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At least 451 records · Page 25

Permanence analysis of a concatenated coding scheme for error control

A concatenated coding scheme for error control in data communications is analyzed. In this scheme, 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 the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for the planetary program, is analyzed.

Costello, D. J., Jr.↗

Probability of undetected error after decoding for a concatenated coding scheme

A concatenated coding scheme for error control in data communications is analyzed. In this scheme, 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 the outer code detects the presence of errors after the inner code decoding. Probability of undetected error is derived and bounded. A particular example, proposed for NASA telecommand system is analyzed.

Costello, D. J., Jr.↗

On the probability of undetected error for the maximum distance separable codes

The performance of maximum-distance-separable codes with symbols from GF(1) when they are used for pure error detection or for simultaneous error correction and detection is investigated. These codes are good for symbol error detection. Their probability of undetected error is upper bounded by q to the -r and decreases monotonically as the symbol error probability epsilon decreases from (q-1)/q to 0, where r is the number of parity-check symbols of a code.

Kasami, T.↗

A concatenated coding scheme for error control

A concatenated coding scheme for error control in data communications is 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 the outer code detects the presence of errors after the inner code decoding. The probability of undetected error of the above error control scheme is derived and upper bounded. Two specific exmaples are analyzed. In the first example, the inner code is a distance-4 shortened Hamming code with generator polynomial (X+1)(X(6)+X+1) = X(7)+X(6)+X(2)+1 and the outer code is a distance-4 shortened Hamming code with generator polynomial (X+1)X(15+X(14)+X(13)+X(12)+X(4)+X(3)+X(2)+X+1) = X(16)+X(12)+X(5)+1 which is the X.25 standard for packet-switched data network. This example is proposed for error control on NASA telecommand links. In the second example, the inner code is the same as that in the first example but the outer code is a shortened Reed-Solomon code with symbols from GF(2(8)) and generator polynomial (X+1)(X+alpha) where alpha is a primitive element in GF(z(8)).

Lin, S.↗

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.↗

A concatenated coding scheme for error control

In this paper, a concatenated coding scheme for error control in data communications is presented and analyzed. In this scheme, 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 (or decoding error) of the proposed scheme is derived. An efficient method for computing this probability is presented. Throughput efficiency of the proposed error control scheme incorporated with a selective-repeat ARQ retransmission strategy is also analyzed. Three specific examples are presented. One of the examples is proposed for error control in the NASA Telecommand System.

Kasami, T.↗

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.↗

An improved error assessment for the GEM-T1 gravitational model

Several tests were designed to determine the correct error variances for the 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 by 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.

Lerch, F. J.↗

System and method for error detection and correction in virtual reality and augmented reality environments

Embodiments of the present disclosure are related to training one or more of machine learning algorithms in a virtual reality environment for error detection and correction and/or for employing one or more trained machine learning models in an augmented reality environment to detect and/or correct user errors associated the performance of one or more tasks.

97 MATHEMATICS AND COMPUTING↗

A method for correcting aspect solution errors in ROSAT HRI observations of compact sources

X-ray point sources observed with the ROSAT High Resolution Imager (HRI) often appear elongated over scales of approximately 5 sec-10 sec from the image core. This elongation has been attributed to errors in the attitude correction as the satellite is wobbled during the observations, and affects sources with both soft and hard X-ray spectra. In this paper, I report the results of an attempt to rid a high signal-to-noise observation of the soft X-ray point source HZ 43 of its characteristic elongation. I divided the observation into 181 separate images, each containing photons from only a small region on the detector through which the source passed during the satellite's wobble. By measuring the positions of the individual image centroids, I found clear evidence for systematic offsets from a common mean by up to approximately +/- 3 sec in both right ascension and declination as a function of phase in the satellite wobble. Shifting the subimages to a common center and then restacking them into a single image measurably improved the symmetry of the point-spread function. HRI observations are wobbled primarily to smooth out variations in the pixel-to-pixel sensitivity of the detector and also to extend the lifetime of the microchannel plates in the detector since these decay at a given location as a function of the number of photons detected. However, the elongations introduced by the aspect errors inhibit the identification of possible extended X-ray emission associated with sources such as pulsars and active galactic nuclei. In light of these results, I suggest that until the aspect errors are understood, observations of compact sources, where this effect may be important, should not be wobbled.

