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All sourcesNASA NTRSDOE OSTI
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 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 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 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 NTRS2014

Method of Error Floor Mitigation in Low-Density Parity-Check Codes

A digital communication decoding method for low-density parity-check coded messages. The decoding method decodes the low-density parity-check coded messages within a bipartite graph having check nodes and variable nodes. Messages from check nodes are partially hard limited, so that every message which would otherwise have a magnitude at or above a certain level is re-assigned to a maximum magnitude.

Hamkins, Jon↗
DOE OSTI2025

Toward a 2D Local Implementation of Quantum Low-Density Parity-Check Codes

Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes that affects code performance and ease of physical realization. For device architectures restricted to two-dimensional (2D) local gates, naively implementing the high-rate codes suitable for low-overhead fault-tolerant quantum computing incurs prohibitive overhead. In this work, we present an error-correction protocol built on a bilayer architecture that aims to reduce operational overheads when restricted to 2D local gates by measuring some generators less frequently than others. We investigate the family of bivariate-bicycle qLDPC codes and show that they are well suited for a parallel syndrome-measurement scheme using fast routing with local operations and classical communication (LOCC). Through circuit-level simulations, we find that in some parameter regimes, bivariate-bicycle codes implemented with this protocol have logical error rates comparable to the surface code while using fewer physical qubits. Published by the American Physical Society 2025

Berthusen, Noah (ORCID:0000000275862786)↗
NASA NTRS2009

Structured Low-Density Parity-Check Codes with Bandwidth Efficient Modulation

In this work, we study the performance of structured Low-Density Parity-Check (LDPC) Codes together with bandwidth efficient modulations. We consider protograph-based LDPC codes that facilitate high-speed hardware implementations and have minimum distances that grow linearly with block sizes. We cover various higher- order modulations such as 8-PSK, 16-APSK, and 16-QAM. During demodulation, a demapper transforms the received in-phase and quadrature samples into reliability information that feeds the binary LDPC decoder. We will compare various low-complexity demappers and provide simulation results for assorted coded-modulation combinations on the additive white Gaussian noise and independent Rayleigh fading channels.

Crew Exploration Vehicle (CEV)↗
NASA NTRS2010

Performance of Low-Density Parity-Check Coded Modulation

This paper reports the simulated performance of each of the nine accumulate-repeat-4-jagged-accumulate (AR4JA) low-density parity-check (LDPC) codes [3] when used in conjunction with binary phase-shift-keying (BPSK), quadrature PSK (QPSK), 8-PSK, 16-ary amplitude PSK (16- APSK), and 32-APSK.We also report the performance under various mappings of bits to modulation symbols, 16-APSK and 32-APSK ring scalings, log-likelihood ratio (LLR) approximations, and decoder variations. One of the simple and well-performing LLR approximations can be expressed in a general equation that applies to all of the modulation types.

Hamkins, Jon↗
DOE OSTI2025

Low-Density Parity-Check Codes as Stable Phases of Quantum Matter

Phases of matter with robust ground-state degeneracy, such as the quantum toric code, are known to be capable of robust quantum information storage. Here, we address the converse question: given a quantum error-correcting code, when does it define a stable gapped quantum phase of matter, whose ground-state degeneracy is robust against perturbations in the thermodynamic limit? We prove that a low-density parity-check (LDPC) code defines such a phase, robust against all few-body perturbations, if its code distance grows at least logarithmically in the number of degrees of freedom, and it exhibits “check soundness.” Many constant-rate quantum LDPC expander codes have such properties, and define stable phases of matter with a constant zero-temperature entropy density, violating the third law of thermodynamics. Our results also show that quantum toric-code phases are robust to spatially nonlocal few-body perturbations. Similarly, phases of matter defined by classical codes are stable against symmetric perturbations. In the classical setting, we present improved locality bounds on the quasiadiabatic evolution operator between two nearby states in the same code phase.

quantum error correction↗
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)↗
DOE OSTI2025

