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NASA NTRS1977

Computer control of a far infrared interferometer

A simple interface has been designed for the automatic control and data collection from a Grubb Parsons Mark III cube interferometer. A computer is used to automatically step the movable mirror on the interferometer. Data may be directly input into the computer for immediate transformation or stored for later analysis via a fast Fourier transformation. The interface is based on a commercial analog-to-digital converter having a parallel-to-serial data converter. The device can also display ASCII characters sent from the computer in parallel binary code. The system is applicable to recording interferograms having long time durations and to measuring multiple interferograms for statistical averaging.

Breecher, J.↗

NASA NTRS1990

The potential for ductility enhancement from surface and interface dislocation sources in NiAl

Limited ductility and toughness of NiAl and related aluminides near room temperature pose major problems in their potential application as structural materials. An analysis of these problems is presented as part of a review of the flow and fracture behavior of binary NiAl. Following this discussion is a demonstration that conditions of elastic and plastic constraint associated with phase boundaries afforded by surface films, internal lamellae, or precipitates may introduce sufficient densities of mobile dislocations to enhance the ductility of NiAl-based materials by significant amounts. Examples of this behavior are presented for several model materials, including 001- and 123-oriented single crystals of oxide-coated NiAl, directionally solidified beta-gamma-prime (Ni70Al30) and beta-gamma (Ni50Fe30Al20) in situ composites, and several NiAl/precipitate systems. The nature of the resulting dislocation substructures and the effects of several materials variables are described.

Noebe, R. D.↗

DOE OSTI2023

Gridtrust: Electricity Grid Root-of-Trust Decentralized Supply Chain Cyber-Security (Final Scientific/Technical Report)

GridTrust represents a departure from reliance on a single organization or a single person to multiple organizations and therefore multiple people across organizational structures. The motivating idea behind involving multiple organizations is the increase in security due to human factors. More specifically, the requirement that distinct people in different organizations sign off on a change or an update makes a cyberattack much less likely due to the inherent requirement that both organizations be penetrated and fooled. GridTrust focuses on the software update process as the primary exemplar for the research and development work. A novel hardware-based technology referred to as a Physical Unclonable Function (PUF) provides a microchip Root-of-Trust (RoT), i.e., a starting point for verifying that the hardware being communicated with is the hardware the control center believes the hardware to be. As a result, staff at power grid control centers can ensure the accurate and reliable identification of hardware devices from the outset. The GridTrust protocol introduces two key innovations, as detailed in this report. Firstly, the utilization of a PUF as a root-of-trust in the initial phase of a software or firmware update. Secondly, the application of multiple cryptographic signatures from two or more organizations to the update binary. These signatures are verified before implementing the update on a power grid device in the field. In terms of GridTrust hardware design, this report outlines two main components. The first is the GridTrust Native Device, integrating PUF technology intrinsically into the hardware device itself. The second is the GridTrust Interfacing Device, which incorporates PUF technology and multiple cryptographic signatures. These signatures are cross-checked within a separate hardware positioned between the power grid control center and the legacy power grid device, functioning as an intermediary. While the GridTrust Interfacing Device offers the advantage of being applicable to existing power grid equipment, it may have reduced security if the intermediary component is targeted. On the other hand, the GridTrust Native Device boasts increased security due to protocol integration within a unified form factor. The effectiveness of GridTrust technology has been extensively demonstrated, with multiple external red-team attackers unable to breach GridTrust's security measures. This was observed both in controlled laboratory settings during Phase 1 of the project and in real-world conditions within a City of Marietta substation during Phase 2 of the project.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Tailoring Growth Interfaces of Virtual Substrates for Power Electronics

