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All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

Combining Ratio Estimation for Low Density Parity Check (LDPC) Coding

The Low Density Parity Check (LDPC) Code decoding algorithm make use of a scaled receive signal derived from maximizing the log-likelihood ratio of the received signal. The scaling factor (often called the combining ratio) in an AWGN channel is a ratio between signal amplitude and noise variance. Accurately estimating this ratio has shown as much as 0.6 dB decoding performance gain. This presentation briefly describes three methods for estimating the combining ratio: a Pilot-Guided estimation method, a Blind estimation method, and a Simulation-Based Look-Up table. The Pilot Guided Estimation method has shown that the maximum likelihood estimates of signal amplitude is the mean inner product of the received sequence and the known sequence, the attached synchronization marker (ASM) , and signal variance is the difference of the mean of the squared received sequence and the square of the signal amplitude. This method has the advantage of simplicity at the expense of latency since several frames worth of ASMs. The Blind estimation method s maximum likelihood estimator is the average of the product of the received signal with the hyperbolic tangent of the product combining ratio and the received signal. The root of this equation can be determined by an iterative binary search between 0 and 1 after normalizing the received sequence. This method has the benefit of requiring one frame of data to estimate the combining ratio which is good for faster changing channels compared to the previous method, however it is computationally expensive. The final method uses a look-up table based on prior simulated results to determine signal amplitude and noise variance. In this method the received mean signal strength is controlled to a constant soft decision value. The magnitude of the deviation is averaged over a predetermined number of samples. This value is referenced in a look up table to determine the combining ratio that prior simulation associated with the average magnitude of the deviation. This method is more complicated than the Pilot-Guided Method due to the gain control circuitry, but does not have the real-time computation complexity of the Blind Estimation method. Each of these methods can be used to provide an accurate estimation of the combining ratio, and the final selection of the estimation method depends on other design constraints.

Mahmoud, Saad↗
NASA NTRS2003

Low Density Parity Check Codes: Bandwidth Efficient Channel Coding

Low Density Parity Check (LDPC) Codes provide near-Shannon Capacity performance for NASA Missions. These codes have high coding rates R=0.82 and 0.875 with moderate code lengths, n=4096 and 8176. Their decoders have inherently parallel structures which allows for high-speed implementation. Two codes based on Euclidean Geometry (EG) were selected for flight ASIC implementation. These codes are cyclic and quasi-cyclic in nature and therefore have a simple encoder structure. This results in power and size benefits. These codes also have a large minimum distance as much as d,,, = 65 giving them powerful error correcting capabilities and error floors less than lo- BER. This paper will present development of the LDPC flight encoder and decoder, its applications and status.

Fong, Wai↗
NASA NTRS2004

Accumulate repeat accumulate codes

In this paper we propose an innovative channel coding scheme called 'Accumulate Repeat Accumulate codes' (ARA). This class of codes can be viewed as serial turbo-like codes, or as a subclass of Low Density Parity Check (LDPC) codes, thus belief propagation can be used for iterative decoding of ARA codes on a graph. The structure of encoder for this class can be viewed as precoded Repeat Accumulate (RA) code or as precoded Irregular Repeat Accumulate (IRA) code, where simply an accumulator is chosen as a precoder. Thus ARA codes have simple, and very fast encoder structure when they representing LDPC codes. Based on density evolution for LDPC codes through some examples for ARA codes, we show that for maximum variable node degree 5 a minimum bit SNR as low as 0.08 dB from channel capacity for rate 1/2 can be achieved as the block size goes to infinity. Thus based on fixed low maximum variable node degree, its threshold outperforms not only the RA and IRA codes but also the best known LDPC codes with the dame maximum node degree. Furthermore by puncturing the accumulators any desired high rate codes close to code rate 1 can be obtained with thresholds that stay close to the channel capacity thresholds uniformly. Iterative decoding simulation results are provided. The ARA codes also have projected graph or protograph representation that allows for high speed decoder implementation.

