Michael E. Mitchell · IRE Transactions on Communications Systems · 1962
An "inhibited" error-correction decoder is defined as one which inhibits its output of decoded information bits when an uncorrectable error is detected. The output bit error rate, probability of false acceptance, and other performance parameters of inhibited decoders are expressed as responses to uncorrectable errors and the effect of such errors on several error-correction decoders of practical interest is described in terms of the numerical results of a computer simulation.
Cited by 3
Frederik K. Marqversen, J. H. Wesenberg, N. T. Zinner et al. · ArXiv.org · 2025
Quantum error correction is essential for achieving fault-tolerant quantum computing. Gottesman-Kitaev-Preskill (GKP) codes are particularly effective at correcting continuous noise, such as Gaussian noise and loss, and can significantly reduce overhead when concatenated with qubit error-correcting codes like surface codes. GKP error correction can be implemented using either a teleportation-based method, known as Knill error correction, or a quantum non-demolition-based approach, known as Steane error correction. In this work, we conduct a comprehensive performance analysis of these established GKP error correction schemes, deriving an analytical expression for the post-correction GKP squeezing and displacement errors. Our results show that there is flexibility in choosing the entangling gate used with the teleportation-based Knill approach. Furthermore, when implemented using the recently introduced qunaught states, the Knill approach not only achieves superior GKP squeezing compared to other variants but is also the simplest to realize experimentally in the optical domain.
Cited by 0Open access
Martin Tomlinson, Cen Jung Tjhai, Marcel Ambroze et al. · Greater South Information System · 2017
The theoretical performance of binary codes for the additive white Gaussian noise (AWGN) channel is discussed. In particular, Gallager's coding theorem for binary codes is treated extensively. By assuming a binomial weight distribution for linear codes, it is shown that the decoder error probability performance of some of the best, known linear, binary codes is the same as the average performance of the ensemble of all randomly chosen, binary nonlinear codes having the same length and dimension. Assuming a binomial weight distribution, an upper bound is determined for the erasure performance of any code, and it is shown that this can be translated into an upper bound for code performance in the AWGN channel. Finally, theoretical bounds on the construction of error-correction codes are discussed.
Cited by 0Open access
Radio and Electronic Engineer · 1984
Cited by 0
William D. Page · Reading World · 1979
Abstract Seven measures of oral reading error correction behavior are examined in relation to comprehension as measured by cloze performance. Two ratio measures; (1) the percent of successfully corrected errors divided by the percent of uncorrected semantically unacceptable errors; and (2) the percent of successfully corrected errors divided by the sum of percents of uncorrected and unsuccessfully corrected errors; prove to be significantly correlated with post oral‐reading cloze test scores. The percent of successfully corrected errors is shown to be moderately correlated with post‐oral reading cloze test scores. Four other measures investigated yield low correlations with post‐oral reading cloze test scores. The study is methodological in that it explores new measures and a way of constructing new measures of correction behavior in oral reading.
Cited by 4
T. Gnanasekaran, Dr K. Duraiswamy · 2013
Cited by 0
Jun Lin · Lehigh Preserve · 2015
Due to the rapid development of the information industry, modern communication and storage systems require much higher data rates and reliability to server various demanding applications. However, these systems suffer from noises from the practical channels. Various error correction codes (ECCs), such as Reed-Solomon (RS) codes, convolutional codes, turbo codes, Low-Density Parity-Check (LDPC) codes and so on, have been adopted in lots of current standards. With the increasing data rate, the research of more advanced ECCs and the corresponding efficient decoders will never stop. Binary LDPC codes have been adopted in lots of modern communication and storage applications due their superior error performance and efficient hardware decoder implementations. Non-binary LDPC (NB-LDPC) codes are an important extension of traditional binary LDPC codes. Compared with its binary counterpart, NB-LDPC codes show better error performance under short to moderate block lengths and higher order modulations. Moreover, NB-LDPC codes have lower error floor than binary LDPC codes. In spite of the excellent error performance, it is hard for current communication and storage systems to adopt NB-LDPC codes due to complex decoding algorithms and decoder architectures. In terms of hardware implementation, current NB-LDPC decoders need much larger area and achieve much lower data throughput. Besides the recently proposed NB-LDPC codes, polar codes, discovered by Ar{\i}kan, appear as a very promising candidate for future communication and storage systems. Polar codes are considered as a major breakthrough in recent coding theory society. Polar codes are proved to be capacity achieving codes over binary input symmetric memoryless channels. Besides, polar codes can be decoded by the successive cancelation (SC) algorithm with of complexity of $\mathcal{O}(N\log_2 N)$, where $N$ is the block length. The main sticking point of polar codes to date is that their error performance under short to moderate block lengths is inferior compared with LDPC codes or turbo codes. The list decoding technique can be used to improve the error performance of SC algorithms at the cost higher computational and memory complexities. Besides, the hardware implementation of current SC based decoders suffer from long decoding latency which is unsuitable for modern high speed communications.ECCs also find their applications in improving the reliability of network coding. Random linear network coding is an efficient technique for disseminating information in networks, but it is highly susceptible to errors. K\"{o}tter-Kschischang (KK) codes and Mahdavifar-Vardy (MV) codes are two important families of subspace codes that provide error control in noncoherent random linear network coding. List decoding has been used to decode MV codes beyond half distance. Existing hardware implementations of the rank metric decoder for KK codes suffer from limited throughput, long latency and high area complexity. The interpolation-based list decoding algorithm for MV codes still has high computational complexity, and its feasibility for hardware implementations has not been investigated.In this exam, we present efficient decoding algorithms and hardware decoder architectures for NB-LDPC codes, polar codes, KK and MV codes. For NB-LDPC codes, an efficient shuffled decoder architecture is presented to reduce the number of average iterations and improve the throughput. Besides, a fully parallel decoder architecture for NB-LDPC codes with short or moderate block lengths is also presented. Our fully parallel decoder architecture achieves much higher throughput and area efficiency compared with the state-of-art NB-LDPC decoders. For polar codes, a memory efficient list decoder architecture is first presented. Based on our reduced latency list decoding algorithm for polar codes, a high throughput list decoder architecture is also presented. At last, we present efficient decoder architectures for both KK and MV codes.
