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NASA NTRSDate not supplied

Revisiting Building-Block Approaches for Structures

The building-block approach is a method for building confidence in designs, working from lower-level components to more complex assemblies, using knowledge gained at each step to inform higher fidelity representations. The goals of this paper are to revisit the basic techniques of the building-block approach as it applies to structural design and analysis and illustrate some best practices that should be considered when developing structural analysis models. The paper demonstrates the process of leveraging existing information to build confidence in the design/development of analysis models, followed by examples of how the building-block approach for analysis was used in NASA hardware and spacecraft development efforts. The paper will also discuss virtual testing and hybrid simulation techniques, which are showing promise for more efficient/cost-effective verification of aerospace structures.

Kenneth R. Hamm Jr.↗

NASA NTRS2014

X-Ray Micro-Computed Tomography of Apollo Samples as a Curation Technique Enabling Better Research

X-ray micro-computed tomography (micro-CT) is a technique that has been used to research meteorites for some time and many others], and recently it is becoming a more common tool for the curation of meteorites and Apollo samples. Micro-CT is ideally suited to the characterization of astromaterials in the curation process as it can provide textural and compositional information at a small spatial resolution rapidly, nondestructively, and without compromising the cleanliness of the samples (e.g., samples can be scanned sealed in Teflon bags). This data can then inform scientists and curators when making and processing future sample requests for meteorites and Apollo samples. Here we present some preliminary results on micro-CT scans of four Apollo regolith breccias. Methods: Portions of four Apollo samples were used in this study: 14321, 15205, 15405, and 60639. All samples were 8-10 cm in their longest dimension and approximately equant. These samples were micro-CT scanned on the Nikon HMXST 225 System at the Natural History Museum in London. Scans were made at 205-220 kV, 135-160 microamps beam current, with an effective voxel size of 21-44 microns. Results: Initial examination of the data identify a variety of mineral clasts (including sub-voxel FeNi metal grains) and lithic clasts within the regolith breccias. Textural information within some of the lithic clasts was also discernable. Of particular interest was a large basalt clast (approx.1.3 cc) found within sample 60639, which appears to have a sub-ophitic texture. Additionally, internal void space, e.g., fractures and voids, is readily identifiable. Discussion: It is clear from the preliminary data that micro-CT analyses are able to identify important "new" clasts within the Apollo breccias, and better characterize previously described clasts or igneous samples. For example, the 60639 basalt clast was previously believed to be quite small based on its approx.0.5 sq cm exposure on the surface of the main mass. These scans show the clast to be approx.4.5 g, however (assuming a density of approx.3.5 g/cc). This is large enough for detailed studies including multiple geo-chronometers. This basalt clast is of particular interest as it is the largest Apollo 16 basalt, and it is the only mid-TiO2 basalt in the Apollo sample suite. By identifying the location of interesting clasts or grains within a sample, we will be able to make more informed decisions about where to cut a sample in order to best expose clasts of interest for future study. Moreover, knowing the location of internal defects (e.g., fractures) will allow more precise chipping and extraction of clasts or grains. By combining micro-CT scans with compositional techniques like micro x-ray fluorescence (particularly on sawn slabs), we will be able to provide even more comprehensive information to scientists trying to best select samples that fit their scientific needs.

Ziegler, R. A.↗

NASA NTRS1992

Clustering methods for removing outliers from vision-based range estimates

The present approach to the automation of helicopter low-altitude flight uses one or more passive imaging sensors to extract environmental obstacle information; this is then processed via computer-vision techniques to yield a time-varying map of range to obstacles in the sensor's field of view along the vehicle's flight path. Attention is given to two related techniques which can eliminate outliers from a sparse range map, clustering sparse range-map information into different spatial classes that rely on a segmented and labeled image to aid in spatial classification within the image plane.

