Search NASA⌕ Search

SEARCH · Search NASA

Results for “block errors”

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.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

The formation and analysis of a 5 deg equal area block terrestrial gravity field

A set of 23,355 1 degree x 1 degree mean free air anomalies were used to predict a set of 5 degree equal area anomalies and their standard errors. Using the 1 degree data incorporating geophysically predicted values of ACIC, 1283 5 degree blocks were computed. Excluding the geophysically predicted anomalies 1249 blocks were computed. The 1 degree data were also used to compute covariance functions and the equatorial gravity and flattening implied by this data. The predicted anomalies were supplemented by model anomalies to form a complete 1654 global anomaly field. These data were used in a weighted least squares to determine potential coefficients to degree 15, and in a summation type formulation to determine potential coefficients to degree 25. These potential coefficients sets are compared to recent satellite determinations.

Rapp, R. H.↗
NASA NTRS1991

Suboptimum decoding of block codes

This paper investigates a class of decomposable codes, their distance and structural properties. it is shown that this class includes several classes of well known and efficient codes as subclasses. Several methods for constructing decomposable codes or decomposing codes are presented. A two-stage soft decision decoding scheme for decomposable codes, their translates or unions of translates is devised. This two-stage soft-decision decoding is suboptimum, and provides an excellent trade-off between the error performance and decoding complexity for codes of moderate and long block length.

Lin, Shu↗
NASA NTRS1998

Trellises and Trellis-Based Decoding Algorithms for Linear Block Codes

A code trellis is a graphical representation of a code, block or convolutional, in which every path represents a codeword (or a code sequence for a convolutional code). This representation makes it possible to implement Maximum Likelihood Decoding (MLD) of a code with reduced decoding complexity. The most well known trellis-based MLD algorithm is the Viterbi algorithm. The trellis representation was first introduced and used for convolutional codes [23]. This representation, together with the Viterbi decoding algorithm, has resulted in a wide range of applications of convolutional codes for error control in digital communications over the last two decades. There are two major reasons for this inactive period of research in this area. First, most coding theorists at that time believed that block codes did not have simple trellis structure like convolutional codes and maximum likelihood decoding of linear block codes using the Viterbi algorithm was practically impossible, except for very short block codes. Second, since almost all of the linear block codes are constructed algebraically or based on finite geometries, it was the belief of many coding theorists that algebraic decoding was the only way to decode these codes. These two reasons seriously hindered the development of efficient soft-decision decoding methods for linear block codes and their applications to error control in digital communications. This led to a general belief that block codes are inferior to convolutional codes and hence, that they were not useful. Chapter 2 gives a brief review of linear block codes. The goal is to provide the essential background material for the development of trellis structure and trellis-based decoding algorithms for linear block codes in the later chapters. Chapters 3 through 6 present the fundamental concepts, finite-state machine model, state space formulation, basic structural properties, state labeling, construction procedures, complexity, minimality, and sectionalization of trellises. Chapter 7 discusses trellis decomposition and subtrellises for low-weight codewords. Chapter 8 first presents well known methods for constructing long powerful codes from short component codes or component codes of smaller dimensions, and then provides methods for constructing their trellises which include Shannon and Cartesian product techniques. Chapter 9 deals with convolutional codes, puncturing, zero-tail termination and tail-biting.Chapters 10 through 13 present various trellis-based decoding algorithms, old and new. Chapter 10 first discusses the application of the well known Viterbi decoding algorithm to linear block codes, optimum sectionalization of a code trellis to minimize computation complexity, and design issues for IC (integrated circuit) implementation of a Viterbi decoder. Then it presents a new decoding algorithm for convolutional codes, named Differential Trellis Decoding (DTD) algorithm. Chapter 12 presents a suboptimum reliability-based iterative decoding algorithm with a low-weight trellis search for the most likely codeword. This decoding algorithm provides a good trade-off between error performance and decoding complexity. All the decoding algorithms presented in Chapters 10 through 12 are devised to minimize word error probability. Chapter 13 presents decoding algorithms that minimize bit error probability and provide the corresponding soft (reliability) information at the output of the decoder. Decoding algorithms presented are the MAP (maximum a posteriori probability) decoding algorithm and the Soft-Output Viterbi Algorithm (SOVA) algorithm. Finally, the minimization of bit error probability in trellis-based MLD is discussed.

