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Consideration is given to the number of minimum-weight code words in a product code. The code is considered as a tensor product of linear codes over a finite field. Complete theorems and proofs are presented.
Two error-erasure decoding algorithms for product codes that correct all the error-erasure patterns guaranteed correctable by the minimum Hamming distance of the product code are given. The first algorithm works when at least one of the component codes is majority-logic decodable. The second algorithm works for any product code. Both algorithms use the decoders of the component codes.
Variable redundancy tensor product codes, discussing encoder modes implementation for adaptive coding and feedback transmission
Tensor products of linear codes, and product codes with dual cyclic component codes
Index of comma freedom in Kronecker product code dictionaries - information processing
Majority logic decodability of product of two majority logic decodable cyclic codes
Interlaced binary BCH codes are described for multiple-burst-error correction for the UNICON 690 laser memory. Other multiple-burst-error-correcting codes, such as Reed-Solomon codes and Product codes, are also briefly mentioned. In particular, an interlaced (31, 21) t = 2 BCH code is selected as an outer code for UNICON double-burst-error correction. This code is shortened to (26,16) and interlaced to degree X = 16. Decoding is implemented by table lookup. This method not only avoids all computations in GF(2(exp 5)), it also offers a decoding time of less than 1 ps. The inner code is an existing (80,64) Fire code capable of correcting a single-burst error of length b less than or equal to 6.
This report focuses on the results obtained during the PI's recent sabbatical leave at the Swiss Federal Institute of Technology (ETH) in Zurich, Switzerland, from January 1, 1995 through June 30, 1995. Two projects investigated various properties of TURBO codes, a new form of concatenated coding that achieves near channel capacity performance at moderate bit error rates. The performance of TURBO codes is explained in terms of the code's distance spectrum. These results explain both the near capacity performance of the TURBO codes and the observed 'error floor' for moderate and high signal-to-noise ratios (SNR's). A semester project, entitled 'The Realization of the Turbo-Coding System,' involved a thorough simulation study of the performance of TURBO codes and verified the results claimed by previous authors. A copy of the final report for this project is included as Appendix A. A diploma project, entitled 'On the Free Distance of Turbo Codes and Related Product Codes,' includes an analysis of TURBO codes and an explanation for their remarkable performance. A copy of the final report for this project is included as Appendix B.
This presentation provides an overview of the progress made by the FLASHFlux working group within the CERES Science Team. FLASHFlux is maintaining operations, continuing validation, migration production code for future production systems, and evaluating new inputs for their impacts on the current radiative flux data products. FLASHFlux data products continue to be served to the community and comprise the low latency solar and thermal infrared data products provided to the energy and agricultural communities at relatively low latency for global gridded data fluxes. (< 7days).
The design of a secure communication system is described. A product code, formed from two pseudorandom sequences of digital bits, is used to encipher or scramble data prior to transmission. The two pseudorandom sequences are periodically changed at intervals before they have had time to repeat. One of the two sequences is transmitted continuously with the scrambled data for synchronization. In the receiver portion of the system, the incoming signal is compared with one of two locally generated pseudorandom sequences until correspondence between the sequences is obtained. At this time, the two locally generated sequences are formed into a product code which deciphers the data from the incoming signal. Provision is made to ensure synchronization of the transmitting and receiving portions of the system.
A FORTRAN computer program for the semi analytic prediction of unsteady thrust augmenting ejector performance has been developed, based on a theoretical analysis for ejectors. That analysis blends classic self-similar turbulent jet descriptions with control-volume mixing region elements. Division of the ejector into an inlet, diffuser, and mixing region allowed flexibility in the modeling of the physics for each region. In particular, the inlet and diffuser analyses are simplified by a quasi-steady-analysis, justified by the assumption that pressure is the forcing function in those regions. Only the mixing region is assumed to be dominated by viscous effects. The present work provides an overview of the code structure, a description of the required input and output data file formats, and the results for a test case. Since there are limitations to the code for applications outside the bounds of the test case, the user should consider TEA as a research code (not as a production code), designed specifically as an implementation of the proposed ejector theory. Program error flags are discussed, and some diagnostic routines are presented.
Model-based development and automated code generation are increasingly used for production code in safety-critical applications, but since code generators are typically not qualified, the generated code must still be fully tested, reviewed, and certified. This is particularly arduous for mathematical and control engineering software which requires reviewers to trace subtle details of textbook formulas and algorithms to the code, and to match requirements (e.g., physical units or coordinate frames) not represented explicitly in models or code. Both tasks are complicated by the often opaque nature of auto-generated code. We address these problems by developing a verification-driven approach to traceability and documentation. We apply the AUTOCERT verification system to identify and then verify mathematical concepts in the code, based on a mathematical domain theory, and then use these verified traceability links between concepts, code, and verification conditions to construct a natural language report that provides a high-level structured argument explaining why and how the code uses the assumptions and complies with the requirements. We have applied our approach to generate review documents for several sub-systems of NASA s Project Constellation.