Hussien, B.↗

NASA NTRS2019

New Horizons in Cosmology with Spectral Distortions of the Cosmic Microwave Background

Following the pioneering observations with COBE in the early 1990s, studies of the cosmic mi- crowave background (CMB) have primarily focused on temperature and polarization anisotropies. CMB spectral distortions – tiny departures of the CMB energy spectrum from that of a perfect blackbody – provide a second, independent probe of fundamental physics, with a reach deep into the primordial Universe. The theoretical foundation of spectral distortions has seen major advances in recent years, highlighting the immense potential of this emerging field. Spectral distortions probe a fundamental property of the Universe – its thermal history – thereby providing additional insight into processes within the cosmological standard model(I) (CSM) as well as new physics beyond. Spectral distortions are an important tool for understanding inflation and the nature of dark matter. They shed new light on the physics of recombination and reionization, both prominent stages in the evolution of our Universe, and furnish critical information on baryonic feedback processes, in addition to probing primordial correlation functions at scales inaccessible to other tracers. In principle the range of signals is vast: many orders of magnitude of discovery space can be explored by detailed observations of the CMB energy spectrum. Several CSM signals are predicted and provide clear experimental targets that are observable with present-day technology. Confirmation of these signals would extend the reach of the CSM by orders of magnitude in physical scale as the Universe evolves from the initial stages to its present form. Their absence would pose a huge theoretical challenge, immediately pointing to new physics. Here, we advocate for a dedicated effort to measure CMB spectral distortions at the largest angular scales (greater than approximately 1°) within the ESA Voyage 2050 Program. We argue that an L-class mission with a pathfinder would allow a precise measurement of all the expected CSM distortions. With an M-class mission, the primordial distortions (created at z >~ 10(exp 3)) would still be detected at modest significance, while the late-time distortions will continue to be measured to high accuracy. Building on the heritage of COBE/FIRAS, a spectrometer that consists of multiple, cooled (approximately equal to 0.1 K), absolutely-calibrated Fourier Transform Spectrometers (FTS) with wide frequency coverage (ν approximately equal to 10 GHz to a few x THz) and all-sky spectral sensitivity at the level of 0.1 0.5 Jy/sr would be the starting point for the M-class option. A scaled and further optimized version of this concept is being envisioned as the L-class option. Such measurements can only be done from space and would deliver hundreds of absolutely-calibrated maps of the Universe at large scales, opening numerous science opportunities for cosmology and astrophysics. This will provide independent probes of inflation, dark matter and particle physics, recombination and the energy output of our Universe from at late times, turning the long-standing spectral distortion limits of COBE/FIRAS into clear detections.

Chluba, J.↗

NASA NTRS2009

Catalysts for Efficient Production of Carbon Nanotubes

Several metal alloys have shown promise as improved catalysts for catalytic thermal decomposition of hydrocarbon gases to produce carbon nanotubes (CNTs). Heretofore almost every experiment on the production of carbon nanotubes by this method has involved the use of iron, nickel, or cobalt as the catalyst. However, the catalytic-conversion efficiencies of these metals have been observed to be limited. The identification of better catalysts is part of a continuing program to develop means of mass production of high-quality carbon nanotubes at costs lower than those achieved thus far (as much as $100/g for purified multi-wall CNTs or $1,000/g for single-wall CNTs in year 2002). The main effort thus far in this program has been the design and implementation of a process tailored specifically for high-throughput screening of alloys for catalyzing the growth of CNTs. The process includes an integral combination of (1) formulation of libraries of catalysts, (2) synthesis of CNTs from decomposition of ethylene on powders of the alloys in a pyrolytic chemical-vapor-decomposition reactor, and (3) scanning- electron-microscope screening of the CNTs thus synthesized to evaluate the catalytic efficiencies of the alloys. Information gained in this process is put into a database and analyzed to identify promising alloy compositions, which are to be subjected to further evaluation in a subsequent round of testing. Some of these alloys have been found to catalyze the formation of carbon nano tubes from ethylene at temperatures as low as 350 to 400 C. In contrast, the temperatures typically required for prior catalysts range from 550 to 750 C.