Low Density Parity Check codes (LDPC)↗
NASA NTRS2004

Accumulate-Repeat-Accumulate-Accumulate-Codes

Inspired by recently proposed Accumulate-Repeat-Accumulate (ARA) codes [15], in this paper we propose a channel coding scheme called Accumulate-Repeat-Accumulate-Accumulate (ARAA) codes. These codes can be seen as serial turbo-like codes or as a subclass of Low Density Parity Check (LDPC) codes, and they have a projected graph or protograph representation; this allows for a high-speed iterative decoder implementation using belief propagation. An ARAA code can be viewed as a precoded Repeat-and-Accumulate (RA) code with puncturing in concatenation with another accumulator, where simply an accumulator is chosen as the precoder; thus ARAA codes have a very fast encoder structure. Using density evolution on their associated protographs, we find examples of rate-lJ2 ARAA codes with maximum variable node degree 4 for which a minimum bit-SNR as low as 0.21 dB from the channel capacity limit can be achieved as the block size goes to infinity. Such a low threshold cannot be achieved by RA or Irregular RA (IRA) or unstructured irregular LDPC codes with the same constraint on the maximum variable node degree. Furthermore by puncturing the accumulators we can construct families of higher rate ARAA codes with thresholds that stay close to their respective channel capacity thresholds uniformly. Iterative decoding simulation results show comparable performance with the best-known LDPC codes but with very low error floor even at moderate block sizes.

density evolution↗
NASA NTRS2004

Accumulate Repeat Accumulate Coded Modulation

In this paper we propose an innovative coded modulation scheme called 'Accumulate Repeat Accumulate Coded Modulation' (ARA coded modulation). This class of codes can be viewed as serial turbo-like codes, or as a subclass of Low Density Parity Check (LDPC) codes that are combined with high level modulation. Thus at the decoder belief propagation can be used for iterative decoding of ARA coded modulation on a graph, provided a demapper transforms the received in-phase and quadrature samples to reliability of the bits.

coded modulation↗
NASA NTRS2006

Protograph LDPC Codes for the Erasure Channel

This viewgraph presentation reviews the use of protograph Low Density Parity Check (LDPC) codes for erasure channels. A protograph is a Tanner graph with a relatively small number of nodes. A "copy-and-permute" operation can be applied to the protograph to obtain larger derived graphs of various sizes. For very high code rates and short block sizes, a low asymptotic threshold criterion is not the best approach to designing LDPC codes. Simple protographs with much regularity and low maximum node degrees appear to be the best choices Quantized-rateless protograph LDPC codes can be built by careful design of the protograph such that multiple puncturing patterns will still permit message passing decoding to proceed

long erasure codes↗
NASA NTRSDate not supplied

Improvements on Low-Density Parity-Check (LDPC) Codes and High-Performance Neuromorphic Engineering for Communication Systems

Belief propagation (BP) on LDPC codes is an iterative decoding algorithm that performs information transfer on the Tanner graph, which represents the code. In each iteration, the algorithm exchanges information (LLR) between variable nodes and check nodes through the edges of the graph. LLR values represent the probability that a given bit in a transmitted codeword equals 0 or 1, given a received word. In the hardware part, recent advancements in intelligent technologies, such as artificial intelligence, big data analytics, autonomous vehicles, and speech/image recognition, have heightened the demand for faster calculations and reduced energy consumption.

Danilo Barrionuevo↗
NASA NTRS1999

Low Density Parity Check Codes Based on Finite Geometries: A Rediscovery and More

Low density parity check (LDPC) codes with iterative decoding based on belief propagation achieve astonishing error performance close to Shannon limit. No algebraic or geometric method for constructing these codes has been reported and they are largely generated by computer search. As a result, encoding of long LDPC codes is in general very complex. This paper presents two classes of high rate LDPC codes whose constructions are based on finite Euclidean and projective geometries, respectively. These classes of codes a.re cyclic and have good constraint parameters and minimum distances. Cyclic structure adows the use of linear feedback shift registers for encoding. These finite geometry LDPC codes achieve very good error performance with either soft-decision iterative decoding based on belief propagation or Gallager's hard-decision bit flipping algorithm. These codes can be punctured or extended to obtain other good LDPC codes. A generalization of these codes is also presented.

