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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Acceptable testing of VLSI components which contain error correctors

If a VLSI chip is partitioned into functional units (FU's) and redundant FU's are added, error correcting codes may be employed to increase the yield and/or reliability of the chip. Acceptable testing is defined to be testing the chip with the error corrector functioning, thus obtaining the maximum increase in yield afforded by the error correction. The acceptable testing theorem shows that the use of coding and error correction in conjunction with acceptable testing can significantly increase the yield of VLSI chips without seriously compromising their reliability.

Cliff, R. A.↗
NASA NTRS1990

Burst error correction extensions for large Reed Solomon codes

Reed Solomon codes are powerful error correcting codes that include some of the best random and burst correcting codes currently known. It is well known that an (n,k) Reed Solomon code can correct up to (n - k)/2 errors. Many applications utilizing Reed Solomon codes require corrections of errors consisting primarily of bursts. In this paper, it is shown that the burst correcting ability of Reed Solomon codes can be increased beyond (n - k)/2 with an acceptable probability of miscorrect.

Owsley, P.↗
NASA NTRS1977

UNICON Laser Memory: Interlaced Codes for Multi-burst-Error Correction

Interlaced binary BCH codes are described for multiple-burst-error correction for the UNICON 690 laser memory. Other multiple-burst-error-correcting codes, such as Reed-Solomon codes and Product codes, are also briefly mentioned. In particular, an interlaced (31, 21) t = 2 BCH code is selected as an outer code for UNICON double-burst-error correction. This code is shortened to (26,16) and interlaced to degree X = 16. Decoding is implemented by table lookup. This method not only avoids all computations in GF(2(exp 5)), it also offers a decoding time of less than 1 ps. The inner code is an existing (80,64) Fire code capable of correcting a single-burst error of length b less than or equal to 6.

Lim, R. S.↗
NASA NTRS1992

An investigation of error characteristics and coding performance

The performance of forward error correcting coding schemes on errors anticipated for the Earth Observation System (EOS) Ku-band downlink are studied. The EOS transmits picture frame data to the ground via the Telemetry Data Relay Satellite System (TDRSS) to a ground-based receiver at White Sands. Due to unintentional RF interference from other systems operating in the Ku band, the noise at the receiver is non-Gaussian which may result in non-random errors output by the demodulator. That is, the downlink channel cannot be modeled by a simple memoryless Gaussian-noise channel. From previous experience, it is believed that those errors are bursty. The research proceeded by developing a computer based simulation, called Communication Link Error ANalysis (CLEAN), to model the downlink errors, forward error correcting schemes, and interleavers used with TDRSS. To date, the bulk of CLEAN was written, documented, debugged, and verified. The procedures for utilizing CLEAN to investigate code performance were established and are discussed.

Ebel, William J.↗
DOE OSTI2025

Logical error rates for the surface code under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions

With fault-tolerant quantum computing (FTQC) on the horizon, it is critical to understand sources of logical errors in plausible hardware implementations of quantum error-correcting codes. Detailed error modeling of computational instructions on particular FTQC architectures will enable the better prediction of error propagation in FT-encoded quantum circuits while revealing where greater attention is needed in hardware design. In this work, we consider logical error rates for the surface code implemented on a hypothetical grid-based trapped-ion quantum charge-coupled device architecture. Specifically, we construct logical channels for the idling surface code and examine its diamond error under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions. We include the coherent dephasing noise that is known to accumulate during physical qubit idling and transport in these systems, determining idling and transport durations using the time-resolved output of an open-source trapped-ion surface code compiler. To estimate expectation values of logical Pauli observables following hardware circuits containing non-Clifford sources of noise, we utilize a Monte Carlo technique to sample from an underlying quasiprobability distribution of Clifford circuits that we independently simulate in a phase-sensitive fashion. We verify error suppression up to code distance 𝑑 = 11 at coherent dephasing rates near and below those of current-generation trapped-ion quantum computers and find that logical error rates align with those of analogous fully stochastic simulations in this regime. Exploring higher dephasing rates at 𝑑 = 3−5, we find evidence for growing coherent rotations about all three logical Pauli axes, increased diagonal logical error process matrix elements relative to those of stochastic simulations, and a reduced dephasing rate threshold. Overall, our work paves a way toward realistic hardware emulation of small fault-tolerant quantum processes, e.g., members of an FTQC instruction set.