Various implementations of the direct simulation Monte Carlo (DSMC) method exist in academia, government and industry. By comparing implementations, deficiencies and merits of each can be discovered. This document reports comparisons between DSMC Analysis Code (DAC) and MONACO. DAC is NASA's standard DSMC production code and MONACO is a research DSMC code developed in academia. These codes have various differences; in particular, they employ distinct computational grid definitions. In this study, DAC and MONACO are compared by having each simulate a blunted flat plate wind tunnel test, using an identical volume mesh. Simulation expense and DSMC metrics are compared. In addition, flow results are compared with available laboratory data. Overall, this study revealed that both codes, excluding grid adaptation, performed similarly. For parallel processing, DAC was generally more efficient. As expected, code accuracy was mainly dependent on physical models employed.
The generalized Hamming weights of linear codes were first introduced by Wei. These are fundamental parameters related to the minimal overlap structures of the subcodes and very useful in several fields. It was found that the chain condition of a linear code is convenient in studying the generalized Hamming weights of the product codes. In this paper we consider a class of codes defined over some varieties in projective spaces over finite fields, whose generalized Hamming weights can be determined by studying the orbits of subspaces of the projective spaces under the actions of classical groups over finite fields, i.e., the symplectic groups, the unitary groups and orthogonal groups. We give the weight hierarchies and generalized weight spectra of the codes from Hermitian varieties and prove that the codes satisfy the chain condition.
Accurate computation of sensitivity derivatives is becoming an important item in Computational Fluid Dynamics (CFD) because of recent emphasis on using nonlinear CFD methods in aerodynamic design, optimization, stability and control related problems. Several techniques are available to compute gradients or sensitivity derivatives of desired flow quantities or cost functions with respect to selected independent (design) variables. Perhaps the most common and oldest method is to use straightforward finite-differences for the evaluation of sensitivity derivatives. Although very simple, this method is prone to errors associated with choice of step sizes and can be cumbersome for geometric variables. The cost per design variable for computing sensitivity derivatives with central differencing is at least equal to the cost of three full analyses, but is usually much larger in practice due to difficulty in choosing step sizes. Another approach gaining popularity is the use of Automatic Differentiation software (such as ADIFOR) to process the source code, which in turn can be used to evaluate the sensitivity derivatives of preselected functions with respect to chosen design variables. In principle, this approach is also very straightforward and quite promising. The main drawback is the large memory requirement because memory use increases linearly with the number of design variables. ADIFOR software can also be cumber-some for large CFD codes and has not yet reached a full maturity level for production codes, especially in parallel computing environments.
The long and highly successful joint SGI-NASA research effort in ever larger SSI systems was to a large degree the result of the successful development of the MLP scalable parallel programming paradigm developed at ARC: 1) MLP scaling in real production codes justified ever larger systems at NAS; 2) MLP scaling on 256p Origin 2000 gave SGl impetus to productize 256p; 3) MLP scaling on 512 gave SGI courage to build 1024p O3K; and 4) History of MLP success resulted in IBM Star Cluster based MLP effort.
The Imaging for Hypersonic Experimental Aeroheating Testing (IHEAT) code is used at NASA Langley Research Center to analyze global aeroheating data on wind tunnel models tested in the Langley Aerothermodynamics Laboratory. One-dimensional, semi-infinite heating data derived from IHEAT are used to design thermal protection systems to mitigate the risks due to the aeroheating loads on hypersonic vehicles, such as re-entry vehicles during descent and landing procedures. This code was originally written in the PV-WAVE programming language to analyze phosphor thermography data from the two-color, relativeintensity system developed at Langley. To increase the efficiency, functionality, and reliability of IHEAT, the code was migrated to MATLAB syntax and compiled as a stand-alone executable file labeled version 4.0. New features of IHEAT 4.0 include the options to batch process all of the data from a wind tunnel run, to map the two-dimensional heating distribution to a three-dimensional computer-aided design model of the vehicle to be viewed in Tecplot, and to extract data from a segmented line that follows an interesting feature in the data. Results from IHEAT 4.0 were compared on a pixel level to the output images from the legacy code to validate the program. The differences between the two codes were on the order of 10-5 to 10-7. IHEAT 4.0 replaces the PV-WAVE version as the production code for aeroheating experiments conducted in the hypersonic facilities at NASA Langley.
Designing missions on expendable launch vehicles (ELV's) includes determining launch vehicle performance capabilities and trajectory characteristics over the range of mission requirements for suitable launch periods. This analysis depends on mathematically modeling both the launch vehicle and the mission requirements. Generally the result is a mathematical model that is described by an objective function to be optimized subject to an assortment of algebraic and dynamic constraints. About 30 years ago, engineers at Lewis Research Center (LeRC) undertook the task of creating a software code to solve 3D versions of such problems and based it on the Calculus of Variations/Optimal Control Theory. One of these codes, DUKSUP, has been in use at LeRC for nearly 25 years, during which time it has played an important role in a large number of studies and actual missions. Currently it is being used by about 12 analysts in the Center's Advanced Space Analysis Office (ASAO) to do mission design, feasibility studies, corroboration of contractor data and planning studies for the Space Exploration Initiative (SEI). Today, it is one of the few ELV mission analysis production codes based on variational methods. With future ELV missions in mind, ASAO is presently creating a new code to upgrade DUKSUP's capabilities.