Lin, Shu↗
NASA NTRS2021

Design and Modeling of a Coded-Interleaving System in the Presence of Fading

Future deep space links are migrating towards higher frequency bands such as Ka band and optical. These links are susceptible to non linear effects (e.g. cloud coverage, atmospheric turbulence, scintillation, antenna mis-pointing, jitter, relative motion, etc.) that cause various degrees of fading loss over various time scales. We consider a channel experiencing block fading where the channel coherence time is a lot longer than the length of a codeword. As long as the fading duration is not excessive, an interleaver can be used in a coded-communication system that randomizes the fades among symbols of multiple codewords. This achieves an “averaging” effect that spreads the signal energy more evenly among the codewords, and improves the likelihood that each of them can be decoded correctly. For simplicity, we consider a block interleaver where adjacent symbols of a codeword have a fixed delay (or separation) with each other, and investigate the error-rate performance of a coded-interleaving system (with fixed and finite interleaving depth) in the presence of block fading. Unlike prior research which assumes theoretical channel coherence models, we aim to build upon our analysis using empirical spacecraft signal measurements obtained with the Deep Space Network, and to use the fundamental theories of probability and statistics (e.g. variations of Law of Large Numbers) to quantify the error-rate performance of the coded-interleaving system. We propose to utilize these results in the design of a two-dimensional coded-interleaving system for fading channels.

Sanchez-Net, Marc↗
NASA NTRS1990

Custom CMOS Reed Solomon coder for the Hubble Space Telescope

A VLSI coder is presented that can function either as an encoder or decoder for Reed-Solomon codes. VLSI is one approach to implementing high-performance Reed-Solomon decoders. There are three VLSI technologies that could be used: gate arrays, standard cells, and full custom. The first two approaches are relatively easy to implement, but are limited in both performance and density. Full-custom VLSI is used to achieve both circuit density and speed, and allows control of the amount of interconnect. Speed, which is a function of capacitance, which is a function of interconnect, is an important parameter in high-performance VLSI. A single 8.2 mm x 8.4 mm, 200,000 transistor CMOS chip implementation of the Reed-Solomon code required by the Hubble Space Telescope is reported. The chip features a 10-MHz sustained byte rate independent of error pattern. The 1.6-micron CMOS integrated circuit has complete decoder and encoder functions and uses a single data/system clock. Block lengths up to 255 bytes and shortened codes are supported with no external buffering. Erasure corrections and random error corrections are supported with programmable correction of up to 10 symbol errors. Correction time is independent of error pattern and the number of errors in the incoming message.

Whitaker, S.↗
NASA NTRS2011

Prioritized LT Codes

The original Luby Transform (LT) coding scheme is extended to account for data transmissions where some information symbols in a message block are more important than others. Prioritized LT codes provide unequal error protection (UEP) of data on an erasure channel by modifying the original LT encoder. The prioritized algorithm improves high-priority data protection without penalizing low-priority data recovery. Moreover, low-latency decoding is also obtained for high-priority data due to fast encoding. Prioritized LT codes only require a slight change in the original encoding algorithm, and no changes at all at the decoder. Hence, with a small complexity increase in the LT encoder, an improved UEP and low-decoding latency performance for high-priority data can be achieved. LT encoding partitions a data stream into fixed-sized message blocks each with a constant number of information symbols. To generate a code symbol from the information symbols in a message, the Robust-Soliton probability distribution is first applied in order to determine the number of information symbols to be used to compute the code symbol. Then, the specific information symbols are chosen uniform randomly from the message block. Finally, the selected information symbols are XORed to form the code symbol. The Prioritized LT code construction includes an additional restriction that code symbols formed by a relatively small number of XORed information symbols select some of these information symbols from the pool of high-priority data. Once high-priority data are fully covered, encoding continues with the conventional LT approach where code symbols are generated by selecting information symbols from the entire message block including all different priorities. Therefore, if code symbols derived from high-priority data experience an unusual high number of erasures, Prioritized LT codes can still reliably recover both high- and low-priority data. This hybrid approach decides not only "how to encode" but also "what to encode" to achieve UEP. Another advantage of the priority encoding process is that the majority of high-priority data can be decoded sooner since only a small number of code symbols are required to reconstruct high-priority data. This approach increases the likelihood that high-priority data is decoded first over low-priority data. The Prioritized LT code scheme achieves an improvement in high-priority data decoding performance as well as overall information recovery without penalizing the decoding of low-priority data, assuming high-priority data is no more than half of a message block. The cost is in the additional complexity required in the encoder. If extra computation resource is available at the transmitter, image, voice, and video transmission quality in terrestrial and space communications can benefit from accurate use of redundancy in protecting data with varying priorities.

