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A test set for integration of data compression/ error correction encoding techniques. II - Error correction encoding considerations
Error correction coding/decoding techniques integration, discussing convolutional and block coding and Viterbi, Sequential and Threshold decoding algorithms
Error-correcting codes for high-speed digital computers
Published document discusses method for correcting errors. According to this method, computer operation becomes fault-tolerant, i.e., its operation is error-free in spite of single hardware element malfunction. Also, method provides for detection and correction of repetitive and spurious processing and transmission errors.
Error correction method and apparatus for electronic timepieces
A method and apparatus for correcting errors in an electronic digital timepiece that includes an oscillator which has a 2 in. frequency output, an n-stage frequency divider for reducing the oscillator output frequency to a time keeping frequency, and means for displaying the count of the time keeping frequency. In first and second embodiments of the invention the timepiece is synchronized with a time standard at the beginning of the period of time T. In the first embodiment of the invention the timepiece user observes E (the difference between the time standard and the timepiece time at the end of the period T) and then operates a switch to correct the time of the timepiece and to obtain a count for E. In the second embodiment of the invention, the user operates a switch at the beginning of T and at the end of T and a count for E is obtained electronically.
Adding Stale-Data Flag to and Error-Correcting Code
A suitable constant "exclusive-Ored" with ECC to flag data without impairing detection of correctable errors.
CaliQEC: In-situ Qubit Calibration for Surface Code Quantum Error Correction
Quantum Error Correction (QEC) is essential for fault-tolerant, large-scale quantum computation. However, error drift in qubits undermines QEC performance during long computations, necessitating frequent calibration. Conventional calibration methods disrupt quantum states, requiring system downtime and rendering in situ calibration impractical. To address this challenge, we propose QECali, a novel framework that enables in situ calibration for surface codes. Our evaluation demonstrates that QECali introduces modest qubit overhead and negligible increases in execution time, offering the first practical solution for in situ calibration in surface code based quantum computation.
Simultaneous error-correction and burst-error detection using binary linear cyclic codes.
Simultaneous error correction and burst error detection, using binary linear cyclic codes
Enhancing quantum memory lifetime with measurement-free local error correction and reinforcement learning
Reliable quantum computation requires systematic identification and correction of errors that occur and accumulate in quantum hardware. To diagnose and correct such errors, standard quantum error-correcting protocols utilize global error information across the system obtained by mid-circuit readout of ancillary qubits. We investigate circuit-level error-correcting protocols that are measurement-free and based on local error information. Such a local error correction (LEC) circuit consists of faulty multi-qubit gates to perform both syndrome extraction and ancilla-controlled error removal. We develop and implement a reinforcement learning framework that takes a fixed set of faulty gates as inputs and outputs an optimized LEC circuit. To evaluate this approach, we quantitatively characterize an extension of logical qubit lifetime by a noisy LEC circuit. For the two-dimensional (2D) classical Ising model and four-dimensional toric code, our optimized LEC circuit performs better at extending a memory lifetime compared with a conventional LEC circuit based on Toom's rule in a subthreshold gate error regime. We further show that such circuits can be used to reduce the rate of mid-circuit readouts to preserve a 2D toric code memory. Lastly, we discuss the application of the LEC protocol on dissipative preparation of quantum states with topological phases.
Universal Optimization and Tighter Fidelity Bounds for Approximate Quantum Error Correction
Approximate quantum error correction (AQEC) not only dictates the performance of discrete- and continuous-variable quantum error correction codes but also serves as a unifying framework across various physical disciplines. Identifying the optimal recovery channel to maximize the entanglement fidelity via standard semidefinite programming is computationally bottlenecked by the exponentially growing number of Kraus operators with system size, rendering large-scale optimization prohibitive. While analytical near-optimal maps exist, they typically work only when the Knill-Laflamme conditions are nearly satisfied. In this Letter, we establish an efficient framework by leveraging the duality between recovery and environment decoupling. This framework yields a tighter analytical lower bound on entanglement fidelity than the conventional limit set by the transpose channel. Furthermore, by exploiting the decayed weights of noise Kraus operators, we introduce a framework based on principal component analysis to reduce the dimension. In thermal loss channels where the weights decay exponentially, our approach achieves a 33-fold computational speedup while maintaining rigorous accuracy. Our approach enables high-precision optimization for AQEC codes that were previously intractable due to the curse of dimensionality.
