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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

High-resolution imaging of the Pluto-Charon system with the Faint Object Camera of the Hubble Space Telescope

Images of the Pluto-Charon system were obtained with the Faint Object Camera (FOC) of the Hubble Space Telescope (HST) after the refurbishment of the telescope. The images are of superb quality, allowing the determination of radii, fluxes, and albedos. Attempts were made to improve the resolution of the already diffraction limited images by image restoration. These yielded indications of surface albedo distributions qualitatively consistent with models derived from observations of Pluto-Charon mutual eclipses.

Albrecht, R.↗
DOE OSTI2020

Model predictive control for voltage restoration in microgrids using temporal logic specifications

Power system operation will encounter numerous voltage variabilities as the proliferation of renewable energy continues. Real-time monitoring and communication technologies can potentially improve voltage stability by enabling the rapid detection of voltage deviations and the implementation of corrective actions. These corrective actions will only be effective in restoring stability if they are chosen in a timely and scalable manner. This paper considers the problem of power systems’ load voltage control in order to simultaneously address both magnitude and time voltage specifications. In order to comply with grid codes and avoid unnecessary relay protection actions, a model predictive control (MPC)-based control strategy employing temporal logic specifications (TLSs) is proposed. The TLSs strategy is introduced as a formalism to control the voltage variation at a critical load bus against operational bounds over time. The control objective is to schedule optimal control input signals from the available supportive energy storage systems, which provide reactive power injections, leading to satisfying the specified finite-time restoration described by the TLSs with minimal control efforts. The simulation results display that the TLSs strategy for power systems’ voltage control synthesis is extremely significant.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Envisioning the Future Renewable and Resilient Energy Grids—A Power Grid Revolution Enabled by Renewables, Energy Storage, and Energy Electronics

Today’s power grids are facing tremendous challenges because of the ever-increasing power demand, system complexity, infrastructure cost, knowledge base, and policy and regulatory issues to achieve supply–demand power balance and resiliency with respect to more frequent extreme weather events and cyberattacks. It is particularly challenging when the transition toward 100% intermittent renewable energy sources is considered. Many countries are calling for building up more transmission and distribution lines to increase power delivery capacities. This article is an attempt to answer two urgent questions: Is more transmission and distribution infrastructure really needed to meet the increasing power demand? What kind of future grid infrastructure should we envision and build? This article attempts to answer these questions and proposes the concept of community-centric asynchronous renewable and resilient energy grids. By clearly differentiating the concepts of grid resilience and reliability, the importance of building resilient power electronics’ devices and robust system-level control algorithms to achieve 100% renewable energy integrated resilient grids is presented. To identify the shortcomings and propose advancements, power electronics’ technologies are categorized using the proposed concepts of natural source frequencies (NSf), energy storage, direct energy conversion/control and fault protection (DeCaFp), and high-efficiency energy consumption and buffering (heECaB) technology. The ability of networked microgrids to greatly reduce power outages and power system restoration time is demonstrated by leveraging robust decentralized and centralized control algorithms, identified through a comprehensive literature review. Future research areas are proposed to further enhance grid stability, controllability, cybersecurity, and protection against faults in the presence of 100% renewable sources by leveraging the advanced capabilities of NSf, DeCaFp, and heECaB devices and system-level control algorithms.

14 SOLAR ENERGY↗
DOE OSTI2022

Design, Deployment, and Characterization of the World’s First Flexible Large Power Transformer