Woo, Simon S.↗
NASA NTRS1990

New multi-level codes over GF(q)

Set partitioning to multi-dimensional signal spaces over GF(q), particularly GF sup q-1(q) and GF sup q (q), and show how to construct both multi-level block codes and multi-level trellis codes over GF(q). Two classes of multi-level (n, k, d) block codes over GF(q) with block length n, number of information symbols k, and minimum distance d sub min greater than or = d, are presented. These two classes of codes use Reed-Solomon codes as component codes. They can be easily decoded as block length q-1 Reed-Solomon codes or block length q or q + 1 extended Reed-Solomon codes using multi-stage decoding. Many of these codes have larger distances than comparable q-ary block codes, as component codes. Low rate q-ary convolutional codes, work error correcting convolutional codes, and binary-to-q-ary convolutional codes can also be used to construct multi-level trellis codes over GF(q) or binary-to-q-ary trellis codes, some of which have better performance than the above block codes. All of the new codes have simple decoding algorithms based on hard decision multi-stage decoding.

Wu, Jiantian↗
NASA NTRS1992

New multilevel codes over GF(q)

Set partitioning to multi-dimensional signal spaces over GF(q), particularly GF sup q-1(q) and GF sup q (q), and show how to construct both multi-level block codes and multi-level trellis codes over GF(q). Two classes of multi-level (n, k, d) block codes over GF(q) with block length n, number of information symbols k, and minimum distance d sub min greater than or = d, are presented. These two classes of codes use Reed-Solomon codes as component codes. They can be easily decoded as block length q-1 Reed-Solomon codes or block length q or q + 1 extended Reed-Solomon codes using multi-stage decoding. Many of these codes have larger distances than comparable q-ary block codes, as component codes. Low rate q-ary convolutional codes, work error correcting convolutional codes, and binary-to-q-ary convolutional codes can also be used to construct multi-level trellis codes over GF(q) or binary-to-q-ary trellis codes, some of which have better performance than the above block codes. All of the new codes have simple decoding algorithms based on hard decision multi-stage decoding.

Wu, Jiantian↗
NASA NTRS1976

Coding for a multiple-access channel

In a simple multiple-access communication system, two geographically separated users attempt to communicate binary data to two data sinks over a common channel called a multiple access channel. User one sends codewords from a block code C sub one, while user two sends codewords from a block code C sub two. The two users occupy the same frequency slot, transmit at the same time, and use the same type of modulation. Block codes which are uniquely decodable and capable of correcting errors are constructed for two multiple-access channel models. The first model is referred to as a noiseless multiple-access binary erasure channel. If the two transmitted bits from the two users are zeros, a zero is transmitted over the channel to the receiver; if the two transmitted bits are ones, a one is transmitted to the receiver; if the two bits are different, an erasure symbol is transmitted to the receiver. The second model is also a multiple-access binary erasure channel but with noise introduced.