Kou, Yu↗
NASA NTRSDate not supplied

Flexible Data and Frame Synchronization Structure for the LunaNet PNT Signal

A LunaNet Lunar Augmented Navigation Service (LANS) is being developed to enable a position, navigation, and timing service for future Lunar operations. The signal includes two components. An in-phase data channel signal is spread by a 1.023 MCPS ranging code that provides a high-rate data message at 250 bps and is encoded by a strong Low Density Parity Check (LDPC) code. A pilot channel with a 5.115 MCPS spreading code is also provided. The pilot code is configured with a secondary (overlay) code that does not currently provide absolute time or frame Synchronization as is the case for L1C. This work shows the advantage of implementing an overlay structure that provides absolute time for the LunaNet LANS signal structure known as the Augmented Forward Signal (AFS). The LunaNet AFS structure was developed to service two classes of user receivers. The first class is a low-complexity user receiver that only receives the 1.023 MCPS signal and does not use the 5.115 MCPS pilot channel. For this class of user, a data frame Sync word is needed. The second class of receiver is a high-end receiver that can processes both data and pilot channels to take advantage of the higher chip rate pilot channel for enhanced robustness and improved accuracy. In the current draft LunaNet LANS AFS design, these users must employ the frame Sync word in the data channel and obtain absolute time after decoding the AFS navigation message. The signal structure would greatly benefit from the addition of a pilot overlay structure that provides absolute time and robust frame Sync for high-end users as done for L1C. To provide a more robust and interoperable AFS structure, this work summarizes a study and recommends alternatives for a new overlay code on the pilot channel that provides absolute time and a Sync word approach on the data channel. The overlay code and Sync word are designed to allow for flexible and robust data synchronization for both low- complexity and high-end user receivers. The new overlay code structure permits frame synchronization performance that is as good as or better than the L1 C signal, while enabling a determination of absolute time upon frame Sync to aid high-end assisted LANS AFS user receivers at low signal to noise levels. We also present the design of rate-matched 5G new radio (5GNR) LDPC codes that fit within the current 6000-symbol frame size along with a time of interval (TOI) word, frame ID (FID) word, and the remaining LunaNet AFS data message blocks. The paper describes and demonstrates robust frame Synchronization performance of the overlay code and Synch word approaches. The results are described in terms of probability of missed detection and probability of false alarm for a correct frame Synchronization at low Eb/No levels expected for decoding the TOI word and LDPC encoded data. Advantages of the proposed data Synchronization structure will be described along with use cases for low-end and high-end receivers. Practical implementation considerations will also be described.

LunaNet↗
NASA NTRSDate not supplied

Flexible Data and Frame Synchronization Structure for the LunaNet PNT Signal

A LunaNet Lunar Augmented Navigation Service (LANS) is being developed to enable a position, navigation, and timing service for future Lunar operations [1]. The signal includes two components. An in-phase data channel signal is spread by a 1.023 MCPS ranging code that provides a high-rate data message at 250 bps and is encoded by a strong Low Density Parity Check (LDPC) code. A pilot channel with a 5.115 MCPS spreading code is also provided. The pilot code is configured with a secondary (overlay) code that does not currently provide absolute time or frame Synchronization as is the case for L1C [2] [3]. This work shows the advantage of implementing an overlay structure that provides absolute time for the LunaNet LANS signal structure known as the Augmented Forward Signal (AFS). The LunaNet AFS structure was developed to service two classes of user receivers. The first class is a low-complexity user receiver that only receives the 1.023 MCPS signal and does not use the 5.115 MCPS pilot channel. For this class of user, a data frame Sync word is needed. The second class of receiver is a high-end receiver that can processes both data and pilot channels to take advantage of the higher chip rate pilot channel for enhanced robustness and improved accuracy. In the current draft LunaNet LANS AFS design, these users must employ the frame Sync word in the data channel and obtain absolute time after decoding the AFS navigation message [2]. The signal structure would greatly benefit from the addition of a pilot overlay structure that provides absolute time and robust frame Sync for high-end users as done for L1C [3]. To provide a more robust and interoperable AFS structure, this work summarizes a study and recommends alternatives for a new overlay code on the pilot channel that provides absolute time and a Sync word approach on the data channel. The overlay code and Sync word are designed to allow for flexible and robust data synchronization for both low- complexity and high-end user receivers. The new overlay code structure permits frame synchronization performance that is as good as or better than the L1 C signal, while enabling a determination of absolute time upon frame Sync to aid high-end assisted LANS AFS user receivers at low signal to noise levels. We also present the design of rate-matched 5G new radio (5GNR) LDPC codes that fit within the current 6000-symbol frame size along with a time of interval (TOI) word, frame ID (FID) word, and the remaining LunaNet AFS data message blocks. The paper describes and demonstrates robust frame Synchronization performance of the overlay code and Synch word approaches. The results are described in terms of probability of missed detection and probability of false alarm for a correct frame Synchronization at low Eb/No levels expected for decoding the TOI word and LDPC encoded data. Advantages of the proposed data Synchronization structure will be described along with use cases for low-end and high-end receivers. Practical implementation considerations will also be described.