Quantum benchmarking↗
NASA NTRS1983

Telemetry Modulation and Coping

Digital telemetry has supplanted analog telemetry for deep space communications. With digital telemetry, the telecommunications systems design engineer may use error correcting codes. This allows increased error protection at the cost of increased bandwidth. All science telemetry returned from the Voyager and Galileo spacecraft are protected by error correcting codes. Both the modulation and coding of digital telemetry for the deep space channel are considered. The descriptions include relative performance of some competing schemes. However, the treatment given here is, of necessity, cursory. A small class of modulation schemes has proven to be best for the deep space channel. The digital telemetry is either phase-shift-keyed onto a squarewave subcarrier and then phase modulated onto the carrier or the digital telemetry is directly phase modulated onto the carrier.

Kinman, P. W.↗
NASA NTRS1990

Asymmetric Memory Circuit Would Resist Soft Errors

Some nonlinear error-correcting codes more efficient in presence of asymmetry. Combination of circuit-design and coding concepts expected to make integrated-circuit random-access memories more resistant to "soft" errors (temporary bit errors, also called "single-event upsets" due to ionizing radiation). Integrated circuit of new type made deliberately more susceptible to one kind of bit error than to other, and associated error-correcting code adapted to exploit this asymmetry in error probabilities.

Buehler, Martin G.↗
NASA NTRS2018

The Utilization Profiles of the CCSDS Unified Space Link Protocol (USLP)

The purpose of this paper is to identify the utilization profiles for interfacing the Data Protocol Sublayer using the Unified Space Link Protocols (USLP) (reference 1) with the space link coding procedures as specified in the CCSDS Coding & Synchronization Blue Books (references 2 through 5), used in both telecommand and telemetry applications. This paper describes how the USLP Protocol utilizes the coding and synchronization sublayer to support: a. Direct to Earth (DTE) telemetry links for engineering and science data b. Direct to Earth (DTE) telemetry links for very high rate science data c. Direct from Earth (DFE) command, sequencing and flight software loads d. Space to Space Links (Proximity) utilized by orbiters for data exchange to/from surface bound assets. The CCSDS has divided the functions of the Data Link Layer into two sublayers: the Data Link Protocol Sublayer (DLP-SL) and the Coding and Synchronization Sublayer (CS-SL). The Data Link Protocol Sublayer (DLP-SL) interfaces to the users, accepting the data that is to be transported, on the sending side of the link, and delivering that data on the receiving end. The Transfer Frame is the data unit that is transferred across the Data Link Protocol Sublayer and the Coding and Synchronization Sublayer boundary. The Coding and Synchronization Sublayer (CS-SL) provides the encoding, randomization, and frame synchronization functions that prepares the USLP Transfer Frame for transport across the space link. The CS-SL is divided into 2 processes: 1) The Frame Interface Processes (FIP) performs the interface functions required to prepare the data for delivery to the Coding/Decoding Process (CDP). This process includes prepending a Frame Start Marker to the provided frame, when management has designated that the frame is not to be aligned to the codeblock or when there is no block code used. 2) The Coding/Decoding Process (CDP) performs the forward error correction processes that are used to optimize the performance of the link and minimize the error rate. The CDP creates the symbol stream that is delivered to the Physical Layer. The transfer of the USLP transfer frames across different types of space links is the focus of this paper. The Protocol Data Unit (PDU) that is passed in both directions between the Data Link Protocol Sublayer (DLP-SL) and Coding and Synchronization Sublayer (CS-SL) is the transfer frame. The USLP frame structure provides flexibility that can be constrained by the functions utilized within the CS-SL that prepare the transfer frame for transit. For example, the USLP transfer frame contains a length field that enables the frame to be of variable length but CS-SL under certain conditions may constrain the frame to be fixed in length. This paper describes 5 operational modes available for use by the Data Link Layer to provide data exchange across the USLP space link. These modes are different because different operational requirements apply to vastly different types of space links and thus the communications implementation requirements differ. The environmental issues include the power or energy available, the distance between the end points of the link, the complexity of the equipment available at those end points, the atmospheric conditions and radiometric frequency selection. The CS-SL utilizes different forward error correcting codes supported by specific operational modes to configure the data for transit. This paper describes all of the operational modes in a series of data models which decompose the functionality between the Data Link Protocol Sublayer and the Coding and Synchronization sublayer. The operational modes described are: 1. Uncoded Mode: has been used for short links that contain significant available power to provide an acceptable frame error rate. The frames in this mode can be variable in length and typically use an error detection algorithm (i.e., CRC) to determine if there are errors in the received frame. 2. Convolutional Only Mode: is currently the prime forward error correction coding used for the proximity links. The frames in this mode can be variable in length and typically use an error detection algorithm (i.e., CRC) to determine if there are errors in the received frame. 3. Variable Length Frame Aligned to Variable Length Codeblock (TC): is used for Direct from Earth links were power levels are high and the simple, least complex code i.e., the BCH code is used. This mode has been in use since the early 1970s. The BCH code is a short code and the decoder is easy to implement. 4. Fixed Length Frame Aligned to Fixed Length Codeblock (AOS/TM): was introduced when the concatenated Convolutional and Reed-Solomon Code was formulated to provide significant reduction in link data error rate and the ability to determine if there was an error in the decoded codeblock. The frame is aligned to the codeblock so that there is a one to one relationship of frame errors to codeblock errors without additional error detection coding being added. This mode requires the protocol frames to be the exact size of the message portion of the codeblock. 5. Frames Unaligned to Fixed Length Codeblocks (Currently used for very high rates and space to space links): This mode is currently used for missions that have a very high data rate that can be controlled adaptively as the environment changes and as the next generation operating mode for the proximity link. This mode from a coded data stream point of view is exactly like that described in 4. above, except that the frame need not be aligned to the codeblock. There is no requirement on frame length when using this mode. Thus when using USLP it can be used to support links that require short or long frames. There is also no mandatory requirement that frames cannot be separated by idle data reducing the tight data rate connection requirements between the data link protocol sublayer and the coding & synchronization sublayer. In conclusion, how these operational modes can be put to use in mission operational scenarios is described for Direct from Earth links (DFE), Direct to Earth links (DTE), and Proximity links.

