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Techniques are presented for detecting and correcting errors in a vector field. These methods employ median filters which are frequently used in image processing to enhance edges and remove noise. A detailed example is given for wind field maps produced by a spaceborne scatterometer. The error detection and replacement algorithm was tested with simulation data from the NASA Scatterometer (NSCAT) project.
Report discusses mathematical principles of Reed-Solomon (RS) error-correction coding, but without rigorous proofs or extreme mathematical detail.
Engineering problems commonly require functional outputs of computational fluid dynamics (CFD) simulations with specified accuracy. These simulations are performed with limited computational resources. Computable error estimates offer the possibility of quantifying accuracy on a given mesh and predicting a fine grid functional on a coarser mesh. Such an estimate can be computed by solving the flow equations and the associated adjoint problem for the functional of interest. An adjoint-based error correction procedure is demonstrated for transonic inviscid and subsonic laminar and turbulent flow. A mesh adaptation procedure is formulated to target uncertainty in the corrected functional and terminate when error remaining in the calculation is less than a user-specified error tolerance. This adaptation scheme is shown to yield anisotropic meshes with corrected functionals that are more accurate for a given number of grid points then isotropic adapted and uniformly refined grids.
A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. For example, some 256K-bit dynamic random access memories are organized as 32K x 8 bit-bytes. Byte-oriented codes such as Reed Solomon (RS) codes provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special high speed decoding techniques for extended single and double error correcting RS codes. These techniques are designed to find the error locations and the error values directly from the syndrome without having to form the error locator polynomial and solve for its roots.
At the Optical Computing Lab in the Jet Propulsion Laboratory (JPL) a binary holographic data storage system was designed and tested with methods of recording and retrieving the binary information. Levels of error correction were introduced to the system including pixel averaging, thresholding, and parity checks. Errors were artificially introduced into the binary holographic data storage system and were monitored as a function of the defect area fraction, which showed a strong influence on data integrity. Average area fractions exceeding one quarter of the bit area caused unrecoverable errors. Efficient use of the available data density was discussed. .
Threshold function effects on changes in feedback gain vector during error correction updating procedure
Technologies related to enhancing security of digital content are described. Linear error correction codes (LECCs) are employed for dual purposes: 1) to obfuscate digital content; and 2) to verify integrity of the digital content. A transmitter computing system obfuscates digital content based upon an obfuscation protocol, wherein the obfuscated digital content includes an LECC. A receiver computing system deobfuscates the digital content by performing the inverse of the obfuscation protocol.
Here, we show that a subset of the basis for the irreducible representations of a tensor-product SU(2) rotation forms a covariant approximate quantum error-correcting code with transversal U(1) logical gates. Generalizing previous work on “thermodynamic codes” to general local spin and different irreducible representations using only properties of the angular momentum algebra, we obtain bounds on the code inaccuracy under generic noise on any known 𝑑 sites, under independent and identically distributed noise, and under heralded 𝑑-local erasures. We demonstrate that this family of codes protects a probe state with quantum Fisher information surpassing the standard quantum limit when the sensing parameter couples to the generator of the U(1) logical gate.
This report provides the test results and performance analysis of the multichannel error correction code decoder (MED) system for a regenerative satellite with asynchronous, frequency-division multiple access (FDMA) uplink channels. It discusses the system performance relative to various critical parameters: the coding length, data pattern, unique word value, unique word threshold, and adjacent-channel interference. Testing was performed under laboratory conditions and used a computer control interface with specifically developed control software to vary these parameters. Needed technologies - the high-speed Bose Chaudhuri-Hocquenghem (BCH) codec from Harris Corporation and the TRW multichannel demultiplexer/demodulator (MCDD) - were fully integrated into the mesh very small aperture terminal (VSAT) onboard processing architecture and were demonstrated.
This paper will be a discussion on dealing with errors. While error correction and communication is important when dealing with spacecraft vehicles, the issue of control system design is also important. There will be certain commands that one wants a motion device to execute. An adequate control system will be necessary to make sure that the instruments and devices will receive the necessary commands. As it will be discussed later, the actual value will not always be equal to the intended or desired value. Hence, an adequate controller will be necessary so that the gap between the two values will be closed.
With the increasing packing densities in VLSI technology, Single Event Upsets (SEU) due to cosmic radiations are becoming more of a critical issue in the design of space avionics systems. In this paper, a method is introduced to compute the fault (mishap) probability for a computer memory of size M words. It is assumed that a Hamming code is used for each word to provide single error correction. It is also assumed that every time a memory location is read, single errors are corrected. Memory is read randomly whose distribution is assumed to be known. In such a scenario, a mishap is defined as two SEU's corrupting the same memory location prior to a read. The paper introduces a method to compute the overall mishap probability for the entire memory for a mission duration of T hours.
An improved pi/4-quadrature phase-shift keying (QPSK) receiver that incorporates a simple nonredundant error correction (NEC) structure is proposed for satellite and land-mobile digital broadcasting. The bit-error-rate (BER) performance of the pi/4-QPSK with NEC is analyzed and evaluated in a fast Rician fading and additive white Gaussian noise (AWGN) environment using computer simulation. It is demonstrated that with simple electronics the performance of a noncoherently detected pi/4-QPSK signal in both AWGN and fast Rician fading can be improved. When the K-factor (a ratio of average power of multipath signal to direct path power) of the Rician channel decreases, the improvement increases. An improvement of 1.2 dB could be obtained at a BER of 0.0001 in the AWGN channel. This performance gain is achieved without requiring any signal redundancy and additional bandwidth. Three types of noncoherent detection schemes of pi/4-QPSK with NEC structure, such as IF band differential detection, baseband differential detection, and FM discriminator, are discussed. It is concluded that the pi/4-QPSK with NEC is an attractive scheme for power-limited satellite land-mobile broadcasting systems.