Sun, Ted X.↗

NASA NTRS2006

X-ray Mapping of Terrestrial and Extraterrestrial Materials Using the Electron Microprobe

Lunar samples returned from the Apollo program motivated development of the Bence-Albee algorithm for the rapid and accurate analysis of lunar materials, and established interlaboratory comparability through its common use. In the analysis of mineral and rock fragments it became necessary to combine micro- and macroscopic analysis by coupling electron-probe microanalysis (EPMA) with automated stage point counting. A coarse grid that included several thousand points was used, and initially wavelength-dispersive (WDS) and later energydispersive (EDS) data were acquired at discrete stage points using approx. 5 sec count times. A approx 50 micrometer beam diameter was used for WDS and up to 500 micrometer beam diameter for EDS analysis. Average analyses of discretely sampled phases were coupled with the point count data to calculate the bulk composition using matrix algebra. Use of a defocused beam resulted in a contribution from multiple phases to each analytical point, and the analytical data were deconvolved relative to end-member phase chemistry on the fly. Impressive agreement was obtained between WDS and EDS measurements as well as comparison with bulk chemistry obtained by other methods. In the 30 years since these methods were developed, significant improvements in EPMA automation and computer processing have taken place. Digital beam control allows routine collection of x-ray maps by EDS, and stage mapping for WDS is conducted continuously at slew speed and incrementally by sampling at discrete points. Digital pulse processing in EDS systems has significantly increased the throughput for EDS mapping, and the ongoing development of Si-drift detector systems promises mapping capabilities rivaling WDS systems. Spectrum imaging allows a data cube of EDS spectra to be acquired and sophisticated processing of the original data is possible using matrix algebra techniques. The study of lunar and meteoritic materials includes the need to conveniently: (1) Characterize the sample at microscopic and macroscopic scales with relatively high sensitivity, (2) Determine the modal abundance of minerals, and (3) Identify and relocate discrete features of interest in terms of size and chemistry. The coupled substitution of cations in minerals can result in significant variation in mineral chemistry, but at similar average Z, leading to poor backscattered-electron (BSE) contrast discrimination of mineralogy. It is necessary to discriminate phase chemistry at both the trace element level and the major element level. To date, the WDS of microprobe systems is preferred for mapping due to high throughput and the ability to obtain the necessary intensity to discriminate phases at both trace and major element concentrations. It is desirable to produce fully quantitative compositional maps of geological materials, which requires the acquisition of k-ratio maps that are background and dead-time corrected, and which have been corrected by phi(delta z> or an equivalent algorithm at each pixel. To date, turnkey systems do not allow the acquisition of k-ratio maps and the rigorous correction in this manner. X-ray maps of a chondrule from the Ourique meteorite, and a comb-layered xenolith from the San Francisco volcanic field, have been analyzed and processed to extract phase information. The Ourique meteorite presents a challenge due to relatively low BSE contrast, and has been studied using spectrum imaging. X-ray maps for Si, Mg, and FeK(alpha) were used to produce RGB images. The xenolith sample contains sector-zoned augite, olivine, plagioclase, and basaltic glass. X-ray maps were processed using Lispix and ImageJ software to produce mineral phase maps. The x-ray maps for Mg, Ca, and Ti were used with traceback to generate binary images that were converted to RGB images. These approaches are successful in discriminating phases, but it is desirable to achieve the methods that were used on lunar samples 30 years ago on current microprobe systems. Curnt research includes x-ray mapping analysis of the Dalgety Downs chondrite by micro x-ray fluorescence and spectrum imaging, in collaboration with Kenny Witherspoon of IXRF Systems and Dale Newbury of NIST.