Greenberg, E.↗
DOE OSTI2025

Mitigating cosmic-ray-like correlated events with a modular quantum processor

Quantum processors based on superconducting qubits are being scaled to larger qubit numbers, enabling the implementation of small-scale quantum error-correction codes. However, catastrophic chip-scale correlated errors have been observed in these processors, attributed to, e.g., cosmic ray impacts, which challenge conventional error-correction codes such as the surface code. These events are characterized by a temporary but pronounced suppression of the qubit-energy relaxation times. Here, in this study, we explore the potential for modular quantum computing architectures to mitigate such correlated energy decay events. We measure cosmic-ray-like events in a quantum processor comprising a motherboard and two flip-chip bonded daughterboard modules, each module containing two superconducting qubits. We monitor the appearance of correlated qubit decay events within a single module and across the physically separated modules. We find that while decay events within one module are strongly correlated (over 85%), events in separate modules only display approximately 2% correlations. We also report coincident decay events in the motherboard and in either of the two daughterboard modules, providing further insight into the nature of these decay events. These results suggest that modular architectures, combined with bespoke errorcorrection codes, offer a promising approach for protecting future quantum processors from chip-scale correlated errors.

Wu, Xuntao [Univ. of Chicago, IL (United States)] ↗
DOE OSTI2025

Low-overhead transversal fault tolerance for universal quantum computation

Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, we can achieve low logical error rates. However, for many practical quantum error correction codes such as the surface code, owing to syndrome measurement errors, standard constructions require multiple extraction rounds—of the order of the code distance d—for fault-tolerant computation, particularly considering fault-tolerant state preparation. Here we show that logical operations can be performed fault-tolerantly with only a constant number of extraction rounds for a broad class of quantum error correction codes, including the surface code with magic state inputs and feedforward, to achieve ‘transversal algorithmic fault tolerance’. Through the combination of transversal operations7 and new strategies for correlated decoding, despite only having access to partial syndrome information, we prove that the deviation from the ideal logical measurement distribution can be made exponentially small in the distance, even if the instantaneous quantum state cannot be made close to a logical codeword because of measurement errors. We supplement this proof with circuit-level simulations in a range of relevant settings, demonstrating the fault tolerance and competitive performance of our approach. Furthermore, our work sheds new light on the theory of quantum fault tolerance and has the potential to reduce the space–time cost of practical fault-tolerant quantum computation by over an order of magnitude.