Philip Dafesh↗
NASA NTRS2008

Direct-detection Free-space Laser Transceiver Test-bed

NASA Goddard Space Flight Center is developing a direct-detection free-space laser communications transceiver test bed. The laser transmitter is a master-oscillator power amplifier (MOPA) configuration using a 1060 nm wavelength laser-diode with a two-stage multi-watt Ytterbium fiber amplifier. Dual Mach-Zehnder electro-optic modulators provide an extinction ratio greater than 40 dB. The MOPA design delivered 10-W average power with low-duty-cycle PPM waveforms and achieved 1.7 kW peak power. We use pulse-position modulation format with a pseudo-noise code header to assist clock recovery and frame boundary identification. We are examining the use of low-density-parity-check (LDPC) codes for forward error correction. Our receiver uses an InGaAsP 1 mm diameter photocathode hybrid photomultiplier tube (HPMT) cooled with a thermo-electric cooler. The HPMT has 25% single-photon detection efficiency at 1064 nm wavelength with a dark count rate of 60,000/s at -22 degrees Celsius and a single-photon impulse response of 0.9 ns. We report on progress toward demonstrating a combined laser communications and ranging field experiment.

Krainak, Michael A.↗
NASA NTRS2011

Soft-Decision-Data Reshuffle to Mitigate Pulsed Radio Frequency Interference Impact on Low-Density-Parity-Check Code Performance

This presentation briefly discusses a research effort on mitigation techniques of pulsed radio frequency interference (RFI) on a Low-Density-Parity-Check (LDPC) code. This problem is of considerable interest in the context of providing reliable communications to the space vehicle which might suffer severe degradation due to pulsed RFI sources such as large radars. The LDPC code is one of modern forward-error-correction (FEC) codes which have the decoding performance to approach the Shannon Limit. The LDPC code studied here is the AR4JA (2048, 1024) code recommended by the Consultative Committee for Space Data Systems (CCSDS) and it has been chosen for some spacecraft design. Even though this code is designed as a powerful FEC code in the additive white Gaussian noise channel, simulation data and test results show that the performance of this LDPC decoder is severely degraded when exposed to the pulsed RFI specified in the spacecraft s transponder specifications. An analysis work (through modeling and simulation) has been conducted to evaluate the impact of the pulsed RFI and a few implemental techniques have been investigated to mitigate the pulsed RFI impact by reshuffling the soft-decision-data available at the input of the LDPC decoder. The simulation results show that the LDPC decoding performance of codeword error rate (CWER) under pulsed RFI can be improved up to four orders of magnitude through a simple soft-decision-data reshuffle scheme. This study reveals that an error floor of LDPC decoding performance appears around CWER=1E-4 when the proposed technique is applied to mitigate the pulsed RFI impact. The mechanism causing this error floor remains unknown, further investigation is necessary.

Ni, Jianjun David↗
NASA NTRS2004

Maximum likelihood decoding analysis of Accumulate-Repeat-Accumulate Codes

Repeat-Accumulate (RA) codes are the simplest turbo-like codes that achieve good performance. However, they cannot compete with Turbo codes or low-density parity check codes (LDPC) as far as performance is concerned. The Accumulate Repeat Accumulate (ARA) codes, as a subclass of LDPC codes, are obtained by adding a pre-coder in front of RA codes with puncturing where an accumulator is chosen as a precoder. These codes not only are very simple, but also achieve excellent performance with iterative decoding. In this paper, the performance of these codes with (ML) decoding are analyzed and compared to random codes by very tight bounds. The weight distribution of some simple ARA codes is obtained, and through existing tightest bounds we have shown the ML SNR threshold of ARA codes approaches very closely to the performance of random codes. We have shown that the use of precoder improves the SNR threshold but interleaving gain remains unchanged with respect to RA code with puncturing.

low density parity codes (LDPC)↗
NASA NTRS2017

DVB-S2 Experiment over NASA's Space Network

The commercial DVB-S2 standard was successfully demonstrated over NASAs Space Network (SN) and the Tracking Data and Relay Satellite System (TDRSS) during testing conducted September 20-22nd, 2016. This test was a joint effort between NASA Glenn Research Center (GRC) and Goddard Space Flight Center (GSFC) to evaluate the performance of DVB-S2 as an alternative to traditional NASA SN waveforms. Two distinct sets of tests were conducted: one was sourced from the Space Communication and Navigation (SCaN) Testbed, an external payload on the International Space Station, and the other was sourced from GRCs S-band ground station to emulate a Space Network user through TDRSS. In both cases, a commercial off-the-shelf (COTS) receiver made by Newtec was used to receive the signal at White Sands Complex. Using SCaN Testbed, peak data rates of 5.7 Mbps were demonstrated. Peak data rates of 33 Mbps were demonstrated over the GRC S-band ground station through a 10MHz channel over TDRSS, using 32-amplitude phase shift keying (APSK) and a rate 89 low density parity check (LDPC) code. Advanced features of the DVB-S2 standard were evaluated, including variable and adaptive coding and modulation (VCMACM), as well as an adaptive digital pre-distortion (DPD) algorithm. These features provided additional data throughput and increased link performance reliability. This testing has shown that commercial standards are a viable, low-cost alternative for future Space Network users.