GE Research and its partner Prolec GE have designed, built and deployed in the field the world’s first flexible power transformer. The flexible power transformer is a transmission class 3-phase autotransformer configurable in impedance and in voltage which allows it to serve as a universal spare for multiple units in a given fleet. However, the key innovation in this new concept is the online adjustable leakage impedance which allows the transformer to change its impedance without interrupting the transmission line operation. The flexible power transformer can be designed with up to three low voltage transmission class ratings and up to 12 impedance values changeable both online and offline. This report provides an overview of the design, manufacturing, testing, and commissioning of the 165kV, 60MVA prototype built including the results of the field performance validation tests. The prototype was specified in collaboration with Cooperative Energy, the utility host. It was designed and tested in the factory according to IEEE standard C57.12.00 and followed all protocols for transportation, installation, and commissioning of a power transformer. In addition to the prototype, a flexible protection system capable of automatically adjusting its settings upon the transformer impedance was also developed and deployed in the for testing and validation. On September 3, 2021 the prototype was energized in Cooperative Energy’s substation in Columbia, Mississippi to become the world’s first flexible power transformer in operation. Its performances and impact on the grid operation were demonstrated through different field tests. Results obtained confirm that the impedance of the flexible transformer can be varied under load through its full range, from 4.3% to 9.3%, without adverse impacts on the line operation, the protection system, the transformer stability and health condition. Results also proved that the flexible transformer is very effective in controlling power transfer through the line or load sharing between units operating in parallel. Indeed, it was proven that higher impedances decrease the thruput power of the transformer while lower impedances increase it. Up to 26MW was controllable on a line loading of 45MVA. It was also possible to demonstrate that the variation of the transformer impedance has no effect on the circulating current between units in parallel, except a minor transient during the impedance change. It was also proven that the flexible protection relay can update its protection settings automatically when the impedance change was detected. The prototype has operated continuously for more than 12 months now with a peak load exceeding 50MVA corresponding to >80% of its ONAN power rating. No alarm, trip or sign of failure has been reported by the utility. In addition to the development and deployment of the flexible transformer prototype, investigations were carried out on new nanodielectric fluids to replace the mineral oil used in power transformers with the goal of reducing their footprint and weight. The key parameters that were targeted for improvement included the breakdown voltage to reduce clearances between windings and tank hence the footprint; viscosity and thermal conductivity to increase the cooling efficiency and therefore to reduce the winding material. Several nanodielectric mixtures with mineral oil including with alumina (Al2O3), titania (TiO2) and Borum Nitrate (BN) with different surfactants have been analyzed and tested. Unfortunately, despite encouraging results no nanofluid candidate has been found viable to replace mineral oil. With the formulations tested, breakdown voltages are generally similar to mineral oil at lower particle contents and worse at higher particle contents. Viscosity appreciably increased at particles concertation over 2 wt% and thermal conductivity increased slightly at 5wt% and appears to be 10-15% higher at 10 wt% particle content. It is recommended to continue investigations to find solutions that can help increase the power density of future flexible power transformers. Flexible power transformers can significantly help the future power grid by providing more flexibility and resiliency. Indeed, by providing voltage and impedance flexibility, flexible power transformers reduce the need for multiple spares, hence inventory costs for utilities. With their online controllable impedance, they can provide support to the grid and help manage short-circuit currents, power flow, line congestion, and grid stability which will become more important with higher penetrations of intermittent renewable resources. During the field validation tests, it was demonstrated that up to 26MW was controllable on a line loading of 45MVA when the transformer impedance was varied from its minimum to its maximum range. Also, with the impedance range, the short-circuit currents could be reduced by up to 38% at the load side of the transformer. With its controllable impedance, flexible transformers can be used in future strategies of grid resilience to help better prepare the grid to face forecasted severe events including storms, heat waves and contingencies. The flexible power transformers can also find role in other applications including high voltage transmission cables such as offshore wind farms where solutions for energizing the cables and managing the reactive power are of critical importance. The designed flexible power transformer is now fully validated and ready for commercialization. Further analysis on the benefits of flexible power transformers for grid stability and short-circuit management including current limiting capability, reclosure and line restoration, control of inrush current, sizing of flexible AC components (FACTS) would help its rapid adoption by the industry.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1992

Astronomical data analysis software and systems I; Proceedings of the 1st Annual Conference, Tucson, AZ, Nov. 6-8, 1991

Consideration is given to a definition of a distribution format for X-ray data, the Einstein on-line system, the NASA/IPAC extragalactic database, COBE astronomical databases, Cosmic Background Explorer astronomical databases, the ADAM software environment, the Groningen Image Processing System, search for a common data model for astronomical data analysis systems, deconvolution for real and synthetic apertures, pitfalls in image reconstruction, a direct method for spectral and image restoration, and a discription of a Poisson imagery super resolution algorithm. Also discussed are multivariate statistics on HI and IRAS images, a faint object classification using neural networks, a matched filter for improving SNR of radio maps, automated aperture photometry of CCD images, interactive graphics interpreter, the ROSAT extreme ultra-violet sky survey, a quantitative study of optimal extraction, an automated analysis of spectra, applications of synthetic photometry, an algorithm for extra-solar planet system detection and data reduction facilities for the William Herschel telescope.