Morse, Jon A.↗

An improved error assessment for the GEM-T1 gravitational model

Several tests have been designed to estimate the correct error variances for the GEM-T1 gravitational solution that was derived exclusively from satellite tracking data. The basic method uses both independent and dependent subset data solutions and produces a coefficient-by-coefficient estimate of the model uncertainties. The GEM-T1 errors have been further analyzed using a method based on eigenvalue-eigenvector analysis, which calibrates the entire covariance matrix. Dependent satellite data sets and independent altimetric, resonant satellite, and surface gravity data sets all confirm essentially the same error assessment. The calibration test results yield very stable calibration factors, which vary only by approximately 10 percent over the range of tests performed. Based on these calibrated error estimates, GEM-T1 is a significantly improved solution, which to degree and order 8 is twice as accurate as earlier satellite derived models like GEM-L2. Also, by being complete to degree and order 36, GEM-T1 is more complete and has significantly reduced aliasing effects that were present in previous models.

Lerch, F. J.↗

Sloppy-slotted ALOHA

Random access signaling, which allows slotted packets to spill over into adjacent slots, is investigated. It is shown that sloppy-slotted ALOHA can always provide higher throughput than conventional slotted ALOHA. The degree of improvement depends on the timing error distribution. Throughput performance is presented for Gaussian timing error distributions, modified to include timing error corrections. A general channel capacity lower bound, independent of the specific timing error distribution, is also presented.

Crozier, Stewart N.↗

Synchronization of Reed-Solomon codes

The synchronization capabilities of Reed-Solomon codes when an appropriate coset of the code is used instead of the code itself are examined. In this case an E-error correcting Reed-Solomon code is transformed into a code capable of determining that there are m symbols out of sync, if e symbol errors occurred, whenever m + e E. In the event that m = 0, i.e., the word is in sync, then decoder will correct any pattern of E - 1 on fewer symbol errors.

Miller, R. L.↗

On correcting radial orbit errors for altimetric satellites using crossover analysis

A method is proposed for correcting radial orbit error in measurements of sea surface height using a satellite altimeter. Traditionally, the orbit error is modeled in terms of a Fourier series with the Fourier coefficients determined by minimizing the residual crossover difference in a least-squares sense. In this method an a priori constraint must be imposed to obtain a unique solution. It is shown that by using singular value decomposition, no such constraint is needed. This proposed method leaves the geographically dependent errors unchanged and makes only those corrections warranted by the information contained in crossover differences. Thus, the resultant ocean topography is free from any undue distortion which might be incurred by an a priori constraint. It is suggested that the method is useful for application to high-accuracy altimetric mission, because the orbit error can be reduced without compromising the accuracy of the measured mean ocean topography.

Fu, Lee-Lueng↗

Correction of satellite tracking data for an arbitrary tropospheric profile.

A procedure is given for deriving elevation-error and range-error correction equations in a form suitable for use in the rapid processing of satellite tracking data. The refractivity of the troposphere is assumed to have spherical symmetry, but may have any given profile that does not depart greatly from standard. When the procedure was tested for numerical accuracy by application to an exponential profile, the corrections calculated agreed with those obtained by ray tracing to 0.3% or better over a range of surface refractivity from 200 to 450 and a range of radiowave arrival angles from horizontal to vertical.

Marini, J. W.↗

An extended Reed Solomon decoder design

It has previously been shown that the Reed-Solomon (RS) codes can correct errors beyond the Singleton and Rieger Bounds with an arbitrarily small probability of a miscorrect. That is, an (n,k) RS code can correct more than (n-k)/2 errors. An implementation of such an RS decoder is presented in this paper. An existing RS decoder, the AHA4010, is utilized in this work. This decoder is especially useful for errors which are patterned with a long burst plus some random errors.

Chen, J.↗

Error-trellis Syndrome Decoding Techniques for Convolutional Codes

An error-trellis syndrome decoding technique for convolutional codes is developed. This algorithm is then applied to the entire class of systematic convolutional codes and to the high-rate, Wyner-Ash convolutional codes. A special example of the one-error-correcting Wyner-Ash code, a rate 3/4 code, is treated. The error-trellis syndrome decoding method applied to this example shows in detail how much more efficient syndrome decoding is than Viterbi decoding if applied to the same problem. For standard Viterbi decoding, 64 states are required, whereas in the example only 7 states are needed. Also, within the 7 states required for decoding, many fewer transitions are needed between the states.

Reed, I. S.↗

Error-trellis syndrome decoding techniques for convolutional codes

An error-trellis syndrome decoding technique for convolutional codes is developed. This algorithm is then applied to the entire class of systematic convolutional codes and to the high-rate, Wyner-Ash convolutional codes. A special example of the one-error-correcting Wyner-Ash code, a rate 3/4 code, is treated. The error-trellis syndrome decoding method applied to this example shows in detail how much more efficient syndrome decordig is than Viterbi decoding if applied to the same problem. For standard Viterbi decoding, 64 states are required, whereas in the example only 7 states are needed. Also, within the 7 states required for decoding, many fewer transitions are needed between the states.

Reed, I. S.↗