Power electronics materials are poised to play a critical role in fulfilling next generation energy needs, with up to 90% of future energy demand predicted to flow through power electronics at some point. AlxGa1-xN ranks high among candidate materials, having bipolar dopability, thermal and chemical stability and an ultra-wide bandgap. However, AlGaN growth is limited by a lack of lattice-matched substrates, ultimately stunting material quality at higher thicknesses needed for power electronics applications. Further, high power applications increasingly call for fully vertical device structures, necessitating a conductive substrate. Recently our group identified the (111) plane of TaC as a conductive surface lattice-matched to Al0.55Ga0.45N, taking inspiration from prior work of AlN and GaN binaries on carbide and boride substrates. In this talk we demonstrate the growth of (111)-oriented TaC by RF sputtering. We investigate the interface of TaC with sapphire and SiC substrates and identify means to suppress competing Ta2C nucleation in order to stabilize (111)-oriented TaC. Potential stacking sequences are identified with respect to crystal structure and observed twinning in the TaC films. We next assess structural changes and film recrystallization that results from face-to-face annealing of TaC thin films at high temperatures above 1500 degrees C. Changes to grain structure and domain size are assessed by x-ray diffraction and surface morphology is explored using atomic force microscopy. Figure 1 shows significant improvements to in- and out-of-plane strain following annealing along with the formation of terraced step edges at the film surface. Strain as a function of material composition and thickness is considered, as this may play a major role in future nucleation of AlGaN layers. (1) R. J. in a face-to-face configuration, as illustrated in the schematic at left. Kaplar et al 2017, ECS J. Solid State Sci. Technol. 6 Q3061; (2) D. M. Roberts et al 2022, https://arxiv.org/abs/2208.11769; (3) T. Aizawa et al 2008, J Crys Growth 310, 1 22; (4) R. Liu et al 2002, Appl. Phys. Lett. 81, 3182-3184.

ENGINEERING↗

DOE OSTI2023

Methane mass transfer in mesoporous silica saturated with liquid hydrocarbons

Mass transfer across gas/liquid interfaces plays a central role in many industrial applications. In particular, gas dissolution and diffusion in liquid hydrocarbon mixtures, confined in nanometer-sized pores, is an essential mechanism during enhanced oil recovery (EOR) from unconventional formations. In this work, we have measured methane (C 1 ) diffusion in n-decane (C 10 ), n-hexadecane (C 16 ), and mixtures of C 10 + C 16 in a mesoporous material with an average pore size of 4 nm at 50 °C and ~ 8 MPa of gas pressure. A key conclusion of this work is that the diffusivities, measured in the bulk phase, for the relevant binary systems, are sufficient to predict the diffusion behavior of the corresponding multicomponent systems in the porous medium by using Wilke’s equation for the evaluation of effective component diffusivities, combined with an accurate equation of state (EOS) representation of the (bulk) phase behavior. This observation can facilitate accurate prediction of recovery processes in unconventional formations and, potentially, guide other applications that entail gas-liquid interface mass transfer in mesoporous materials.

42 ENGINEERING↗

DOE OSTI2023

Tailoring Growth Interfaces of Virtual Substrates for Power Electronics

Power electronics materials are poised to play a critical role in fulfilling next generation energy needs, with up to 90% of future energy demand predicted to flow through power electronics at some point.[1] Among a number of candidate materials, AlxGa1-xN is the strongest, having bipolar dopability, thermal and chemical stability, an ultra-wide bandgap, and demonstrated experimental feasibility. However, AlGaN growth is limited by a lack of lattice-matched substrates, ultimately stunting material quality at higher thicknesses needed for power electronics applications. Further, high power applications increasingly call for fully vertical device structures, necessitating a conductive substrate. [1] Recently our group identified the (111) plane of TaC as a conductive surface lattice-matched to Al0.55Ga0.45N, taking inspiration from prior work of AlN and GaN binaries on carbide and boride substrates. [2,3,4] In this talk we demonstrate the growth of (111)-oriented TaC by RF sputtering. We investigate the interface of TaC with sapphire and SiC substrates and identify means to suppress competing Ta2C nucleation in order to stabilize (111)-oriented TaC. Potential stacking sequences are identified with respect to crystal structure and observed twinning in the TaC films. We next assess structural changes and film recrystallization that results from face-to-face annealing of TaC thin films at high temperatures above 1500 degrees Celsius. Changes to grain structure and domain size are assessed by x-ray diffraction and surface morphology is explored using atomic force microscopy. Figure 1 shows significant improvements to in- and out-of-plane strain following annealing along with the formation of terraced step edges at the film surface. Strain as a function of material composition and thickness is considered, as this may play a major role in future nucleation of AlGaN layers.

CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SU↗

NASA NTRS1992

PCIPS 2.0: Powerful multiprofile image processing implemented on PCs

Over the years, the processing power of personal computers has steadily increased. Now, 386- and 486-based PC's are fast enough for many image processing applications, and inexpensive enough even for amateur astronomers. PCIPS is an image processing system based on these platforms that was designed to satisfy a broad range of data analysis needs, while requiring minimum hardware and providing maximum expandability. It will run (albeit at a slow pace) even on a 80286 with 640K memory, but will take full advantage of bigger memory and faster CPU's. Because the actual image processing is performed by external modules, the system can be easily upgraded by the user for all sorts of scientific data analysis. PCIPS supports large format lD and 2D images in any numeric type from 8-bit integer to 64-bit floating point. The images can be displayed, overlaid, printed and any part of the data examined via an intuitive graphical user interface that employs buttons, pop-up menus, and a mouse. PCIPS automatically converts images between different types and sizes to satisfy the requirements of various applications. PCIPS features an API that lets users develop custom applications in C or FORTRAN. While doing so, a programmer can concentrate on the actual data processing, because PCIPS assumes responsibility for accessing images and interacting with the user. This also ensures that all applications, even custom ones, have a consistent and user-friendly interface. The API is compatible with factory programming, a metaphor for constructing image processing procedures that will be implemented in future versions of the system. Several application packages were created under PCIPS. The basic package includes elementary arithmetics and statistics, geometric transformations and import/export in various formats (FITS, binary, ASCII, and GIF). The CCD processing package and the spectral analysis package were successfully used to reduce spectra from the Nordic Telescope at La Palma. A photometry package is also available, and other packages are being developed. A multitasking version of PCIPS that utilizes the factory programming concept is currently under development. This version will remain compatible (on the source code level) with existing application packages and custom applications.

Smirnov, O. M.↗

DOE OSTI2025

Creating Apptainer Workflows with Docker-Compose-like Utilities

Creating Apptainer Workflows with Docker-Compose-like Utilities In this presentation, I will explore the utilization of a tool called process-compose, inspired by docker-compose, to create Apptainer-based services. This approach allows for easy deployment and management of fully containerized applications on High Performance Computing (HPC) systems without requiring elevated privileges. Benefits to the Ecosystem: By incorporating process-compose and Apptainer, I aim to address several key challenges in the HPC ecosystem: Simplified Workflow Management: Process-compose provides a user-friendly interface for defining and managing complex containerized application services, reducing the setup time and lowering the barrier to entry for new users. Enhanced Portability: Apptainer ensures that containerized applications can run consistently across different HPC environments, promoting greater portability and reducing compatibility issues. Process-compose is also a single binary that does not need to be installed by admin level users. Community Driven Solutions: This approach aligns with the goals of the High Performance Software Foundation (HPSF) to advance community-driven solutions. By sharing our experiences and insights, I hope to foster collaboration and innovation within the HPC community. Increased Productivity: The combination of process-compose and Apptainer streamlines the serve deployment process, allowing researchers and developers to focus more on their scientific work rather than the intricacies of system or service administration. Through this presentation, attendees will gain valuable insights into the practical implementation of containerized workflows on HPC systems, learn about the benefits of using process-compose and Apptainer, and understand how these tools can contribute to a more efficient HPC ecosystem.