Zhou, Hengyun [QuEra Computing, Boston, MA (United↗
NASA NTRS2011

Coded Modulation in C and MATLAB

This software, written separately in C and MATLAB as stand-alone packages with equivalent functionality, implements encoders and decoders for a set of nine error-correcting codes and modulators and demodulators for five modulation types. The software can be used as a single program to simulate the performance of such coded modulation. The error-correcting codes implemented are the nine accumulate repeat-4 jagged accumulate (AR4JA) low-density parity-check (LDPC) codes, which have been approved for international standardization by the Consultative Committee for Space Data Systems, and which are scheduled to fly on a series of NASA missions in the Constellation Program. The software implements the encoder and decoder functions, and contains compressed versions of generator and parity-check matrices used in these operations.

Hamkins, Jon↗
DOE OSTI2024

Phase diagram of the three-dimensional subsystem toric code

Subsystem quantum error-correcting codes typically involve measuring a sequence of noncommuting parity check operators. They can sometimes exhibit greater fault tolerance than conventional codes, which use commuting checks. However, unlike subspace codes, it is unclear if subsystem codes—in particular their advantages—can be understood in terms of ground-state properties of a physical Hamiltonian. In this paper, we address this question for the three-dimensional subsystem toric code (3D STC), as recently constructed by Kubica and Vasmer [], which exhibits single-shot error correction. Motivated by a conjectured relation between single-shot properties and thermal stability, we study the zero- and finite-temperature phases of an associated noncommuting Hamiltonian. By mapping the Hamiltonian model to a pair of 3D Z 2 gauge theories coupled by a kinetic constraint, we find various phases at zero temperature, all separated by first-order transitions: There are 3D toric code-like phases with deconfined point-like excitations in the bulk, and there are phases with a confined bulk supporting a 2D toric code on the surface when appropriate boundary conditions are chosen. The latter is similar to the surface topological order present in 3D STC. However, the similarities between the single-shot correction in 3D STC and the confined phases are only partial: they share the same sets of degrees of freedom, but they are governed by different dynamical rules. Instead, we argue that the process of single-shot error correction can more suitably be associated with a path (rather than a point) in the zero-temperature phase diagram, a perspective, which inspires alternative measurement sequences enabling single-shot error correction. Moreover, since none of the above-mentioned phases survives at nonzero temperature, the single-shot error-correction property of the code does not imply thermal stability of the associated Hamiltonian phase. Published by the American Physical Society 2024

Li, Yaodong (ORCID:0000000337421944)↗
NASA NTRS2009

LDPC Codes with Minimum Distance Proportional to Block Size

Low-density parity-check (LDPC) codes characterized by minimum Hamming distances proportional to block sizes have been demonstrated. Like the codes mentioned in the immediately preceding article, the present codes are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. The previously mentioned codes have low decoding thresholds and reasonably low error floors. However, the minimum Hamming distances of those codes do not grow linearly with code-block sizes. Codes that have this minimum-distance property exhibit very low error floors. Examples of such codes include regular LDPC codes with variable degrees of at least 3. Unfortunately, the decoding thresholds of regular LDPC codes are high. Hence, there is a need for LDPC codes characterized by both low decoding thresholds and, in order to obtain acceptably low error floors, minimum Hamming distances that are proportional to code-block sizes. The present codes were developed to satisfy this need. The minimum Hamming distances of the present codes have been shown, through consideration of ensemble-average weight enumerators, to be proportional to code block sizes. As in the cases of irregular ensembles, the properties of these codes are sensitive to the proportion of degree-2 variable nodes. A code having too few such nodes tends to have an iterative decoding threshold that is far from the capacity threshold. A code having too many such nodes tends not to exhibit a minimum distance that is proportional to block size. Results of computational simulations have shown that the decoding thresholds of codes of the present type are lower than those of regular LDPC codes. Included in the simulations were a few examples from a family of codes characterized by rates ranging from low to high and by thresholds that adhere closely to their respective channel capacity thresholds; the simulation results from these examples showed that the codes in question have low error floors as well as low decoding thresholds. As an example, the illustration shows the protograph (which represents the blueprint for overall construction) of one proposed code family for code rates greater than or equal to 1.2. Any size LDPC code can be obtained by copying the protograph structure N times, then permuting the edges. The illustration also provides Field Programmable Gate Array (FPGA) hardware performance simulations for this code family. In addition, the illustration provides minimum signal-to-noise ratios (Eb/No) in decibels (decoding thresholds) to achieve zero error rates as the code block size goes to infinity for various code rates. In comparison with the codes mentioned in the preceding article, these codes have slightly higher decoding thresholds.