New double-byte error-correcting codes for memory systems
Error-correcting or error-detecting codes have been used in the computer industry to increase reliability, reduce service costs, and maintain data integrity. The single-byte error-correcting and double-byte error-detecting (SbEC-DbED) codes have been successfully used in computer memory subsystems. There are many methods to construct double-byte error-correcting (DBEC) codes. In the present paper we construct a class of double-byte error-correcting codes, which are more efficient than those known to be optimum, and a decoding procedure for our codes is also considered.
Exact determination of probability of bit error for perfect single error correcting codes
Bit error probability after decoding for binary perfect single error correcting codes
On codes with multi-level error-correction capabilities
In conventional coding for error control, all the information symbols of a message are regarded equally significant, and hence codes are devised to provide equal protection for each information symbol against channel errors. However, in some occasions, some information symbols in a message are more significant than the other symbols. As a result, it is desired to devise codes with multilevel error-correcting capabilities. Another situation where codes with multi-level error-correcting capabilities are desired is in broadcast communication systems. An m-user broadcast channel has one input and m outputs. The single input and each output form a component channel. The component channels may have different noise levels, and hence the messages transmitted over the component channels require different levels of protection against errors. Block codes with multi-level error-correcting capabilities are also known as unequal error protection (UEP) codes. Structural properties of these codes are derived. Based on these structural properties, two classes of UEP codes are constructed.
An error control system with multiple-stage forward error corrections
A robust error-control coding system is presented. This system is a cascaded FEC (forward error control) scheme supported by parity retransmissions for further error correction in the erroneous data words. The error performance and throughput efficiency of the system are analyzed. Two specific examples of the error-control system are studied. The first example does not use an inner code, and the outer code, which is not interleaved, is a shortened code of the NASA standard RS code over GF(28). The second example, as proposed for NASA, uses the same shortened RS code as the base outer code C2, except that it is interleaved to a depth of 2. It is shown that both examples provide high reliability and throughput efficiency even for high channel bit-error rates in the range of 0.01.
Windowed region-of-interest non-uniformity correction and range walk error correction of a 3D flash LiDAR camera
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A Systematic Error Correction Method for TOVS Radiances
Treatment of systematic errors is crucial for the successful use of satellite data in a data assimilation system. Systematic errors in TOVS radiance measurements and radiative transfer calculations can be as large or larger than random instrument errors. The usual assumption in data assimilation is that observational errors are unbiased. If biases are not effectively removed prior to assimilation, the impact of satellite data will be lessened and can even be detrimental. Treatment of systematic errors is important for short-term forecast skill as well as the creation of climate data sets. A systematic error correction algorithm has been developed as part of a 1D radiance assimilation. This scheme corrects for spectroscopic errors, errors in the instrument response function, and other biases in the forward radiance calculation for TOVS. Such algorithms are often referred to as tuning of the radiances. The scheme is able to account for the complex, air-mass dependent biases that are seen in the differences between TOVS radiance observations and forward model calculations. We will show results of systematic error correction applied to the NOAA 15 Advanced TOVS as well as its predecessors. We will also discuss the ramifications of inter-instrument bias with a focus on stratospheric measurements.
Rare events and Griffiths phases in topological quantum error correction
The performance of quantum error correcting (QEC) codes is often studied under the assumption of spatiotemporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. Here, in this work, we study the effects of nonuniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatiotemporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code.
Design study of error-detecting and error correcting shift register
Design of error detecting and error correcting shift register
Augmented burst-error correction for UNICON laser memory
A single-burst-error correction system is described for data stored in the UNICON laser memory. In the proposed system, a long fire code with code length n greater than 16,768 bits was used as an outer code to augment an existing inner shorter fire code for burst error corrections. The inner fire code is a (80,64) code shortened from the (630,614) code, and it is used to correct a single-burst-error on a per-word basis with burst length b less than or equal to 6. The outer code, with b less than or equal to 12, would be used to correct a single-burst-error on a per-page basis, where a page consists of 512 32-bit words. In the proposed system, the encoding and error detection processes are implemented by hardware. A minicomputer, currently used as a UNICON memory management processor, is used on a time-demanding basis for error correction. Based upon existing error statistics, this combination of an inner code and an outer code would enable the UNICON system to obtain a very low error rate in spite of flaws affecting the recorded data.