97 - MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Benefits of using Electronic Data Sheets (EDS) with coreFlight Systems (cFS) - A Project Example

Recently there has been interest in the incorporation of core Flight Systems (cFS) with Spacecraft Onboard Interface Services (SOIS) Electronic Data Sheets (EDS) in the spaceflight software community. The Regenerative Fuel Cell project at the Glenn Research Center is using cFS architecture with EDS support for its monitoring and control software. The presentation will outline the benefits to using cFS with EDS support: First, EDS establishes a single source of truth for the definitions of data structures used throughout an entire mission that may otherwise be programmed in different languages and designed with different processor architectures. Not only does this help with inter-application communication via the software bus, but it also greatly simplifies communication between systems. An EDS Application Programming Interface (API) library allows the conversion of EDS data structures to and from native data structures. Second, bindings for other programming languages (e.g. Lua, Python, JSON) have been written to allow the creation and manipulation of EDS data objects within those languages. The RFC project uses Lua scripts to automatically generate binary configuration files at build time to be loaded into our cFS programs. We also use Python bindings in a graphical user interface (GUI) to allow an operator to send commands and view telemetry messages sent from cFS instances. Finally, using Lua scripts we can set up specific simulation scenarios to perform automatic functional testing. During the development of the RFC software, the software team put together a generic python GUI called “cFS-EDS-GroundStation” that provides a basic interface to an instance of cFS with EDS support. The GUI includes a basic telecommand and telemetry system that reads directly from the generated EDS databases. In the telecommand system, dropdown menus are populated with all user commands that are defined in EDS. In the telemetry system, telemetry messages are automatically decoded, written to the screen, and saved to a binary file. Additional Python scripts have been written to convert the binary data files into a comma separated value (CSV) format for further processing. We will demonstrate the basic use of the cFS-EDS-GroundStation software including adding additional commands and telemetry payload values in EDS and see them appear automatically in the cFS-EDS-Groundstation software. About the RFC project: The Regenerative Fuel Cell project is tasked with developing and demonstrating a power system consisting of a fuel cell and electrolyzer to provide power during a lunar day/night cycle. During the night, the fuel cell takes Hydrogen and Oxygen gasses and converts them into electricity, water, and heat. During the day, the electrolyzer takes input power (e.g. from a photovoltaic array) and converts water back into Hydrogen and Oxygen gasses.

Mathew Mccaskey↗

DOE OSTI2024

A Comparison between Invariant and Equivariant Classical and Quantum Graph Neural Networks

Machine learning algorithms are heavily relied on to understand the vast amounts of data from high-energy particle collisions at the CERN Large Hadron Collider (LHC). The data from such collision events can naturally be represented with graph structures. Therefore, deep geometric methods, such as graph neural networks (GNNs), have been leveraged for various data analysis tasks in high-energy physics. One typical task is jet tagging, where jets are viewed as point clouds with distinct features and edge connections between their constituent particles. The increasing size and complexity of the LHC particle datasets, as well as the computational models used for their analysis, have greatly motivated the development of alternative fast and efficient computational paradigms such as quantum computation. In addition, to enhance the validity and robustness of deep networks, we can leverage the fundamental symmetries present in the data through the use of invariant inputs and equivariant layers. In this paper, we provide a fair and comprehensive comparison of classical graph neural networks (GNNs) and equivariant graph neural networks (EGNNs) and their quantum counterparts: quantum graph neural networks (QGNNs) and equivariant quantum graph neural networks (EQGNN). The four architectures were benchmarked on a binary classification task to classify the parton-level particle initiating the jet. Based on their area under the curve (AUC) scores, the quantum networks were found to outperform the classical networks. However, seeing the computational advantage of quantum networks in practice may have to wait for the further development of quantum technology and its associated application programming interfaces (APIs).

Forestano, Roy T. (ORCID:0000000203552076)↗

DOE OSTI2023

Machine-Guided Design of Oxidation-Resistant Superconductors for Quantum Information Applications

Decoherence in superconducting qubits has long been attributed to two-level systems arising from the surfaces and interfaces present in real devices. A recent significant step in reducing decoherence was the replacement of superconducting niobium by superconducting tantalum, resulting in a tripling of transmon qubit lifetimes (T1). The identity, thickness, and quality of the native surface oxide, is thought to play a major role, as tantalum only has one oxide whereas niobium has several. Here we report the development of a thermodynamic metric to rank materials based on their potential to form a well-defined, thin, surface oxide. We first computed this metric for known binary and ternary metal alloys using data available from the Materials Project and experimentally validated the strengths and limits of this metric through the preparation and controlled oxidation of eight known metal alloys. Then we trained a convolutional neural network to predict the value of this metric from atomic composition and atomic properties. This allowed us to compute the metric for materials that are not present in the Materials Project, including a large selection of known superconductors, and, when combined with Tc, allowed us to identify new candidate superconductors for quantum information science and engineering (QISE) applications. We tested the oxidation resistance of a pair of these predictions experimentally. Our results are expected to lay the foundation for the tailored and rapid selection of improved superconductors for QISE.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1993

