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Mathematical analysis for digital data transmission calculates optimum number of binary error-correcting repeaters to install in given number of wideband channel links. Asymptotic results compared to computed numerical results.
The continuous-variable (CV) Gaussian no-go theorem fundamentally limits the suppression of Gaussian displacement errors using only Gaussian gates and states. Prior studies have employed Gottesman-Kitaev-Preskill (GKP) states as ancillary qumodes to suppress small Gaussian displacement errors. However, when the displacement magnitude becomes large, inevitable lattice-crossing errors arise beyond the correctable range of the GKP state. To address this issue, we concatenate the Gaussian-noise-suppression circuit with an outer analog Steane code that corrects such occasional lattice-crossing events as well as other abrupt displacement errors. Contrary to conventional concatenation, which primarily aims to reduce logical error rates, the Steane-GKP duality in encoding provides complementary protection against displacement errors at different scales: The inner GKP layer employs non-Gaussian resources to suppress continuous Gaussian noise and reduce residual variance, while the outer analog Steane code corrects discrete lattice-crossing events that exceed the GKP correctable range. It is precisely this separation of error-mitigation roles that enables CV error correction. In contrast to prior work on concatenating GKP and repetition codes to establish error correction for discrete qubit/qudit encoding, we provide correction in the continuous encoding space. Analytical studies show that, under infinite squeezing, the concatenated code suppresses the variance of Gaussian displacement errors acting on all qumodes by up to 50%, while enabling unbiased correction of lattice-crossing errors with a success probability determined by the ratio between the residual Gaussian error standard deviation and the lattice-crossing magnitude. Even with finite squeezing, the proposed architecture still provides Gaussian-error suppression and lattice-crossing correction. Moreover, the presence of the outer analog Steane code relaxes the squeezing requirement of the inner GKP states, indicating near-term experimental feasibility. This work establishes a viable route toward fault-tolerant continuous-variable quantum computation and provides insight into the design of concatenated CV error-correcting architectures.
Under-performance of solar PV systems is an important issue that increases risks for stakeholders, including developers, investors and operators. Recently some attention has focused on underestimation of inverter clipping losses as a possible source of over-prediction where sub-hourly solar variability is high. Several models and data sets have been analyzed over the past few years, with the aim of quantifying, predicting, and correcting underestimated clipping loss errors for systems with high DC/AC ratio and solar variability. In this research, we apply a machine learning model developed at NREL to two physical PV systems, to correct for subhourly clipping losses. For each system, we compare overall AC power output for the model taken at 1-minute intervals to AC power output taken at 1-hour intervals with the addition of the subhourly clipping correction. Our findings consistently show that the addition of the clipping loss correction lead to a reduction in mean bias error of 0.8% and 1.2% for systems A and B, respectively, with no additional filtering applied. When examining high solar variability periods where clipping is more pronounced, system A and B experienced a 1.8% and 2.7% reduction in mean bias error, respectively, when the clipping correction was applied.
Under-performance of solar PV systems is an important issue that increases risks for stakeholders, including developers, investors and operators. Recently some attention has focused on underestimation of inverter clipping losses as a possible source of over-prediction where sub-hourly solar variability is high. Several models and data sets have been analyzed over the past few years, with the aim of quantifying, predicting, and correcting underestimated clipping loss errors for systems with high DC/AC ratio and solar variability. In this research, we apply a machine learning model developed at NREL to two physical PV systems, to correct for subhourly clipping losses. For each system, we compare overall AC power output for the model taken at 1-minute intervals to AC power output taken at 1-hour intervals with the addition of the subhourly clipping correction. Our findings consistently show that the addition of the clipping loss correction lead to a reduction in mean bias error of 0.6\% and 1.1\% for systems A and B, respectively, with no additional filtering applied. When examining high solar variability periods where clipping is more pronounced, system A and B experienced a 1.4\% and 2.5\% reduction in mean bias error, respectively, when the clipping correction was applied.
