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NASA NTRS1992

Cascaded convolutional codes

Due to the hardware design of Galileo's Command and Data Subsystem (CDS), the channel code usable in an S-band (2290-2300 MHz) mission must include the NASA standard (7,1/2) convolutional code. Galileo's hardware encoder for the (15,1/4) code is not usable in S-band mode. However, the need for higher coding gain dictates the use of long constraint length convolutional codes. Theoretical results show how a large subclass of such codes is realizable by using a software encoder in the CDS cascaded with the hardware encoder for the NASA standard code.

Pollara, F.↗

NASA NTRS1994

Mapping Between Distinct Reed-Solomon Codes

One-to-one mapping between two Reed-Solomon (RS) codes devised to enable decoder designed for one of codes to operate on other one also. Codes in question must have same N and K parameters (defined below) but otherwise be two distinct RS codes. Mapping intended to enable same ground-based decoder to decode telemetry signals from two spacecraft in two different RS codes of (N,K) = (255,223). Also useful in purely terrestrial data communications and in optical and magnetic recording and playback of digitized audio and video signals. Implemented in interface circuitry and/or software to enable communication between coding systems of different manufacturers using different RS codes within same (N,K) family.

Perlman, Marvin↗

NASA NTRS1993

Exploiting the cannibalistic traits of Reed-Solomon codes

In Reed-Solomon codes and all other maximum distance separable codes, there is an intrinsic relationship between the size of the symbols in a codeword and the length of the codeword. Increasing the number of symbols in a codeword to improve the efficiency of the coding system thus requires using a larger set of symbols. However, long Reed-Solomon codes are difficult to implement and many communications or storage systems cannot easily accommodate an increased symbol size, e.g., M-ary frequency shift keying (FSK) and photon-counting pulse-position modulation demand a fixed symbol size. A technique for sharing redundancy among many different Reed-Solomon codewords to achieve the efficiency attainable in long Reed-Solomon codes without increasing the symbol size is described. Techniques both for calculating the performance of these new codes and for determining their encoder and decoder complexities is presented. These complexities are usually found to be substantially lower than conventional Reed-Solomon codes of similar performance.

Collins, O.↗

NASA NTRS1993

Users manual for the NASA Lewis three-dimensional ice accretion code (LEWICE 3D)

A description of the methodology, the algorithms, and the input and output data along with an example case for the NASA Lewis 3D ice accretion code (LEWICE3D) has been produced. The manual has been designed to help the user understand the capabilities, the methodologies, and the use of the code. The LEWICE3D code is a conglomeration of several codes for the purpose of calculating ice shapes on three-dimensional external surfaces. A three-dimensional external flow panel code is incorporated which has the capability of calculating flow about arbitrary 3D lifting and nonlifting bodies with external flow. A fourth order Runge-Kutta integration scheme is used to calculate arbitrary streamlines. An Adams type predictor-corrector trajectory integration scheme has been included to calculate arbitrary trajectories. Schemes for calculating tangent trajectories, collection efficiencies, and concentration factors for arbitrary regions of interest for single droplets or droplet distributions have been incorporated. A LEWICE 2D based heat transfer algorithm can be used to calculate ice accretions along surface streamlines. A geometry modification scheme is incorporated which calculates the new geometry based on the ice accretions generated at each section of interest. The three-dimensional ice accretion calculation is based on the LEWICE 2D calculation. Both codes calculate the flow, pressure distribution, and collection efficiency distribution along surface streamlines. For both codes the heat transfer calculation is divided into two regions, one above the stagnation point and one below the stagnation point, and solved for each region assuming a flat plate with pressure distribution. Water is assumed to follow the surface streamlines, hence starting at the stagnation zone any water that is not frozen out at a control volume is assumed to run back into the next control volume. After the amount of frozen water at each control volume has been calculated the geometry is modified by adding the ice at each control volume in the surface normal direction.

Bidwell, Colin S.↗

NASA NTRS1993

Separable concatenated codes with iterative map decoding for Rician fading channels

Very efficient signalling in radio channels requires the design of very powerful codes having special structure suitable for practical decoding schemes. In this paper, powerful codes are obtained by combining comparatively simple convolutional codes to form multi-tiered 'separable' convolutional codes. The decoding of these codes, using separable symbol-by-symbol maximum a posteriori (MAP) 'filters', is described. It is known that this approach yields impressive results in non-fading additive white Gaussian noise channels. Interleaving is an inherent part of the code construction, and consequently, these codes are well suited for fading channel communications. Here, simulation results for communications over Rician fading channels are presented to support this claim.