Worrall, Diana M.↗
DOE OSTI2025

Assessing Heterogeneity of Surface Water Temperature Following Stream Restoration and a High-Intensity Fire from Thermal Imagery

Thermal heterogeneity of rivers is essential to support freshwater biodiversity. Salmon behaviorally thermoregulate by moving from patches of warm water to cold water. When implementing river restoration projects, it is essential to monitor changes in temperature and thermal heterogeneity through time to assess the impacts to a river’s thermal regime. Lightweight sensors that record both thermal infrared (TIR) and multispectral data carried via unoccupied aircraft systems (UASs) present an opportunity to monitor temperature variations at high spatial (<0.5 m) and temporal resolution, facilitating the detection of the small patches of varying temperatures salmon require. Here, we present methods to classify and filter visible wetted area, including a novel procedure to measure canopy cover, and extract and correct radiant surface water temperature to evaluate changes in the variability of stream temperature pre- and post-restoration followed by a high-intensity fire in a section of the river corridor of the South Fork McKenzie River, Oregon. We used a simple linear model to correct the TIR data by imaging a water bath where the temperature increased from 9.5 to 33.4 °C. The resulting model reduced the mean absolute error from 1.62 to 0.35 °C. We applied this correction to TIR-measured temperatures of wetted cells classified using NDWI imagery acquired in the field. We found warmer conditions (+2.6 °C) after restoration (p < 0.001) and median absolute deviation for pre-restoration (0.30) to be less than both that of post-restoration (0.85) and post-fire (0.79) orthomosaics. In addition, there was statistically significant evidence to support the hypothesis of shifts in temperature distributions pre- and post-restoration (KS test 2009 vs. 2019, p < 0.001, D = 0.99; KS test 2019 vs. 2021, p < 0.001, D = 0.10). Moreover, we used a Generalized Additive Model (GAM) that included spatial and environmental predictors (i.e., canopy cover calculated from multispectral NDVI and photogrammetrically derived digital elevation model) to model TIR temperature from a transect along the main river channel. This model explained 89% of the deviance, and the predictor variables showed statistical significance. Collectively, our study underscored the potential of a multispectral/TIR sensor to assess thermal heterogeneity in large and complex river systems.

Barker, Matthew I. (ORCID:0000000252864930)↗
DOE OSTI2021

Power System Resilience Metrics Augmentation for Critical Load Prioritization

One of the major goals of new grid operation regimes, such as transactive energy systems (TESs), is to make the power grid more resilient to withstand natural or man-made disasters and potential reliability events, and to continue to serve the maximum number of its customers. But it is a well-known fact to system operators that not all customers are the same. This implies that any discussion of TESs’ impacts on the resilience of the power system should consider the needs of its critical customers (such as the power system operation centers, fire and police stations, and hospitals) over those of other customers. When evaluating the resilience of the system, bonus points must be awarded to any system that could maintain its power supply to critical customers during a disturbance that may cause an outage. This report discusses critical infrastructure (CI) as found in the literature and then categorizes it based on the field to which the operations belong (such as human life/safety-related, operations management, necessary city operation, industrial customers, etc.). Each of these CI categories is further divided into types of critical customers (e.g., the human life/safety-related category has different types of customers like hospitals, fire and police stations, etc.). The entire demand of each of the critical customer types is not categorized as critical load (CL); instead, only a portion of the total load of these critical customers is characterized as critical load. This is done based on the categories of equipment, the function of which is crucial in the operation of the overall facility. CL categorization is performed to provide the ratio of the critical load portion to the overall load , so that it can serve as a parameter in the resilience evaluation of the grid through a metrics-based approach. Such categorization is important as it helps to augment the existing quantifiable resilience metrics with CL categorization. The metrics for a power system need to not only consider how well a system performed during a disturbance event, but also how it reduced strain and supplied power to its CLs. The first step in this process is characterize CLs in the system. After CL characterization, the next step is the inclusion of these loads in the resilience metrics. To that end, in this report weight-based augmentation of resilience metrics is proposed, where certain customers (the ones that are categorized as critical) are assigned higher weights than others. Though an overview of assigning weights to customers is discussed, there is no one-size-fits-all approach for every power system. The decisions made about assigning such weights to customers vary greatly from one operator to another, based on their unique systems and the current and predicted states of critical customers. This decision-making can include the type of disturbance event, which might only affect certain parts of the system. In general, analyzing critical customers before an event helps understand system vulnerabilities. It also helps in planning and conducting operations during the event, evaluating system performance after the event, and supporting better planning for future events. An alternative to the current practices of managing the grid for outages is an innovative TES, which has the potential to provide a platform for including distributed energy resources for managing CLs. This report also describes how TES qualities can help (1) to maintain power supply to critical customers for uninterrupted operations and (2) to restore lost power supply to the critical customers rapidly.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Resilience assessment and planning in power distribution systems: Past and future considerations

