unrealistic, this assumption was imposed in order to avoid the difficulty of determining the respective probabilities that a fault induces an error and the error is then detected in a random amount of time after its occurrence. As a remedy for this problem a model is proposed to analyze the impact of error detection on computer performance under moderate assumptions. Error latency, the time interval between occurrence and the moment of detection, is used to measure the effectiveness of a detection mechanism. This model is used to: (1) predict the probability of producing an unreliable result, and (2) estimate the loss of computation due to fault and/or error.

Shin, K. C.↗

NASA NTRS1985

Error Growth in Operational 10-day Forecasts

The rate of growth of forecast errors has been estimated previously, using as data base 100 consecutive 10-day operational forecasts from the European Center for Medium Range Forecasting (ECMWF). The growth of the difference between two model forecasts verifying the same day was parameterized. This parameterization of error growth was extended by including the effect of model deficiencies as well as their scale dependence. In this way the forecaster are able to fit real forecast error growth and determine the scale dependence of the derived parameters (rate of error growth, external error source due to model errors, and saturation levels). This work is a necessary step in the application of the Lagged Average Forecasting (LAF) technique to the ECMWF 10-day forecasts. It is found that for both the analyses and the forecasts, there is an approximate equipartition of energy between all the zonal wavenumbers m corresponding to the same total wavenumber n.

Kalnay, E.↗

NASA NTRS1985

A concatenated coding scheme for error control

A concatenated coding scheme for error contol in data communications was analyzed. The inner code is used for both error correction and detection, however the outer code is used only for error detection. A retransmission is requested if either the inner code decoder fails to make a successful decoding or the outer code decoder detects the presence of errors after the inner code decoding. Probability of undetected error of the proposed scheme is derived. An efficient method for computing this probability is presented. Throughout efficiency of the proposed error control scheme incorporated with a selective repeat ARQ retransmission strategy is analyzed.

Lin, S.↗

NASA NTRS1984

Errors in radiometric remote sensing of sea-surface temperature and salinity

Techniques for remote measurement of sea-surface physical temperature and salinity using radiometric measurements from aircraft or satellite are reviewed. Studies have been conducted to determine the sensitivity of the errors in surface temperature and salinity to errors in the measured brightness temperatures using combinations of UHF, L, S, and C-band measurements. These investigations were made using values of conductivity, static dielectric constant, and relaxation time derived from the regression equations of Klein and Swift (1977). Results of the error sensitivity study are presented in the form of error contour plots which permit the calculation of errors in the estimation of the physical parameters for given errors in the raw radiometric measurements.

Britt, C. L., Jr.↗

NASA NTRS1984

A model for the prediction of latent errors using data obtained during the development process

A model implemented in a program that runs on the IBM PC for estimating the latent (or post ship) content of a body of software upon its initial release to the user is presented. The model employs the count of errors discovered at one or more of the error discovery processes during development, such as a design inspection, as the input data for a process which provides estimates of the total life-time (injected) error content and of the latent (or post ship) error content--the errors remaining a delivery. The model presented presumes that these activities cover all of the opportunities during the software development process for error discovery (and removal).

Gaffney, J. E., Jr.↗

NASA NTRS1986

Orifice-induced pressure error studies in Langley 7- by 10-foot high-speed tunnel

For some time it has been known that the presence of a static pressure measuring hole will disturb the local flow field in such a way that the sensed static pressure will be in error. The results of previous studies aimed at studying the error induced by the pressure orifice were for relatively low Reynolds number flows. Because of the advent of high Reynolds number transonic wind tunnels, a study was undertaken to assess the magnitude of this error at high Reynolds numbers than previously published and to study a possible method of eliminating this pressure error. This study was conducted in the Langley 7- by 10-Foot High-Speed Tunnel on a flat plate. The model was tested at Mach numbers from 0.40 to 0.72 and at Reynolds numbers from 7.7 x 1,000,000 to 11 x 1,000,000 per meter (2.3 x 1,000,000 to 3.4 x 1,000,000 per foot), respectively. The results indicated that as orifice size increased, the pressure error also increased but that a porous metal (sintered metal) plug inserted in an orifice could greatly reduce the pressure error induced by the orifice.

Plentovich, E. B.↗

NASA NTRS1985

The error associated with use of various forms of the divergence equation to diagnose geopotential and temperature

An experimental study was made of errors arising from diagnosing the geopotential and temperature for numerical weather prediction models by means of an inviscid divergence equation (DE). The experiment consisted of a simulation of a snow storm which occurred in 1979, with observational data being input for every point of the model grid and for the geopotential boundary condition, thereby eliminating errors in the horizontal and vertical analysis. The DE terms were recorded at each grid point, and were found to include synoptic-scale geopotential height errors up to 23 m and rms temperature errors exceeding 26 C in the PBL. The errors were minimal above 800 mb. The various unsuccessful attempts to reduce or eliminate the errors are described.

Modica, G. M.↗

NASA NTRS1987

Effect of atmospheric turbulence on the bit error probability of a space to ground near infrared laser communications link using binary pulse position modulation and an avalanche photodiode detector

The effect of atmospheric turbulence on the bit error rate of a space-to-ground near infrared laser communications link is investigated, for a link using binary pulse position modulation and an avalanche photodiode detector. Formulas are presented for the mean and variance of the bit error rate as a function of signal strength. Because these formulas require numerical integration, they are of limited practical use. Approximate formulas are derived which are easy to compute and sufficiently accurate for system feasibility studies, as shown by numerical comparison with the exact formulas. A very simple formula is derived for the bit error rate as a function of signal strength, which requires only the evaluation of an error function. It is shown by numerical calculations that, for realistic values of the system parameters, the increase in the bit error rate due to turbulence does not exceed about thirty percent for signal strengths of four hundred photons per bit or less. The increase in signal strength required to maintain an error rate of one in 10 million is about one or two tenths of a db.