Architecture for fast implementation of quantum low-density parity-check codes with optimized Rydberg gates

Here, we propose an implementation of bivariate bicycle codes [S. Bravyi et al., Nature (London) 627, 778 (2024)] based on long-range Rydberg gates between stationary neutral atom qubits. An optimized layout of data and ancilla qubits reduces the maximum Euclidean communication distance needed for nonlocal parity-check operators. An optimized Rydberg gate pulse design enables 𝖢𝖹 entangling operations with fidelity $\mathscr{F}$ >0.999 at a distance greater than 12 µ⁢m. The combination of optimized layout and gate design leads to a quantum error correction cycle time of ∼1.2⁢8 ms for a [[144,12,12]] code, which is nearly a factor-of-two improvement over previous designs.

Poole, C. [Univ. of Wisconsin, Madison, WI (United↗
NASA NTRS2008

ARA type protograph codes

An apparatus and method for encoding low-density parity check codes. Together with a repeater, an interleaver and an accumulator, the apparatus comprises a precoder, thus forming accumulate-repeat-accumulate (ARA codes). Protographs representing various types of ARA codes, including AR3A, AR4A and ARJA codes, are described. High performance is obtained when compared to the performance of current repeat-accumulate (RA) or irregular-repeat-accumulate (IRA) codes.

Divsalar, Dariush↗
DOE OSTI2025

Low-Density Parity-Check Stabilizer Codes as Gapped Quantum Phases: Stability under Graph-Local Perturbations

We generalize the proof of stability of topological order, due to Bravyi, Hastings, and Michalakis, to stabilizer Hamiltonians corresponding to low-density parity-check (LDPC) codes without the restriction of geometric locality in Euclidean space. We consider Hamiltonians 𝐻 0 defined by ⟦𝑁,𝐾,𝑑⟧ LDPC codes, which obey certain topological quantum order conditions: (i) code distance 𝑑 ≥ 𝑐⁢log (𝑁), implying local indistinguishability of ground states, and (ii) a mild condition on local and global compatibility of ground states—these include good quantum LDPC codes and the toric code on a hyperbolic lattice, among others. We consider stability under weak perturbations that are quasilocal on the interaction graph defined by 𝐻 0 and that can be represented as sums of bounded-norm terms. As long as the local perturbation strength is smaller than a finite constant, we show that the perturbed Hamiltonian has well-defined spectral bands originating from the 𝑂⁡(1) smallest eigenvalues of 𝐻 0 . The band originating from the smallest eigenvalue has 2 𝐾 states, is separated from the rest of the spectrum by a finite energy gap, and has exponentially narrow bandwidth 𝛿 =𝐶⁢𝑁⁢𝑒 −Θ⁡(𝑑) , which is tighter than the best-known bounds even in the Euclidean case. We also obtain that the new ground-state subspace is related to the initial-code subspace by a quasilocal unitary, allowing one to relate their physical properties. Our proof uses an iterative procedure that performs successive rotations to eliminate non-frustration-free terms in the Hamiltonian. Our results extend to quantum Hamiltonians built from classical LDPC codes, which give rise to stable symmetry-breaking phases. These results show that LDPC codes very generally define stable gapped quantum phases, even in the non-Euclidean setting, initiating a systematic study of such phases of matter.

mathematical physics↗
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↗
NASA NTRS2025

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.

LunaNet↗
DOE OSTI2025

Opportunities in full-stack design of low-overhead fault-tolerant quantum computation

Quantum error correction provides a route to realizing large-scale quantum computation but incurs substantial resource overheads. Here, in this work, we highlight recent advances that reduce these overheads by co-designing different levels of the computational stack, including algorithms, quantum-error-correction strategies and hardware architecture. We then discuss opportunities for further optimization such as leveraging flexible qubit connectivity and quantum low-density parity check codes. These strategies can bring useful quantum computation closer to reality as experiments advance in the coming years.

quantum information↗