High impact low probability (HILP) events such as hurricanes, heat waves, and floods have instigated widespread power outages and blackouts around the globe in the past decade. With the increasing challenges concerning the threats to the power distribution systems and the growing need to mitigate the impacts of the HILP events, resilience has become a crucial requirement for the power grid infrastructures. Numerous efforts have been made to define, measure, and characterize the resilience of power distribution systems. This study thoroughly reviews the state-of-the-art methods on the existing resilience evaluation framework and metrics. Here, the desirable characteristics of resilience metrics are highlighted, and the challenges associated with formulating, developing, and calculating such metrics are discussed. Next, we detail the state-of-the-art literature on planning solutions to ensure distribution system resilience. This paper aims to extract a deep insight into this challenging and critical research area and envision future opportunities that can guide the power distribution system operators/planners to formulate more effective mitigation strategies to enhance the resilience of power distribution systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1986

Nitrogen and dry-matter partitioning in soybean plants during onset of and recovery from nitrogen stress

The study tested the hypothesis that resupplying nitrogen after a period of nitrogen stress leads to restoration of the balance between root and shoot growth and normal functional activity. Nonnodulated soybean plants were grown hydroponically for 14 days with 1.0 mM NO3- in a complete nutrient solution. One set of plants was continued on the complete nutrient solution for 25 days; a second set was given 0.0 mM NO3- for 25 days; and the third set was given 0.0 mM NO3- for 10 days followed by transfer to the complete solution with 1.0 mM NO3- for 15 days. In continuously nitrogen-stressed plants, emergence and expansion of main-stem and branch leaves were severely inhibited as low nitrogen content limited further growth. This was followed by a shift in partitioning of dry matter from the leaves to the roots, resulting in an initial stimulation of root growth and a decreased shoot:root ratio. Reduced nitrogen also was redistributed from the leaves into the stem and roots. When nitrogen stress was relieved, leaf initiation and expansion were renewed. With the restoration of the balance between root and shoot function, the shoot:root ratio and distribution of reduced nitrogen within the plant organs returned to levels similar to those of nonstressed plants.

NASA Discipline Number 61-10↗
DOE OSTI2021

Kickstart Your Federal Microgrid Resiliency Project: Financing Opportunities and Best Practices

Recent high-impact events such as hurricanes and wildfires have resulted in the loss of utility grid power to federal sites, highlighting the need for energy system resilience. To sustain critical functions, site loads may need to operate during an electric grid outage or at least have power restored quickly after the event. A microgrid can provide reliable backup power to critical loads when electric utility power is interrupted, and may also provide value during normal operations.

DER↗
DOE OSTI2024

Pore Structures in Detritusphere of Soils Under Switchgrass and Restored Prairie Vegetation Community