Safren, H. G.↗

NASA NTRS1988

Common but unappreciated sources of error in one, two, and multiple-color pyrometry

The most common sources of error in optical pyrometry are examined. They can be classified as either noise and uncertainty errors, stray radiation errors, or speed-of-response errors. Through judicious choice of detectors and optical wavelengths the effect of noise errors can be minimized, but one should strive to determine as many of the system properties as possible. Careful consideration of the optical-collection system can minimize stray radiation errors. Careful consideration must also be given to the slowest elements in a pyrometer when measuring rapid phenomena.

Spjut, R. Erik↗

NASA NTRS1988

A general model for attitude determination error analysis

An overview is given of a comprehensive approach to filter and dynamics modeling for attitude determination error analysis. The models presented include both batch least-squares and sequential attitude estimation processes for both spin-stabilized and three-axis stabilized spacecraft. The discussion includes a brief description of a dynamics model of strapdown gyros, but it does not cover other sensor models. Model parameters can be chosen to be solve-for parameters, which are assumed to be estimated as part of the determination process, or consider parameters, which are assumed to have errors but not to be estimated. The only restriction on this choice is that the time evolution of the consider parameters must not depend on any of the solve-for parameters. The result of an error analysis is an indication of the contributions of the various error sources to the uncertainties in the determination of the spacecraft solve-for parameters. The model presented gives the uncertainty due to errors in the a priori estimates of the solve-for parameters, the uncertainty due to measurement noise, the uncertainty due to dynamic noise (also known as process noise or measurement noise), the uncertainty due to the consider parameters, and the overall uncertainty due to all these sources of error.

Markley, F. Landis↗

NASA NTRS1988

An improved error assessment for the GEM-T1 gravitational model

Several tests were designed to determine the correct error variances for the Goddard Earth Model (GEM)-T1 gravitational solution which was derived exclusively from satellite tracking data. The basic method employs both wholly independent and dependent subset data solutions and produces a full field coefficient estimate of the model uncertainties. The GEM-T1 errors were further analyzed using a method based upon eigenvalue-eigenvector analysis which calibrates the entire covariance matrix. Dependent satellite and independent altimetric and surface gravity data sets, as well as independent satellite deep resonance information, confirm essentially the same error assessment. These calibrations (utilizing each of the major data subsets within the solution) yield very stable calibration factors which vary by approximately 10 percent over the range of tests employed. Measurements of gravity anomalies obtained from altimetry were also used directly as observations to show that GEM-T1 is calibrated. The mathematical representation of the covariance error in the presence of unmodeled systematic error effects in the data is analyzed and an optimum weighting technique is developed for these conditions. This technique yields an internal self-calibration of the error model, a process which GEM-T1 is shown to approximate.

Lerch, F. J.↗

NASA NTRS1989

Dynamical predictability in a simple general circulation model - Average error growth

Average predictability and error growth in a simple realistic two-level general circulation model (GCM) were investigated using a series of Monte Carlo experiments for fixed external forcing (perpetual winter in the Northern Hemisphere). It was found that, for realistic initial errors, the dependence of the limit of dynamic predictability on total wavenumber was similar to that found for the ECMWF model for the 1980/1981 winter conditions, with the lowest wavenumbers showing significant skill for forecast ranges of more than 1 month. On the other hand, for very small amplitude errors distributed according to the climate spectrum, the total error growth was superexponential, reaching a maximum growth rate (2-day doubling time) in about 1 week. A simple empirical model of error variance, which involved two broad wavenumber bands and incorporating a 3/2 power saturation term, was found to provide an excellent fit to the GCM error growth behavior.

Schubert, Siegfried D.↗

NASA NTRS1989

Sensitivity of mesoscale-model forecast skill to some initial-data characteristics, data density, data position, analysis procedure and measurement error

The effects of horizontal and vertical data resolution, data density, data location, different objective analysis algorithms, and measurement error on mesoscale-forecast accuracy are studied with observing-system simulation experiments. Domain-averaged errors are shown to generally decrease with time. It is found that the vertical distribution of error growth depends on the initial vertical distribution of the error itself. Larger gravity-inertia wave noise is produced in forecasts with coarser vertical data resolution. The use of a low vertical resolution observing system with three data levels leads to more forecast errors than moderate and high vertical resolution observing systems with 8 and 14 data levels. Also, with poor vertical resolution in soundings, the initial and forecast errors are not affected by the horizontal data resolution.

Warner, Thomas T.↗

NASA NTRS1990

Asymmetric Memory Circuit Would Resist Soft Errors

Some nonlinear error-correcting codes more efficient in presence of asymmetry. Combination of circuit-design and coding concepts expected to make integrated-circuit random-access memories more resistant to "soft" errors (temporary bit errors, also called "single-event upsets" due to ionizing radiation). Integrated circuit of new type made deliberately more susceptible to one kind of bit error than to other, and associated error-correcting code adapted to exploit this asymmetry in error probabilities.

Buehler, Martin G.↗