Carpenter, P.↗

NASA NTRS2010

Product Lifecycle Management and the Quest for Sustainable Space Exploration Solutions

Product Lifecycle Management (PLM) is an outcome of lean thinking to eliminate waste and increase productivity. PLM is inextricably tied to the systems engineering business philosophy, coupled with a methodology by which personnel, processes and practices, and information technology combine to form an architecture platform for product design, development, manufacturing, operations, and decommissioning. In this model, which is being implemented by the Engineering Directorate at the National Aeronautics and Space Administration's (NASA's) Marshall Space Flight Center, total lifecycle costs are important variables for critical decisionmaking. With the ultimate goal to deliver quality products that meet or exceed requirements on time and within budget, PLM is a powerful tool to shape everything from engineering trade studies and testing goals, to integrated vehicle operations and retirement scenarios. This paper will demonstrate how the Engineering Directorate is implementing PLM as part of an overall strategy to deliver safe, reliable, and affordable space exploration solutions. It has been 30 years since the United States fielded the Space Shuttle. The next generation space transportation system requires a paradigm shift such that digital tools and knowledge management, which are central elements of PLM, are used consistently to maximum effect. The outcome is a better use of scarce resources, along with more focus on stakeholder and customer requirements, as a new portfolio of enabling tools becomes second nature to the workforce. This paper will use the design and manufacturing processes, which have transitioned to digital-based activities, to show how PLM supports the comprehensive systems engineering and integration function. It also will go through a launch countdown scenario where an anomaly is detected to show how the virtual vehicle created from paperless processes will help solve technical challenges and improve the likelihood of launching on schedule, with less hands-on labor needed for processing and troubleshooting. Sustainable space exploration solutions demand that all lifecycle phases be optimized. Adopting PLM, which has been used by the automotive industry for many years, for aerospace applications provides a foundation for strong, disciplined systems engineering and accountable return on investment by making lifecycle considerations variables in an iterative decision-making process. This paper combines the perspectives of the founding father of PLM, along with the experience of Engineering leaders who are implementing these processes and practices real-time. As the nation moves from an industrial-based society to one where information is a valued commodity, future NASA programs and projects will benefit from the experience being gained today for the exploration missions of tomorrow.

Caruso, Pamela W.↗

NASA NTRS1983

Building an information model (with the help of PSL/PSA)

Problem Statement Language/Problem Statement Analyzer (PSL/PSA) applications, which were once a one-step process in which product system information was immediately translated into PSL statements, have in light of experience been shown to result in inconsistent representations. These shortcomings have prompted the development of an intermediate step, designated the Product System Information Model (PSIM), which provides a basis for the mutual understanding of customer terminology and the formal, conceptual representation of that product system in a PSA data base. The PSIM is initially captured as a paper diagram, followed by formal capture in the PSL/PSA data base.

Callender, E. D.↗

NASA NTRS1966

Apollo network

Although the design of the Apollo network followed closely behind the Manned Space Flight Network (MSFN) modification for the Gemini program, many site modifications were necessary to provide Apollo support due to the greater scope of the Apollo program. The Apollo program requires instrumentation for support of the S-I, S-11, S IV-B/IU, Command Service Module (CSM) and Lunar Excursion Module (LEM) stages. Command Service Module (CSM) and Lunar Excursion Module (LEM) stages. Support must also be provided at both orbital and lunar distances. Increased data processing capability is required for processing and displaying significantly larger amounts of information. The ground network requires the capability of processing both Pulse Code Modulation (PCM) telemetry and command data for the CSM, LEM, and S IV-B/IU. In various stages of the Apollo program, both tone (on UHF) and digital [on Unified S-Band (USB) and UHF] command capabilities are required. Also at various stages both USB and VHF telemetry links are required.