waveforms↗
NASA NTRS2012

SCaN Network Ground Station Receiver Performance for Future Service Support

Objectives: Examine the impact of providing the newly standardized CCSDS Low Density Parity Check (LDPC) codes to the SCaN return data service on the SCaN SN and DSN ground stations receivers: SN Current Receiver: Integrated Receiver (IR). DSN Current Receiver: Downlink Telemetry and Tracking (DTT) Receiver. Early Commercial-Off-The-Shelf (COTS) prototype of the SN User Service Subsystem Component Replacement (USS CR) Narrow Band Receiver. Motivate discussion of general issues of ground station hardware design to enable simple and cheap modifications for support of future services.

Deep Space Network (DSN)↗
NASA NTRS2018

Assessment of Potential Mars Relay Network Enhancements

In anticipation of increased demands on Mars relay services, including planned arrivals of NASA’s InSight Lander in November 2018, and of NASA’s Mars 2020 rover and ESA’s ExoMars Rover & Surface Platform mission in Feb-Mar.2021, we have assessed a number of potential modifications and upgrades to Mars relay orbiters and quantified their impacts in terms of key relay support metrics, to support NASA and ESA programmatic decisions. Specific areas of investigation include: 1) implementation of “split-pass” relay capability for support to collocated landers, 2) modifications of the extended mission orbit for the Mars Atmosphere and Volatile EvolutioN Mission (MAVEN), and 3) introduction of Low-Density Parity Check (LDPC) coding. We report here on each of these potential upgrades, quantify the performance implications each would have on future Mars relay services in the context of future mission support scenarios, and provide a status on implementation.

Wenkert, Daniel↗
NASA NTRSDate not supplied

The Design of a Flexible, Interoperable Navigation Signal for Future Lunar Missions

The LunaNet Interoperability Specification (LNIS) is a set of standards currently under development by NASA, ESA, and JAXA, which define a common, interoperable set of services and interfaces for lunar communication and navigation. The LNIS includes specifications for the GNSS-like Augmented Forward Signal (AFS). The LANS (Lunar Augmented Navigation Service) will be comprised of Multiple LunaNet Service Provider (LNSP) nodes broadcasting the AFS, such as NASA’s LCRNS (Lunar Communications Relay and Navigation Systems), ESA’s Moonlight LCNS (Lunar Communication and Navigation Services) and the Japan LNSS (Lunar Navigation Satellite System). The LANS will provide a GNSS-like capability enabling orbiting and surface users in lunar space (such as Artemis) to estimate their position, velocity and time as described in Giordano et al., (2023). Initial capabilities will focus on providing service to the lunar South pole region. The specification of AFS defines two orthogonal signal components on a single carrier, with the in-phase component (AFS-I) being a lower-chip-rate data channel tailored for applications where low SWaP is critical (e.g., IoT devices or search and rescue), and the quadrature component (AFS-Q) being a high-chip-rate data-less pilot signal for high-precision, robust lunar navigation and positioning applications. An initial description of AFS was provided in the LNIS, (2023), and initial analysis results were shown in Dafesh, et al., (2024). In this work, we provide rationale for updates to the LNIS that define key aspects of the signal including the primary spreading code designs for the data and pilot channels, and a three-tiered overlay code approach for the pilot channel that provides flexible signal acquisition alternatives, rapid time dissemination and robust frame Sync. The paper also describes a robust data sync word that is designed to enable frame Sync. for low-SWaP receivers that only use the I channel, as well as a low-density parity check code (LDPC) data message encoding design and interleaving definition. The work further describes the impact of the updated AFS design in terms of improved acquisition performance, interference resistance, navigation message capabilities and rapid absolute time dissemination for users able to access clock and ephemeris data over an external network. The cross-correlation and synchronization performance of the AFS design is also compared to potential alternatives, further providing rationale for the final signal design configuration.

LANS↗