Root detritusphere, that is, the soil in the vicinity of decomposing root residues, plays an important role in soil microbial activity and C sequestration. Pore structure (size distributions and connectivity of soil pores) in the detritusphere serves as a major driver for these processes and, in turn, is influenced by the physical characteristics of both soil and roots. This study compared pore structure characteristics in the root detritusphere of soils of contrasting texture and mineralogy subjected to > 6 years of contrasting vegetation: monoculture switchgrass and polyculture prairie systems. Soil samples were collected from five experimental sites in the US Midwest representing three soil types. Soil texture and mineralogy were measured using a hydrometer and x-ray powder diffraction, respectively. The intact cores were scanned with x-ray computed micro-tomography to identify visible soil pores, biopores, and particulate organic matter (POM). We specifically focused on pore structure within the detritusphere around the POM of root origin. Results showed that the detritusphere of coarser textured soils, characterized by high sand and quartz contents, had lower porosity in the vicinity of POM compared with finer textured soils. POM vicinities in finer textured soils had high proportions of large (> 300 μm diameter) pores, and their pores were better connected than in the coarser soils. Lower porosity in the outer (> 1 mm) parts of the detritusphere of switchgrass than of prairie suggested soil compaction by roots, with the effect especially pronounced in the coarser soils. Here, the results demonstrated that soil texture and mineralogy played a major, while vegetation played a more modest, role in defining the pore structure in the root detritusphere.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1977

Photovoltaic, gravitationally-stabilized solid-state, satellite solar power station /GSS4PS/

The salient feature of a gravitationally-stabilized satellite solar power system (SSPS) for a photovoltaic system is that the large solar array is separated into smaller segments or subunits, joined together in a linear array oriented along the local vertical. Applicability of gravitational stabilization to the design of photovoltaic SSPS is demonstrated. Both actively controlled systems using multiple solar panels oriented to the sun and passively controlled systems requiring no sun orientation are considered and determined to be feasible. Expressions for gravity-gradient induced tension and restoring torques about the local vertical are assessed. Particular attention is directed to the applicability of solid-state approaches to the design of SSPS. It is shown that an all solid-state SSPS utilizing the LITOMIC (light-to-microwave conversion) concept is feasible but that a hybrid system employing a combination of both solid-state and cryogenic cooled low-voltage techniques to the design of the power management and distribution subsystem may also provide a solution.

Cantafio, L. J.↗
NASA NTRS2005

International Space Station Electric Power System Performance Code-SPACE

The System Power Analysis for Capability Evaluation (SPACE) software analyzes and predicts the minute-by-minute state of the International Space Station (ISS) electrical power system (EPS) for upcoming missions as well as EPS power generation capacity as a function of ISS configuration and orbital conditions. In order to complete the Certification of Flight Readiness (CoFR) process in which the mission is certified for flight each ISS System must thoroughly assess every proposed mission to verify that the system will support the planned mission operations; SPACE is the sole tool used to conduct these assessments for the power system capability. SPACE is an integrated power system model that incorporates a variety of modules tied together with integration routines and graphical output. The modules include orbit mechanics, solar array pointing/shadowing/thermal and electrical, battery performance, and power management and distribution performance. These modules are tightly integrated within a flexible architecture featuring data-file-driven configurations, source- or load-driven operation, and event scripting. SPACE also predicts the amount of power available for a given system configuration, spacecraft orientation, solar-array-pointing conditions, orbit, and the like. In the source-driven mode, the model must assure that energy balance is achieved, meaning that energy removed from the batteries must be restored (or balanced) each and every orbit. This entails an optimization scheme to ensure that energy balance is maintained without violating any other constraints.

Hojnicki, Jeffrey↗
DOE OSTI2023

Secondary Frequency Control for Reconfigurable Interconnecting Microgrids

Microgrids and microgrid technologies offer an operations and control framework for realizing the needed aggregation of a growing share of distributed energy resources. As the number of microgrids increases, so will the incentive to interconnect them, leading to a combinatorial growth of potential operating states. At the same time, their growing complexity nudges interconnected microgrids conceptually closer to balancing authorities in the bulk power system. This paper focuses on secondary frequency control and leverages the conceptual similarity between balancing authorities and interconnected microgrids to adopt an automatic generation control design with some adaptations. Frequency control and restoration is demonstrated via several use-cases with switching and reconfiguration events.

Schweitzer, Eran↗
DOE OSTI2026

Safe Deep Reinforcement Learning for Robust Frequency and Voltage-Constrained Networked Microgrid Restoration

Here, this paper proposes a safe soft actor-critic reinforcement learning (RL) algorithm–based controller for networked microgrid restoration. It formulates the post black-start start as a finite-horizon constrained Markov decision process. The RL agent co-optimizes real and reactive power set-points for both grid-forming and grid-following inverters under explicit voltage and frequency constraints, while enforcing proper power sharing via the Mean Active Power Sharing Index (MPSI) and Mean Reactive Power Sharing Index (MQSI). Numerical results obtained on the IEEE 123-bus distribution system show that the proposed method achieves a mean voltage build-up time of 0.01 s without breaching the 5% sharing-violation budget under various load scenarios, considering MPSI and MQSI indices. These findings demonstrate that the proposed method yields fast and safe black-start schedules without resorting to heuristic penalties.