A brief overview of a processing satellite for a mesh very-small-aperture (VSAT) communications network is provided. The multichannel error correction code (ECC) decoder system, the uplink signal generation and link simulation equipment, and the time-shared decoder are described. The testing is discussed. Applications of the time-shared decoder are recommended.
A computer program performs Monte Carlo direct numerical simulations for testing sparse permutation channel codes, which offer strong error-correction capabilities at high code rates and are considered especially suitable for storage of digital data in holographic and volume memories. A word in a code of this type is characterized by, among other things, a sparseness parameter (M) and a fixed number (K) of 1 or "on" bits in a channel block length of N.
Abstract High-fidelity and rapid readout of a qubit state is key to quantum computing and communication, and it is a prerequisite for quantum error correction. We present a readout scheme for superconducting qubits that combines two microwave techniques: applying a shelving technique to the qubit that reduces the contribution of decay error during readout, and a two-tone excitation of the readout resonator to distinguish among qubit populations in higher energy levels. Using a machine-learning algorithm to post-process the two-tone measurement results further improves the qubit-state assignment fidelity. We perform single-shot frequency-multiplexed qubit readout, with a 140 ns readout time, and demonstrate 99.5% assignment fidelity for two-state readout and 96.9% for three-state readout–without using a quantum-limited amplifier.
Results are presented in the form of 14 theorems specifying sufficient conditions under which it is possible to construct new more efficient single- and multi error correcting codes from existing one when the method used to construct existing codes is known.
A generalized theory is presented for the construction of a systematic subcode for a given AN code in such a way that error control properties of the AN code are preserved in this new code. The 'systematic weight' and 'systematic distance' functions in this new code depend not only on its number representation system but also on its addition structure. Finally, to illustrate this theory, a simple error-correcting adder organization using a systematic subcode of 29 N code is sketched in some detail.
A holographic CFT description of asymptotically flat spacetimes inherits vacuum degeneracies and IR divergences from its gravitational dual. We devise a Quantum Error Correcting (QEC) framework to encode both effects as correctable fluctuations on the CFT dual. The framework is physically motivated by embedding a chain of qudits in the so-called Klein spacetime and then taking a continuum 𝑁 → ∞ limit. At finite 𝑁 the qudit chain 1) enjoys a discrete version of celestial symmetries and 2) supports a Gottesman-Kitaev-Preskill (GKP) code. The limit results in hard states with quantized BMS hair in the celestial torus forming the logical subspace, robust under errors induced by soft radiation. Technically, the construction leverages the recently studied 𝑤 1+∞ hierarchy of soft currents and its realization from a sigma model in twistor space.
A random access scheme for unreliable data channels is investigated in conjunction with an adaptive Hybrid-II Automatic Repeat Request (ARQ) scheme using Rate Compatible Punctured Codes (RCPC) Forward Error Correction (FEC). A simple scheme with fixed frame length and equal slot sizes is chosen and reservation is implicit by the first packet transmitted randomly in a free slot, similar to Reservation Aloha. This allows the further transmission of redundancy if the last decoding attempt failed. Results show that a high channel utilization and superior throughput can be achieved with this scheme that shows a quite low implementation complexity. For the example of an interleaved Rayleigh channel and soft decision utilization and mean delay are calculated. A utilization of 40 percent may be achieved for a frame with the number of slots being equal to half the station number under high traffic load. The effects of feedback channel errors and some countermeasures are discussed.
This paper reports a single 8.2mm by 8.4mm, 200,000 transistor CMOS chip implementation of the Reed Solomon code required by the Space Telescope. The chip features a 10 MHz sustained byte rate independent of error pattern. The 1.6 micron CMOS integrated circuit has complete decoder and encoder functions and uses a single data/system clock. Block lengths up to 255 bytes as well as shortened codes are supported with no external buffering. Erasure corrections as well as random error corrections are supported with programmable corrections of up to 10 symbol errors. Correction time is independent of error pattern and the number of errors.