Ground support system↗

NASA NTRS2020

Using XRD to Characterize Sediment Sorting in a Mars Analog Glacio-Fluvio-Eolian Basaltic Sedimentary System in Iceland

The martian surface has a primarily basaltic composition and is dominated by sedimentary deposits. Ancient layered sedimentary rocks have been identified across the planet from orbit, have been studied in situ by the Mars Exploration Rovers and the Mars Science Laboratory rover, and will be studied by the Mars 2020 rover. These ancient sedimentary rocks were deposited in fluvial, lacustrine, and eolian environments during a warmer and wetter era on Mars. It is important to study the composition of sediments in Mars analog environments to characterize how minerals in basaltic sedimentary systems are sorted and/or aqueously altered. This information can help us better interpret sedimentary processes from similar deposits on Mars and derive information about the igneous source rocks. Sediment sorting has been studied extensively on Earth, but not typically in basaltic environments. Previous work has addressed sorting of basaltic sediments through experimental techniques and in modern eolian basaltic systems and aqueous alteration in subglacial and proglacial environments. We add to this body of research by studying sediment sorting and aqueous alteration in a glacio-fluvio-eolian basaltic system in southwest Iceland.

Rampe, E. B.↗

NASA NTRS2004

Overview of High Speed Close-Up Imaging in an Icing Environment

The Icing Branch and Imaging Technology Center at NASA Glenn Research Center have recently been involved in several projects where high speed close-up imaging was used to investigate water droplet impact/splash, and also ice particle impact/bounce in an icing wind tunnel. The combination of close-up and high speed imaging capabilities were required because the particles being studied were relatively small (d < 1 mm in diameter), and the impact process occurred in a very short time period (t(sub impact) << 1 sec). High speed close-up imaging was utilized to study the dynamics of droplet impact and splash in simulated Supercooled Large Droplet (SLD) icing conditions. The objective of this test was to evaluate the capability of a ultra high speed camera system to acquire quantitative information about the impact process (e.g., droplet size, velocity). Imaging data were obtained in an icing wind tunnel for spray cloud MVD > 50 m. High speed close-up imaging was also utilized to characterize the impact of ice particles on an airfoil with a thermally protected leading edge. The objective of this investigation was to determine whether ice particles tend to "stick" or "bounce" after impact. Imaging data were obtained for cases where the airfoil surface was heated and unheated. Based on the results from this test, follow on tests were conducted to investigate ice particle impact on the sensing elements of water content measurement devices. This paper will describe the use of the imaging systems to support these experimental investigations, present some representative results, and summarize what was learned about the use of these systems in an icing environment.

Miller, Dean R.↗

NASA NTRS1993

Application of the airborne ocean color imager for commercial fishing

The objective of the investigation was to develop a commercial remote sensing system for providing near-real-time data (within one day) in support of commercial fishing operations. The Airborne Ocean Color Imager (AOCI) had been built for NASA by Daedalus Enterprises, Inc., but it needed certain improvements, data processing software, and a delivery system to make it into a commercial system for fisheries. Two products were developed to support this effort: the AOCI with its associated processing system and an information service for both commercial and recreational fisheries to be created by Spectro Scan, Inc. The investigation achieved all technical objectives: improving the AOCI, creating software for atmospheric correction and bio-optical output products, georeferencing the output products, and creating a delivery system to get those products into the hands of commercial and recreational fishermen in near-real-time. The first set of business objectives involved Daedalus Enterprises and also were achieved: they have an improved AOCI and new data processing software with a set of example data products for fisheries applications to show their customers. Daedalus' marketing activities showed the need for simplification of the product for fisheries, but they successfully marketed the current version to an Italian consortium. The second set of business objectives tasked Spectro Scan to provide an information service and they could not be achieved because Spectro Scan was unable to obtain necessary venture capital to start up operations.