Divsalar, Dariush↗
NASA NTRS1991

Asymmetric soft-error resistant memory

A memory system is provided, of the type that includes an error-correcting circuit that detects and corrects, that more efficiently utilizes the capacity of a memory formed of groups of binary cells whose states can be inadvertently switched by ionizing radiation. Each memory cell has an asymmetric geometry, so that ionizing radiation causes a significantly greater probability of errors in one state than in the opposite state (e.g., an erroneous switch from '1' to '0' is far more likely than a switch from '0' to'1'. An asymmetric error correcting coding circuit can be used with the asymmetric memory cells, which requires fewer bits than an efficient symmetric error correcting code.

Buehler, Martin G.↗
DOE OSTI2025

Perturbative Stability and Error-Correction Thresholds of Quantum Codes

Topologically ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding general Calderbank-Shor-Steane codes and classical linear codes. Our construction encodes correction success probabilities under uncorrelated bit-flip and phase-flip errors, and simultaneously describes a generalized ℤ 2 lattice-gauge theory with quenched disorder. We observe that the clean limit of the latter is precisely the discretized imaginary-time path integral of the corresponding quantum code Hamiltonian when the errors are turned into a perturbative 𝑋 or 𝑍 magnetic field. Motivated by error-correction considerations, we define general order parameters for all such generalized ℤ 2 lattice-gauge theories, and show that they are generally lower bounded by success probabilities of error correction. For CSS codes satisfying the low-density parity-check condition and with a sufficiently large code distance, we prove the existence of a low-temperature ordered phase of the corresponding lattice-gauge theories, particularly for those lacking Euclidean spatial locality and/or when there is a nonzero code rate. We further argue that these results provide evidence for stable phases in the corresponding perturbed quantum Hamiltonians, obtained in the limit of continuous imaginary time. To do so, we distinguish space- and timelike defects in the lattice-gauge theory. A high free-energy cost of spacelike defects corresponds to a successful “memory experiment” and suppresses the energy splitting among the ground states, while a high free-energy cost of timelike defects corresponds to a successful “stability experiment” and points to a nonzero gap to local excitations.

quantum error correction↗
NASA NTRS2009

LDPC-PPM Coding Scheme for Optical Communication

In a proposed coding-and-modulation/demodulation-and-decoding scheme for a free-space optical communication system, an error-correcting code of the low-density parity-check (LDPC) type would be concatenated with a modulation code that consists of a mapping of bits to pulse-position-modulation (PPM) symbols. Hence, the scheme is denoted LDPC-PPM. This scheme could be considered a competitor of a related prior scheme in which an outer convolutional error-correcting code is concatenated with an interleaving operation, a bit-accumulation operation, and a PPM inner code. Both the prior and present schemes can be characterized as serially concatenated pulse-position modulation (SCPPM) coding schemes. Figure 1 represents a free-space optical communication system based on either the present LDPC-PPM scheme or the prior SCPPM scheme. At the transmitting terminal, the original data (u) are processed by an encoder into blocks of bits (a), and the encoded data are mapped to PPM of an optical signal (c). For the purpose of design and analysis, the optical channel in which the PPM signal propagates is modeled as a Poisson point process. At the receiving terminal, the arriving optical signal (y) is demodulated to obtain an estimate (a^) of the coded data, which is then processed by a decoder to obtain an estimate (u^) of the original data.

Barsoum, Maged↗
DOE OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.

Gu, Shouzhen [Yale U.]↗