Opto-electronic morphological processor

The opto-electronic morphological processor of the present invention is capable of receiving optical inputs and emitting optical outputs. The use of optics allows implementation of parallel input/output, thereby overcoming a major bottleneck in prior art image processing systems. The processor consists of three components, namely, detectors, morphological operators and modulators. The detectors and operators are fabricated on a silicon VLSI chip and implement the optical input and morphological operations. A layer of ferro-electric liquid crystals is integrated with a silicon chip to provide the optical modulation. The implementation of the image processing operators in electronics leads to a wide range of applications and the use of optical connections allows cascadability of these parallel opto-electronic image processing components and high speed operation. Such an opto-electronic morphological processor may be used as the pre-processing stage in an image recognition system. In one example disclosed herein, the optical input/optical output morphological processor of the invention is interfaced with a binary phase-only correlator to produce an image recognition system.

Yu, Jeffrey W.↗

DOE OSTI2024

Refining HPCToolkit for application performance analysis at exascale

As part of the US Department of Energy’s Exascale Computing Project (ECP), Rice University has been refining its HPCToolkit performance tools to better support measurement and analysis of applications executing on exascale supercomputers. To efficiently collect performance measurements of GPU-accelerated applications, HPCToolkit employs novel non-blocking data structures to communicate performance measurements between tool threads and application threads. To attribute performance information in detail to source lines, loop nests, and inlined call chains, HPCToolkit performs parallel analysis of large CPU and GPU binaries involved in the execution of an exascale application to rapidly recover mappings between machine instructions and source code. To analyze terabytes of performance measurements gathered during executions at exascale, HPCToolkit employs distributed-memory parallelism, multithreading, sparse data structures, and out-of-core streaming analysis algorithms. To support interactive exploration of profiles up to terabytes in size, HPCToolkit’s hpcviewer graphical user interface uses out-of-core methods to visualize performance data. The result of these efforts is that HPCToolkit now supports collection, analysis, and presentation of profiles and traces of GPU-accelerated applications at exascale. These improvements have enabled HPCToolkit to efficiently measure, analyze and explore terabytes of performance data for executions using as many as 64K MPI ranks and 64K GPU tiles on ORNL’s Frontier supercomputer. HPCToolkit’s support for measurement and analysis of GPU-accelerated applications has been employed to study a collection of open-science applications developed as part of ECP. This paper reports on these experiences, which provided insight into opportunities for tuning applications, strengths and weaknesses of HPCToolkit itself, as well as unexpected behaviors in executions at exascale.

Adhianto, Laksono↗

DOE OSTI2024

Ionic-like Superlattices by Charged Nanoparticles: A Step Toward Photonics Applications

Controlling interactions among nanoparticles is paramount to achieving assemblies vital to technologies seeking to exploit their cutting-edge collective properties. Although various techniques have been advanced, robust ones are necessary for upscaling nanoparticle assembly and crystallization. Here, we show that by grafting gold nanoparticles (AuNPs) with charge-end-group-thiolated poly(ethylene glycol), we control the charge of each AuNP. Such control facilitates the formation of various two-dimensional structures of oppositely charged binary constituents at vapor/liquid interfaces. Using surface-sensitive synchrotron X-ray diffraction techniques, we established the formation of distinct checkerboard square lattice structures at a range of pH values and molar ratios of the constituents. By regulating pH, the superlattices can transform from a square to a hexagonal lattice, or vice versa, and to a single-component superstructure at the interface. In conclusion, our recipe for the control of charges and their consequent interactions among nanoparticles can be readily exploited in the assembly of photonics and plasmonics devices in two and three dimensions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Generalized master equation for particle transport in binary random media with renewal statistics

Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general non-exponential statistics. Our approach is to Markovianize the problem by augmenting the {material type, particle flux} state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age, and subsequently reduced to a generalized Master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean/variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of non-exponential statistics can introduce large errors in transmittance and interior flux profiles. Lastly, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.