Wrigley, Robert C.↗

NASA NTRS1986

Polarization photometer to measure bidirectional reflectance factor R(55 deg, 0 deg, 55 deg, 180 deg) of leaves

A polarization photometer has been developed for rapidly determining the bidirectional, polarized, and diffuse light-scattering properties of individual leavs illuminated and measured 'in vivo' at an angle of 55 deg (approximately Brewster's angle) in six wavelength bands in the visible and near-IR wavelength regions. The optical performance and data quality of the system are evaluated to estimate the magnitude of the variation in the data attributable to the instrument system and to measurement procedures. The potential to discriminate between three species of oak is demonstrated using data acquired by the polarization photometer. The instrument is being used to increase understanding of the radiation transfer process in plant canopies and specifically to determine how agronomic information of the physical and chemical processes in leaves, plants, and plant canopies is expressed in these light-scattering properties.

Vanderbilt, V. C.↗

NASA NTRS1993

Operator Performance Support System (OPSS)

In the complex and fast reaction world of military operations, present technologies, combined with tactical situations, have flooded the operator with assorted information that he is expected to process instantly. As technologies progress, this flow of data and information have both guided and overwhelmed the operator. However, the technologies that have confounded many operators today can be used to assist him -- thus the Operator Performance Support Team. In this paper we propose an operator support station that incorporates the elements of Video and Image Databases, productivity Software, Interactive Computer Based Training, Hypertext/Hypermedia Databases, Expert Programs, and Human Factors Engineering. The Operator Performance Support System will provide the operator with an integrating on-line information/knowledge system that will guide expert or novice to correct systems operations. Although the OPSS is being developed for the Navy, the performance of the workforce in today's competitive industry is of major concern. The concepts presented in this paper which address ASW systems software design issues are also directly applicable to industry. the OPSS will propose practical applications in how to more closely align the relationships between technical knowledge and equipment operator performance.

Conklin, Marlen Z.↗

NASA NTRS2018

NASA GeneLab Project: Bridging Space Radiation Omics with Ground Studies

Accurate assessment of risk factors for long-term space missions is critical for human space exploration: therefore it is essential to have a detailed understanding of the biological effects on humans living and working in deep space. Ionizing radiation from Galactic Cosmic Rays (GCR) is one of the major risk factors factor that will impact health of astronauts on extended missions outside the protective effects of the Earth's magnetic field. Currently there are gaps in our knowledge of the health risks associated with chronic low dose, low dose rate ionizing radiation, specifically ions associated with high (H) atomic number (Z) and energy (E). The GeneLab project (genelab.nasa.gov) aims to provide a detailed library of Omics datasets associated with biological samples exposed to HZE. The GeneLab Data System (GLDS) currently includes datasets from both spaceflight and ground-based studies, a majority of which involve exposure to ionizing radiation. In addition to detailed information for ground-based studies, we are in the process of adding detailed, curated dosimetry information for spaceflight missions. GeneLab is the first comprehensive Omics database for space related research from which an investigator can generate hypotheses to direct future experiments utilizing both ground and space biological radiation data. In addition to previously acquired data, the GLDS is continually expanding as Omics related data are generated by the space life sciences community. Here we provide a brief summary of space radiation related data available at GeneLab.

Genelab↗

NASA NTRS1993

Miniature wide field-of-view star trackers for spacecraft attitude sensing and navigation

Introducing a family of miniature, wide field-of-view star trackers for low cost, high performance spacecraft attitude determination and navigation applications. These devices, derivative of the WFOV Star Tracker Camera developed cooperatively by OCA Applied Optics and the Lawrence Livermore National Laboratory for the Brilliant Pebbles program, offer a suite of options addressing a wide range of spacecraft attitude measurement and control requirements. These sensors employ much wider fields than are customary (ranging between 20 and 60 degrees) to assure enough bright stars for quick and accurate attitude determinations without long integration intervals. The key benefit of this approach are light weight, low power, reduced data processing loads and high information carrier rates for wide ACS bandwidths. Devices described range from the proven OCA/LLNL WFOV Star Tracker Camera (a low-cost, space-qualified star-field imager utilizing the spacecraft's own computer and centroiding and position-finding), to a new autonomous subsystem design featuring dual-redundant cameras and completely self-contained star-field data processing with output quaternion solutions accurate to 100 micro-rad, 3 sigma, for stand-alone applications.