Lodge, J. H.↗

NASA NTRS1994

Convolutional encoding of self-dual codes

There exist almost complete convolutional encodings of self-dual codes, i.e., block codes of rate 1/2 with weights w, w = 0 mod 4. The codes are of length 8m with the convolutional portion of length 8m-2 and the nonsystematic information of length 4m-1. The last two bits are parity checks on the two (4m-1) length parity sequences. The final information bit complements one of the extended parity sequences of length 4m. Solomon and van Tilborg have developed algorithms to generate these for the Quadratic Residue (QR) Codes of lengths 48 and beyond. For these codes and reasonable constraint lengths, there are sequential decodings for both hard and soft decisions. There are also possible Viterbi-type decodings that may be simple, as in a convolutional encoding/decoding of the extended Golay Code. In addition, the previously found constraint length K = 9 for the QR (48, 24;12) Code is lowered here to K = 8.

Solomon, G.↗

NASA NTRS1994

Computer code for determination of thermally perfect gas properties

A set of one-dimensional compressible flow relations for a thermally perfect, calorically imperfect gas is derived for the specific heat c(sub p), expressed as a polynomial function of temperature, and developed into the thermally perfect gas (TPG) computer code. The code produces tables of compressible flow properties similar to those of NACA Rep. 1135. Unlike the tables of NACA Rep. 1135 which are valid only in the calorically perfect temperature regime, the TPG code results are also valid in the thermally perfect calorically imperfect temperature regime which considerably extends the range of temperature application. Accuracy of the TPG code in the calorically perfect temperature regime is verified by comparisons with the tables of NACA Rep. 1135. In the thermally perfect, calorically imperfect temperature regime, the TPG code is validated by comparisons with results obtained from the method of NACA Rep. 1135 for calculating the thermally perfect calorically imperfect compressible flow properties. The temperature limits for application of the TPG code are also examined. The advantage of the TPG code is its applicability to any type of gas (monatomic, diatomic, triatomic, or polyatomic) or any specified mixture thereof, whereas the method of NACA Rep. 1135 is restricted to only diatomic gases.

Witte, David W.↗

NASA NTRS1995

Turbo codes for deep-space communications

Turbo codes were recently proposed by Berrou, Glavieux, and Thitimajshima, and it has been claimed these codes achieve near-Shannon-limit error correction performance with relatively simple component codes and large interleavers. A required E(b)/N(o) of 0.7 dB was reported for a bit error rate of 10(exp -5), using a rate 1/2 turbo code. However, some important details that are necessary to reproduce these results were omitted. This article confirms the accuracy of these claims, and presents a complete description of an encoder/decoder pair that could be suitable for deep-space applications, where lower rate codes can be used. We describe a new simple method for trellis termination, analyze the effect of interleaver choice on the weight distribution of the code, and introduce the use of unequal rate component codes, which yield better performance.

Divsalar, D.↗

NASA NTRS1995

Enhancements to the SSME transfer function modeling code

This report details the results of a one year effort by Ohio University to apply the transfer function modeling and analysis tools developed under NASA Grant NAG8-167 (Irwin, 1992), (Bartholomew, 1992) to attempt the generation of Space Shuttle Main Engine High Pressure Turbopump transfer functions from time domain data. In addition, new enhancements to the transfer function modeling codes which enhance the code functionality are presented, along with some ideas for improved modeling methods and future work. Section 2 contains a review of the analytical background used to generate transfer functions with the SSME transfer function modeling software. Section 2.1 presents the 'ratio method' developed for obtaining models of systems that are subject to single unmeasured excitation sources and have two or more measured output signals. Since most of the models developed during the investigation use the Eigensystem Realization Algorithm (ERA) for model generation, Section 2.2 presents an introduction of ERA, and Section 2.3 describes how it can be used to model spectral quantities. Section 2.4 details the Residue Identification Algorithm (RID) including the use of Constrained Least Squares (CLS) and Total Least Squares (TLS). Most of this information can be found in the report (and is repeated for convenience). Section 3 chronicles the effort of applying the SSME transfer function modeling codes to the a51p394.dat and a51p1294.dat time data files to generate transfer functions from the unmeasured input to the 129.4 degree sensor output. Included are transfer function modeling attempts using five methods. The first method is a direct application of the SSME codes to the data files and the second method uses the underlying trends in the spectral density estimates to form transfer function models with less clustering of poles and zeros than the models obtained by the direct method. In the third approach, the time data is low pass filtered prior to the modeling process in an effort to filter out high frequency characteristics. The fourth method removes the presumed system excitation and its harmonics in order to investigate the effects of the excitation on the modeling process. The fifth method is an attempt to apply constrained RID to obtain better transfer functions through more accurate modeling over certain frequency ranges. Section 4 presents some new C main files which were created to round out the functionality of the existing SSME transfer function modeling code. It is now possible to go from time data to transfer function models using only the C codes; it is not necessary to rely on external software. The new C main files and instructions for their use are included. Section 5 presents current and future enhancements to the XPLOT graphics program which was delivered with the initial software. Several new features which have been added to the program are detailed in the first part of this section. The remainder of Section 5 then lists some possible features which may be added in the future. Section 6 contains the conclusion section of this report. Section 6.1 is an overview of the work including a summary and observations relating to finding transfer functions with the SSME code. Section 6.2 contains information relating to future work on the project.