Kasami, T.↗
NASA NTRS2013

Analysis of a Split-Plot Experimental Design Applied to a Low-Speed Wind Tunnel Investigation

A procedure to analyze a split-plot experimental design featuring two input factors, two levels of randomization, and two error structures in a low-speed wind tunnel investigation of a small-scale model of a fighter airplane configuration is described in this report. Standard commercially-available statistical software was used to analyze the test results obtained in a randomization-restricted environment often encountered in wind tunnel testing. The input factors were differential horizontal stabilizer incidence and the angle of attack. The response variables were the aerodynamic coefficients of lift, drag, and pitching moment. Using split-plot terminology, the whole plot, or difficult-to-change, factor was the differential horizontal stabilizer incidence, and the subplot, or easy-to-change, factor was the angle of attack. The whole plot and subplot factors were both tested at three levels. Degrees of freedom for the whole plot error were provided by replication in the form of three blocks, or replicates, which were intended to simulate three consecutive days of wind tunnel facility operation. The analysis was conducted in three stages, which yielded the estimated mean squares, multiple regression function coefficients, and corresponding tests of significance for all individual terms at the whole plot and subplot levels for the three aerodynamic response variables. The estimated regression functions included main effects and two-factor interaction for the lift coefficient, main effects, two-factor interaction, and quadratic effects for the drag coefficient, and only main effects for the pitching moment coefficient.

Erickson, Gary E.↗
NASA NTRSDate not supplied

Aeroheating Predictions for a Hypersonic, Turbulent Near-Wake

The accuracy of heating predictions using various turbulence models is examined for an axisymmetric near-wake at Mach 6. The CFD predictions are compared with experimental data collected under AGARD Working Group 18 on the wake of a 70-degree sphere-cone. The impact of grid resolution and discretization error is estimated, which allows a comparison of stacked-block and conventional structured meshes. The accuracy of steady Reynolds-averaged Navier-Stokes (RANS) models is contrasted with that of a hybrid RANS/Large-Eddy Simulation model. The predictions are made with three different CFD codes (LAURA, FUN3D, and HyperSolve), to demonstrate the code-to-code variation in the results. Steady SST models capture the qualitative nature of the heating in the wake, including the increasing peak heating with increasing Reynolds number. Spalart-Allmaras models, including SA-Catris, under-predicted the peak heating in the wake. Hybrid RANS/LES models improve upon the SA results but have their own modeling difficulties near the shear layer impingement. These results are generally consistent across solvers and grid topologies.

RANS↗
NASA NTRSDate not supplied

Aeroheating Predictions for a Hypersonic, Turbulent Near-Wake

The accuracy of heating predictions using various turbulence models is examined for an axisymmetric near-wake at Mach 6. The CFD predictions are compared with experimental data collected under AGARD Working Group 18 on the wake of a 70-degree sphere-cone. The impact of grid resolution and discretization error is estimated, which allows a comparison of stacked-block and conventional structured meshes. The accuracy of steady Reynolds-averaged Navier-Stokes (RANS) models is contrasted with that of a hybrid RANS/Large-Eddy Simulation model. The predictions are made with three different CFD codes (LAURA, FUN3D, and HyperSolve), to demonstrate the code-to-code variation in the results. Steady SST models capture the qualitative nature of the heating in the wake, including the increasing peak heating with increasing Reynolds number. Spalart-Allmaras models, including SA-Catris, under-predicted the peak heating in the wake. Hybrid RANS/LES models improve upon the SA results but have their own modeling difficulties near the shear layer impingement. These results are generally consistent across solvers and grid topologies.