Mccarty, William↗

NASA NTRS1973

Parameter estimation supplement to the Mission Analysis Evaluation and Space Trajectory Operations program (MAESTRO)

This Parameter Estimation Supplement describes the PEST computer program and gives instructions for its use in determination of lunar gravitation field coefficients. PEST was developed for use in the RAE-B lunar orbiting mission as a means of lunar field recovery. The observations processed by PEST are short-arc osculating orbital elements. These observations are the end product of an orbit determination process obtained with another program. PEST's end product it a set of harmonic coefficients to be used in long-term prediction of the lunar orbit. PEST employs some novel techniques in its estimation process, notably a square batch estimator and linear variational equations in the orbital elements (both osculating and mean) for measurement sensitivities. The program's capabilities are described, and operating instructions and input/output examples are given. PEST utilizes MAESTRO routines for its trajectory propagation. PEST's program structure and subroutines which are not common to MAESTRO are described. Some of the theoretical background information for the estimation process, and a derivation of linear variational equations for the Method 7 elements are included.

Bjorkman, W. S.↗

NASA NTRS2010

Performance Bounds on Two Concatenated, Interleaved Codes

A method has been developed of computing bounds on the performance of a code comprised of two linear binary codes generated by two encoders serially concatenated through an interleaver. Originally intended for use in evaluating the performances of some codes proposed for deep-space communication links, the method can also be used in evaluating the performances of short-block-length codes in other applications. The method applies, more specifically, to a communication system in which following processes take place: At the transmitter, the original binary information that one seeks to transmit is first processed by an encoder into an outer code (Co) characterized by, among other things, a pair of numbers (n,k), where n (n > k)is the total number of code bits associated with k information bits and n k bits are used for correcting or at least detecting errors. Next, the outer code is processed through either a block or a convolutional interleaver. In the block interleaver, the words of the outer code are processed in blocks of I words. In the convolutional interleaver, the interleaving operation is performed bit-wise in N rows with delays that are multiples of B bits. The output of the interleaver is processed through a second encoder to obtain an inner code (Ci) characterized by (ni,ki). The output of the inner code is transmitted over an additive-white-Gaussian- noise channel characterized by a symbol signal-to-noise ratio (SNR) Es/No and a bit SNR Eb/No. At the receiver, an inner decoder generates estimates of bits. Depending on whether a block or a convolutional interleaver is used at the transmitter, the sequence of estimated bits is processed through a block or a convolutional de-interleaver, respectively, to obtain estimates of code words. Then the estimates of the code words are processed through an outer decoder, which generates estimates of the original information along with flags indicating which estimates are presumed to be correct and which are found to be erroneous. From the perspective of the present method, the topic of major interest is the performance of the communication system as quantified in the word-error rate and the undetected-error rate as functions of the SNRs and the total latency of the interleaver and inner code. The method is embodied in equations that describe bounds on these functions. Throughout the derivation of the equations that embody the method, it is assumed that the decoder for the outer code corrects any error pattern of t or fewer errors, detects any error pattern of s or fewer errors, may detect some error patterns of more than s errors, and does not correct any patterns of more than t errors. Because a mathematically complete description of the equations that embody the method and of the derivation of the equations would greatly exceed the space available for this article, it must suffice to summarize by reporting that the derivation includes consideration of several complex issues, including relationships between latency and memory requirements for block and convolutional codes, burst error statistics, enumeration of error-event intersections, and effects of different interleaving depths. In a demonstration, the method was used to calculate bounds on the performances of several communication systems, each based on serial concatenation of a (63,56) expurgated Hamming code with a convolutional inner code through a convolutional interleaver. The bounds calculated by use of the method were compared with results of numerical simulations of performances of the systems to show the regions where the bounds are tight (see figure).

Moision, Bruce↗