Current, near-term quantum devices have shown great progress in the last several years culminating recently with a demonstration of quantum supremacy. In the medium-term, however, quantum machines will need to transition to greater reliability through error correction, likely through promising techniques like surface codes which are well suited for near-term devices with limited qubit connectivity. We discover quantum memory, particularly resonant cavities with transmon qubits arranged in a 2.5D architecture, can efficiently implement surface codes with substantial hardware savings and performance/fidelity gains. Specifically, we virtualize logical qubits by storing them in layers of qubit memories connected to each transmon. Surprisingly, distributing each logical qubit across many memories has a minimal impact on fault tolerance and results in substantially more efficient operations. Our design permits fast transversal application of CNOT operations between logical qubits sharing the same physical address (same set of cavities) which are 6x faster than standard lattice surgery CNOTs. We develop a novel embedding which saves approximately 10x in transmons with another 2x savings from an additional optimization for compactness. Although qubit virtualization pays a 10x penalty in serialization, advantages in the transversal CNOT and in area efficiency result in fault-tolerance and performance comparable to conventional 2D transmon-only architectures. Our simulations show our system can achieve fault tolerance comparable to conventional two-dimensional grids while saving substantial hardware. Furthermore, our architecture can produce magic states at 1.22x the baseline rate given a fixed number of transmon qubits. Here, this is a critical benchmark for future fault-tolerant quantum computers as magic states are essential and machines will spend the majority of their resources continuously producing them. This architecture substantially reduces the hardware requirements for fault-tolerant quantum computing and puts within reach a proof-of-concept experimental demonstration of around 10 logical qubits, requiring only 11 transmons and 9 attached cavities in total.
This report describes the progress made towards the completion of a specific task on error-correcting coding. The proposed research consisted of investigating the use of modulation block codes as the inner code of a concatenated coding system in order to improve the overall space link communications performance. The study proposed to identify and analyze candidate codes that will complement the performance of the overall coding system which uses the interleaved RS (255,223) code as the outer code.
The authors describe an error-correction coding approach that allows operation in either burst or continuous modes at data rates of multiple hundreds of megabits per second. Bandspreading is low since the code rate is 7/8 or greater, which is consistent with high-rate link operation. The encoder, along with a hard-decision decoder, fits on a single application-specific integrated circuit (ASIC) chip. Soft-decision decoding is possible utilizing applique hardware in conjunction with the hard-decision decoder. Expected coding gain is a function of the application and is approximately 2.5 dB for hard-decision decoding at 10-5 bit-error rate with phase-shift-keying modulation and additive Gaussian white noise interference. The principal use envisioned for this technique is to achieve a modest amount of coding gain on high-data-rate, bandwidth-constrained channels. Data rates of up to 300 Mb/s can be accommodated by the codec chip. The major objective is burst-mode communications, where code words are composed of 32 n data bits followed by 32 overhead bits.
Human liver-derived metabolically competent HepaRG cells have been successfully employed in both two-dimensional (2D) and 3D spheroid formats for performing the comet assay and micronucleus (MN) assay. In the present study, we have investigated expanding the genotoxicity endpoints evaluated in HepaRG cells by detecting mutagenesis using two error-corrected next generation sequencing (ecNGS) technologies, Duplex Sequencing (DS) and High-Fidelity (HiFi) Sequencing. Both HepaRG 2D cells and 3D spheroids were exposed for 72 h to N-nitrosodimethylamine (NDMA), followed by an additional incubation for the fixation of induced mutations. NDMA-induced DNA damage, chromosomal damage, and mutagenesis were determined using the comet assay, MN assay, and ecNGS, respectively. The 72-h treatment with NDMA resulted in concentration-dependent increases in cytotoxicity, DNA damage, MN formation, and mutation frequency in both 2D and 3D cultures, with greater responses observed in the 3D spheroids compared to 2D cells. The mutational spectrum analysis showed that NDMA induced predominantly A:T → G:C transitions, along with a lower frequency of G:C → A:T transitions, and exhibited a different trinucleotide signature relative to the negative control. These results demonstrate that the HepaRG 2D cells and 3D spheroid models can be used for mutagenesis assessment using both DS and HiFi Sequencing, with the caveat that severe cytotoxic concentrations should be avoided when conducting DS. With further validation, the HepaRG 2D/3D system may become a powerful human-based metabolically competent platform for genotoxicity testing.
This tutorial attempts to provide a frank, step-by-step approach to Reed-Solomon (RS) error correction coding. RS encoding and RS decoding both with and without erasing code symbols are emphasized. There is no need to present rigorous proofs and extreme mathematical detail. Rather, the simple concepts of groups and fields, specifically Galois fields, are presented with a minimum of complexity. Before RS codes are presented, other block codes are presented as a technical introduction into coding. A primitive (15, 9) RS coding example is then completely developed from start to finish, demonstrating the encoding and decoding calculations and a derivation of the famous error-locator polynomial. The objective is to present practical information about Reed-Solomon coding in a manner such that it can be easily understood.
Laboratory test set for integration of data compression and error correction encoding of digital communications system