RANS↗
NASA NTRS1993

DCT quantization matrices visually optimized for individual images

This presentation describes how a vision model incorporating contrast sensitivity, contrast masking, and light adaptation is used to design visually optimal quantization matrices for Discrete Cosine Transform image compression. The Discrete Cosine Transform (DCT) underlies several image compression standards (JPEG, MPEG, H.261). The DCT is applied to 8x8 pixel blocks, and the resulting coefficients are quantized by division and rounding. The 8x8 'quantization matrix' of divisors determines the visual quality of the reconstructed image; the design of this matrix is left to the user. Since each DCT coefficient corresponds to a particular spatial frequency in a particular image region, each quantization error consists of a local increment or decrement in a particular frequency. After adjustments for contrast sensitivity, local light adaptation, and local contrast masking, this coefficient error can be converted to a just-noticeable-difference (jnd). The jnd's for different frequencies and image blocks can be pooled to yield a global perceptual error metric. With this metric, we can compute for each image the quantization matrix that minimizes the bit-rate for a given perceptual error, or perceptual error for a given bit-rate. Implementation of this system demonstrates its advantages over existing techniques. A unique feature of this scheme is that the quantization matrix is optimized for each individual image. This is compatible with the JPEG standard, which requires transmission of the quantization matrix.

Watson, Andrew B.↗
NASA NTRS1993

An operational method for estimating signal to noise ratios from data acquired with imaging spectrometers

A method, using the concept of local means and local standard deviations of small imaging blocks and using a box counting procedure, has been developed for unsupervised estimation of the average signal to noise ratios of images in which the noise is additive. The method has been applied to simulated images with Gaussian noise, to images acquired with the Airborne Visible Infrared Imaging Spectrometer and with the Geophysical and Environmental Research Imaging Spectrometer. The method is compared with other techniques for estimating signal to noise ratios from imaging data. It is believed that the method is generally applicable to images having many small homogeneous blocks. Because the method does not take into account interband effects, it is not appropriate to use the method to estimate signal to noise ratios from images having nonnegligible interband radiometric calibration errors at spatial scales less than or equal to the size of the small imaging blocks used in the noise estimation.

Gao, Bo-Cai↗
NASA NTRS1990

Computational enhancement of an unsymmetric block Lanczos algorithm

An unsymmetric block Lanczos algorithm has been employed for the dynamic analysis of a large system which has arbitrary damping and/or repeated (or closely spaced) eigenvalues. In the algorithm development, the right and left Lanczos vectors are all theoretically biorthogonal to each other. However, these vectors may lose the biorthogonality owing to cancellation and roundoff errors. For the unsymmetric case there can be a breakdown, even without numerical errors. This paper describes computational techniques which have led to a robust unsymmetric block Lanczos algorithm.

Kim, Hyoung M.↗
NASA NTRS1975

Performance of some block codes on a Gaussian channel

A technique proposed by Chase (1972) is used to evaluate the performance of several fairly long binary block codes on a wideband additive Gaussian channel. Considerations leading to the use of Chase's technique are discussed. Chase's concepts are first applied to the most powerful practical class of binary codes, the BCH codes with Berlekamp's (1972) decoding algorithm. Chase's algorithm is then described along with proposed selection of candidate codes. Results are presented of applying Chase's algorithm to four binary codes: (23, 12) Golay code, (32, 16) second-order Reed-Muller code, (63, 36) 5-error correcting BCH code, and (95, 39) 9-error correcting shortened BCH code. It is concluded that there are many block codes of length not exceeding 100 with extremely attractive maximum likelihood decoding performance on a Gaussian channel. BCH codes decoded via Berlekamp's binary decoding algorithm and Chase's idea are close to being practical competitors to short-constraint length convolutional codes with Viterbi decoding.

Baumert, L. D.↗
NASA NTRS1983

Development of software fault-tolerance techniques

As computers become more widely used, and in particular as they become used in more safety critical applications, the reliability of the computer system and its software becomes more important. There is also an increasing need for high levels of reliability in applications involving very large numbers of inexpensive units where recall of the units would be disproportionately expensive. The nature of faults and the assumptions made by different approaches to correct operation are considered. The recovery block approach is described and a probabilistic analysis of its effectiveness, with and without correlated design errors is provided. Mechanisms for generating acceptance tests from specifications, and for providing recovery in the presence of asynchrony, are described. An analysis of, and design for, the provision of recovery blocks in the microprogram of the Bendix BDX930 processor is provided. An example of the use of recovery blocks in a simple operating system is also provided.

Melliar-Smith, P. M.↗