Fluctuations & noise↗

NASA NTRS1996

Convective Influence on Radial Segregation During Unidirectional Solidification of the Binary Alloy HgCdTe

In order to simulate the space environment for basic research into the crystal growth mechanism, Hg(0.8)Cd(0.2)Te crystals were grown by the vertical Bridgman-Stockbarger method in the presence of an applied axial magnetic field. The influence of convection, by magneto hydrodynamic damping, on mass transfer in the melt and segregation at the solid-liquid interface was investigated by measuring the axial and radial compositional variations in the grown samples. The reduction of convective mixing in the melt through the application of the magnetic field is found to have a large effect on radial segregation and interface morphology in the grown crystals. Direct comparisons are made with a Hg(0.8)Cd(0.2)Te crystal grown without field and also in the microgravity environment of space during the second United States Microgravity Payload Mission (USMP-2).

Watring, D. A.↗

DOE OSTI2022

Ephemeral antibubbles: Spatiotemporal evolution from direct numerical simulations

Antibubbles, which consist of a shell of a low-density fluid inside a high-density fluid, have several promising applications. We show, via extensive direct numerical simulations (DNSs), in both two and three dimensions, that the spatiotemporal evolution of antibubbles can be described naturally by the coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations for a binary fluid. Our DNSs capture elegantly the gravity-induced thinning and breakup of an antibubble via the time evolution of the Cahn-Hilliard scalar-order-parameter field $\phi$, which varies continuously across interfaces, so we do not have to enforce complicated boundary conditions at the moving antibubble interfaces. To ensure that our results are robust, we supplement our CHNS simulations with sharp-interface volume-of-fluid DNSs. We track the thickness of the antibubble and calculate the dependence of the lifetime of an antibubble on several parameters; we show that our DNS results agree with various experimental results; in particular, the velocity with which the arms of the antibubble retract after breakup scales as σ 1/2 , where σ is the surface tension.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2019

Bit Error Rate and Frame Error Rate Data Processing for Space Communications and Navigation-Related Communication System Analysis Tools

One of the capabilities that the Space Communications and Navigation (SCaN) Strategic Center for Networking, Integration, and Communications (SCENIC) user interface (UI) web application intends to provide its users is the addition of network protocol and link encryption augmentations of communication system analyses. Before any of these analyses capabilities can be modeled, the simulations of bit error rate (BER) and frame error rate (FER) against signal-to-noise ratio (SNR) have been conducted, requiring parameters from several known coding types (low-density parity-check (LDPC), convolutional, etc.), signal modulations (binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), etc.), coding rates (1/2, 1/3, etc.), and frame sizes (1,280, 3,580, etc.). However, in order to extract useful information from the results of these simulations, a curve fitting technique has been applied to each resulting dataset to extend and extrapolate the curve fit of BER and FER down to 10–30 using MATLAB® Curve Fitting Toolbox™ (The MathWorks, Inc.). This is a necessary step because simulations of BER and FER were only performed to around 10–9 due to the extensive simulation time that would be required to obtain significant simulation results at the error levels desired. Furthermore, the fitted curve results were applied to a finer resolution for the SNR at 0.01-dB interval instead of the 0.05-dB interval limitation used in the simulation. All the possible combinations of the coding types, signal modulations, coding rates, frame sizes, and the extension of BER and FER curves would enable users to capture a wide range of link performances that directly relates to the addition of higher level networking data encapsulated in a frame. The curve fitting results also led to the modeling of the optical link error rate performance by solving for coding gain, FER_BER SNR delta, coded optical BER-SNR, and coded optical FER–SNR.

Communication link analysis↗