Selim, Alaa [Dartmouth College, Hanover, NH (Unite↗
DOE OSTI2022

Interplay between disorder and collective coherent response: Superradiance and spectral motional narrowing in the time domain

The interplay between static and dynamic disorder and collective optical response in molecular ensembles is an important characteristic of nanoplasmonic and nanophotonic molecular systems. Here we investigate the cooperative superradiant response of a molecular ensemble of quantum emitters under the influence of environmental disorder, including inhomogeneous broadening (as induced by a static random distribution of the molecular transition frequencies) and motional narrowing (as induced by stochastic modulation of these excitation energies). The effect of inhomogeneous broadening is to destroy the coherence of the collective molecular excitation and suppress superradiant emission. However, fast stochastic modulation of the molecular excitation energy can effectively restore the coherence of the quantum emitters and lead to a recovery of superradiant emission, which is an unexpected manifestation of motional narrowing. For a light-scattering process as induced by an off-resonant incident pulse, stochastic modulation leads to inelastic fluorescence emission at the average excitation energy at long times and suggests that dynamic disorder effects can actually lead to collective excitation of the molecular ensemble.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

FLISR in the Presence of DERs ADMS Test Bed Use Case

Fault location, isolation, and restoration (FLISR) is one of the distribution automation applications that utilities are most interested in. It operates groups of switches on distribution feeders to improve the reliability of power delivery after localizing outages. FLISR is an essential function for enabling a self-healing grid, and it directly affects grid reliability and resilience. The presence of DERs brings both new opportunities and challenges for FLISR applications. For instance, some DERs can work as backup generation sources and help energize local networks so more switching options can be achieved with the coordination of FLISR operations; however, the existence of DERs also brings new challenges. The bidirectional power flow resulting from DERs might require dynamic changes to protective devices' fault current settings, and thus the FLISR application will need to dynamically adjust its operations in coordination with the dynamic protection settings. Also, some FLISR applications make their service restoration decisions and close tie-switches based on predefined rules; however, the presence of DERs and their impact on altering net loads on the local feeder network are not considered. For this use case, the project team is using the FLISR application of the Survalent ADMS operating on a real-time simulation of a feeder from Central Georgia EMC, a cooperative electric utility. The performance of the FLISR application is being evaluated for different locations and combinations of DERs, including grid-forming battery energy storage systems.

ADMS↗
NASA NTRS1999

Investigation of Near Shannon Limit Coding Schemes

Turbo codes can deliver performance that is very close to the Shannon limit. This report investigates algorithms for convolutional turbo codes and block turbo codes. Both coding schemes can achieve performance near Shannon limit. The performance of the schemes is obtained using computer simulations. There are three sections in this report. First section is the introduction. The fundamental knowledge about coding, block coding and convolutional coding is discussed. In the second section, the basic concepts of convolutional turbo codes are introduced and the performance of turbo codes, especially high rate turbo codes, is provided from the simulation results. After introducing all the parameters that help turbo codes achieve such a good performance, it is concluded that output weight distribution should be the main consideration in designing turbo codes. Based on the output weight distribution, the performance bounds for turbo codes are given. Then, the relationships between the output weight distribution and the factors like generator polynomial, interleaver and puncturing pattern are examined. The criterion for the best selection of system components is provided. The puncturing pattern algorithm is discussed in detail. Different puncturing patterns are compared for each high rate. For most of the high rate codes, the puncturing pattern does not show any significant effect on the code performance if pseudo - random interleaver is used in the system. For some special rate codes with poor performance, an alternative puncturing algorithm is designed which restores their performance close to the Shannon limit. Finally, in section three, for iterative decoding of block codes, the method of building trellis for block codes, the structure of the iterative decoding system and the calculation of extrinsic values are discussed.

Kwatra, S. C.↗