On macroevolutionary timescales, extensive mutations and phylogenetic uncertainty mask the signals of genotype–phenotype associations underlying convergent evolution. To overcome this problem, we extended the widely used framework of non-synonymous to synonymous substitution rate ratios and developed the novel metric ω C , which measures the error-corrected convergence rate of protein evolution. While ω C distinguishes natural selection from genetic noise and phylogenetic errors in simulation and real examples, its accuracy allows an exploratory genome-wide search of adaptive molecular convergence without phenotypic hypothesis or candidate genes. Using gene expression data, we explored over 20 million branch combinations in vertebrate genes and identified the joint convergence of expression patterns and protein sequences with amino acid substitutions in functionally important sites, providing hypotheses on undiscovered phenotypes. We further extended our method with a heuristic algorithm to detect highly repetitive convergence among computationally non-trivial higher-order phylogenetic combinations. Our approach allows bidirectional searches for genotype–phenotype associations, even in lineages that diverged for hundreds of millions of years.
Ten subjects served as their own controls in two conditions of continuous, centrifugally produced hypergravity (+2 Gz) and a 1-G control condition. Before and after exposure, open-loop measures were obtained of (1) motor control, (2) visual localization, and (3) hand-eye coordination. During exposure in the visual feedback/hypergravity condition, subjects received terminal visual error-corrective feedback from their target pointing, and in the no-visual feedback/hypergravity condition they pointed open loop. As expected, the motor control measures for both experimental conditions revealed very short lived underreaching (the muscle-loading effect) at the outset of hypergravity and an equally transient negative aftereffect on returning to 1 G. The substantial (approximately 17 degrees) initial elevator illusion experienced in both hypergravity conditions declined over the course of the exposure period, whether or not visual feedback was provided. This effect was tentatively attributed to habituation of the otoliths. Visual feedback produced a smaller additional decrement and a postexposure negative after-effect, possible evidence for visual recalibration. Surprisingly, the target-pointing error made during hypergravity in the no-visual-feedback condition was substantially less than that predicted by subjects' elevator illusion. This finding calls into question the neural outflow model as a complete explanation of this illusion.
Abstract One of the most promising routes toward scalable quantum computing is a modular approach. We show that distinct surface code patches can be connected in a fault-tolerant manner even in the presence of substantial noise along their connecting interface. We quantify analytically and numerically the combined effect of errors across the interface and bulk. We show that the system can tolerate 14 times higher noise at the interface compared to the bulk, with only a small effect on the code’s threshold and subthreshold behavior, reaching threshold with ~1% bulk errors and ~10% interface errors. This implies that fault-tolerant scaling of error-corrected modular devices is within reach using existing technology.
Abstract Spurred by recent advances in detector technology and X-ray optics, upgrades to scanning-probe-based tomographic imaging have led to an exponential growth in the amount and complexity of experimental data and have created a clear opportunity for tomographic imaging to approach single-atom sensitivity. The improved spatial resolution, however, is highly susceptible to systematic and random experimental errors, such as center of rotation drifts, which may lead to imaging artifacts and prevent reliable data extraction. Here, we present a model-based approach that simultaneously optimizes the reconstructed specimen and sinogram alignment as a single optimization problem for tomographic reconstruction with center of rotation error correction. Our algorithm utilizes an adaptive regularizer that is dynamically adjusted at each alternating iteration step. Furthermore, we describe its implementation in a software package targeting high-throughput workflows for execution on distributed-memory clusters. We demonstrate the performance of our solver on large-scale synthetic problems and show that it is robust to a wide range of noise and experimental drifts with near-ideal throughput.
Papers on the following topics are presented: considerations of testing the Orbital Maneuvering Vehicle (OMV) system with CLASS; OMV CLASS test results (first go around); equivalent system gain available from R-S encoding versus a desire to lower the power amplifier from 25 watts to 20 watts for OMV; command word acceptance/rejection rates for OMV; a memo concerning energy-to-noise ratio for the Viterbi-BSC Channel and the impact of Manchester coding loss; and an investigation of error correcting techniques for OMV and Advanced X-ray Astrophysics Facility (AXAF).
Error detection codes and correction devices for Deep Space Network /DSN/ teletypewriter systems