Irwin, R. Dennis↗

NASA NTRS1995

Trellis complexity bounds for decoding linear block codes

We consider the problem of finding a trellis for a linear block code that minimizes one or more measures of trellis complexity. The domain of optimization may be different permutations of the same code or different codes with the same parameters. Constraints on trellises, including relationships between the minimal trellis of a code and that of the dual code, are used to derive bounds on complexity. We define a partial ordering on trellises: If a trellis is optimum with respect to this partial ordering, if has the desirable property that it simultaneously minimizes all of the complexity measures examined. We examine properties of such optimal trellises and give examples of optimal permutations of codes, most notably the (48,24,12) quadratic residue code.

Kiely, A. B.↗

NASA NTRS1995

X-Antenna: A graphical interface for antenna analysis codes

This report serves as the user's manual for the X-Antenna code. X-Antenna is intended to simplify the analysis of antennas by giving the user graphical interfaces in which to enter all relevant antenna and analysis code data. Essentially, X-Antenna creates a Motif interface to the user's antenna analysis codes. A command-file allows new antennas and codes to be added to the application. The menu system and graphical interface screens are created dynamically to conform to the data in the command-file. Antenna data can be saved and retrieved from disk. X-Antenna checks all antenna and code values to ensure they are of the correct type, writes an output file, and runs the appropriate antenna analysis code. Volumetric pattern data may be viewed in 3D space with an external viewer run directly from the application. Currently, X-Antenna includes analysis codes for thin wire antennas (dipoles, loops, and helices), rectangular microstrip antennas, and thin slot antennas.

Goldstein, B. L.↗

NASA NTRS1996

Communications and information research: Improved space link performance via concatenated forward error correction coding

With the development of new advanced instruments for remote sensing applications, sensor data will be generated at a rate that not only requires increased onboard processing and storage capability, but imposes demands on the space to ground communication link and ground data management-communication system. Data compression and error control codes provide viable means to alleviate these demands. Two types of data compression have been studied by many researchers in the area of information theory: a lossless technique that guarantees full reconstruction of the data, and a lossy technique which generally gives higher data compaction ratio but incurs some distortion in the reconstructed data. To satisfy the many science disciplines which NASA supports, lossless data compression becomes a primary focus for the technology development. While transmitting the data obtained by any lossless data compression, it is very important to use some error-control code. For a long time, convolutional codes have been widely used in satellite telecommunications. To more efficiently transform the data obtained by the Rice algorithm, it is required to meet the a posteriori probability (APP) for each decoded bit. A relevant algorithm for this purpose has been proposed which minimizes the bit error probability in the decoding linear block and convolutional codes and meets the APP for each decoded bit. However, recent results on iterative decoding of 'Turbo codes', turn conventional wisdom on its head and suggest fundamentally new techniques. During the past several months of this research, the following approaches have been developed: (1) a new lossless data compression algorithm, which is much better than the extended Rice algorithm for various types of sensor data, (2) a new approach to determine the generalized Hamming weights of the algebraic-geometric codes defined by a large class of curves in high-dimensional spaces, (3) some efficient improved geometric Goppa codes for disk memory systems and high-speed mass memory systems, and (4) a tree based approach for data compression using dynamic programming.

Rao, T. R. N.↗

NASA NTRS1996

Generalized Bezout's Theorem and its applications in coding theory

This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed.

Berg, Gene A.↗

NASA NTRS1996

Establishment of a Beta Test Center for the NPARC Code at Central State University

Central State University has received a supplementary award to purchase computer workstations for the NPARC (National Propulsion Ames Research Center) computational fluid dynamics code BETA Test Center. The computational code has also been acquired for installation on the workstations. The acquisition of this code is an initial step for CSU in joining an alliance composed of NASA, AEDC, The Aerospace Industry, and academia. A post-Doctoral research Fellow from a neighboring university will assist the PI in preparing a template for Tutorial documents for the BETA test center. The major objective of the alliance is to establish a national applications-oriented CFD capability, centered on the NPARC code. By joining the alliance, the BETA test center at CSU will allow the PI, as well as undergraduate and post-graduate students to test the capability of the NPARC code in predicting the physics of aerodynamic/geometric configurations that are of interest to the alliance. Currently, CSU is developing a once a year, hands-on conference/workshop based upon the experience acquired from running other codes similar to the NPARC code in the first year of this grant.

Okhio, Cyril B.↗

NASA NTRS1996

A Comparison of Computer Codes for the Propagation of Sonic Booms Through Realistic Atmospheres Utilizing Actual Acoustic Signatures

A numerical exercise to compare computer codes for the propagation of sonic booms through the atmosphere is reported. For the initial portion of the comparison, artificial, yet realistic, waveforms were numerically propagated through identical atmospheres. In addition to this comparison, one of these codes has been used to make preliminary predictions of the boom generated from a recent SR-71 flight. For the initial comparison, ground waveforms are calculated using four different codes or algorithms: (1) weak shock theory, an analytical prediction, (2) SHOCKN, a mixed time and frequency domain code developed at the University of Mississippi, (3) ZEPHYRUS, another mixed time and frequency code developed at the University of Texas, and (4) THOR, a pure time domain code recently developed at the University of Texas. The codes are described and their differences noted.

Chambers, James P.↗

NASA NTRS1997

Guide to AERO2S and WINGDES Computer Codes for Prediction and Minimization of Drag Due to Lift

The computer codes, AER02S and WINGDES, are now widely used for the analysis and design of airplane lifting surfaces under conditions that tend to induce flow separation. These codes have undergone continued development to provide additional capabilities since the introduction of the original versions over a decade ago. This code development has been reported in a variety of publications (NASA technical papers, NASA contractor reports, and society journals). Some modifications have not been publicized at all. Users of these codes have suggested the desirability of combining in a single document the descriptions of the code development, an outline of the features of each code, and suggestions for effective code usage. This report is intended to supply that need.

Carlson, Harry W.↗

NASA NTRS2004

Synthesizing Safety Conditions for Code Certification Using Meta-Level Programming

In code certification the code consumer publishes a safety policy and the code producer generates a proof that the produced code is in compliance with the published safety policy. In this paper, a novel viewpoint approach towards an implementational re-use oriented framework for code certification is taken. It adopts ingredients from Necula's approach for proof-carrying code, but in this work safety properties can be analyzed on a higher code level than assembly language instructions. It consists of three parts: (1) The specification language is extended to include generic pre-conditions that shall ensure safety at all states that can be reached during program execution. Actual safety requirements can be expressed by providing domain-specific definitions for the generic predicates which act as interface to the environment. (2) The Floyd-Hoare inductive assertion method is refined to obtain proof rules that allow the derivation of the proof obligations in terms of the generic safety predicates. (3) A meta-interpreter is designed and experimentally implemented that enables automatic synthesis of proof obligations for submitted programs by applying the modified Floyd-Hoare rules. The proof obligations have two separate conjuncts, one for functional correctness and another for the generic safety obligations. Proof of the generic obligations, having provided the actual safety definitions as context, ensures domain-specific safety of program execution in a particular environment and is simpler than full program verification.

Eusterbrock, Jutta↗

NASA NTRS2003

CFD Code Development for Combustor Flows

During the lifetime of this grant, work has been performed in the areas of model development, code development, code validation and code application. For model development, this has included the PDF combustion module, chemical kinetics based on thermodynamics, neural network storage of chemical kinetics, ILDM chemical kinetics and assumed PDF work. Many of these models were then implemented in the code, and in addition many improvements were made to the code, including the addition of new chemistry integrators, property evaluation schemes, new chemistry models and turbulence-chemistry interaction methodology. Validation of all new models and code improvements were also performed, while application of the code to the ZCET program and also the NPSS GEW combustor program were also performed. Several important items remain under development, including the NOx post processing, assumed PDF model development and chemical kinetic development. It is expected that this work will continue under the new grant.

Norris, Andrew↗