Cited by 0Open access
Xiwen Du · Applied and Computational Engineering · 2023
With the rapid development of information technology and advances in science and technology, people are constantly interacting with data and coding. Error correction codes are integral to ensuring the security, robustness, and accuracy of information and systems, used not only in various engineering fields but in our daily lives as well. Systems that incorporate error correction codes have been proven to perform significantly better than those that do not, which makes it essential to understand the principles behind coding, encoding techniques, and their performance in specific domains.This paper focuses on three widely used error correction codes: Hamming code, RS code, and convolutional code. By introducing each code separately and evaluating their performance in different practical areas using proper simulations and relevant research results, this paper provides a comprehensive understanding of the vital role of error correction codes in channel encoding. Each code has its strengths, weaknesses, and specific applications. Hamming code, for example, is suitable for correcting bit errors in computer memories and communication systems. RS code is widely used in digital storage and broadcast systems due to its high level of error correction capability. Convolutional code is ideal for correcting bit-errors in continuous channels, making it an excellent choice for wireless communication systems. Overall, the results demonstrate that these error correction codes are crucial to guaranteeing data transmission integrity and system robustness. Understanding their principles and performance can guide future research and development of coding techniques in advancing technological progress and improving our daily lives.
Cited by 1Open access
Jain, Aditya · UWSpace (University of Waterloo) · 2023
Building large scale quantum computers is one of the most exciting ventures being pursued by researchers in the 21st century. However, the presence of noise in quantum systems poses a major hindrance towards this ambitious goal. Unlike the developmental history of classical computers where noise levels were brought under reasonable threshold levels early on, the field of quantum computing is struggling to do the same. Nonetheless, there have been many significant theoretical and experimental advancements in the past decade. Quantum error correction and fault tolerance in general is believed to be a reliable long term strategy to mitigate noise and perform arbitrarily long quantum computations. Optimizing and assessing the quality of components in fault-tolerance scheme is a crucial task. We address these tasks in this thesis. \n \nIn the first part of the thesis, we provide a method to efficiently estimate the performance of a large class of codes called concatenated stabilizer codes. We show how to employ noise tailoring techniques developed for computations at the physical level to circuits protected by quantum error correction to enable this estimation. We also develop a metric called the logical estimator, which is an approximation of the logical infidelity of the code. We show that this metric can be used to guide the selection of the optimal (concatenated stabilizer) code and the optimal (lookup style) decoder for a given device. Moreover, the metric also aids in estimating the resource requirements for a target logical error rate efficiently and reliably. \n \nIn the second part, we show how a combination of noise tailoring tools with quantum error correction can improve the performance of concatenated stabilizer codes by several orders of magnitude. These gains in turn bring down the resource overheads for quantum error correction. We explore the gains using concatenated Steane code under a wide variety of physically motivated error models including arbitrary rotations and combinations of coherent and stochastic noise. We also study the variation of gains with the number of levels of concatenation. For the simple case of rotations about a Pauli axis, we show that the gain scales doubly exponentially with the number of levels in the code. We analyze and show the presence of threshold rotation angles below which the gains can be arbitrarily magnified by increasing the number of levels in the code. \n \nThe last part of the thesis explores the testing of an important property of error correcting codes - the minimum distance, often referred to as the distance. We operate in the regime of large classical binary linear codes described in terms of their parity check matrices. We are given access to these codes in terms of an oracle which when supplied an index, returns a single column of the parity check matrix corresponding to that index. We derive lower and upper bounds on the query complexity of finding the minimum distance of a given code. We also ask and (partially) answer the same question in the property testing framework. In particular, we provide a tester which queries a sub-linear number of columns of the parity check matrix and certifies whether a code has high distance or is far away from all codes which have high distance. We also provide non-trivial lower bounds for this task. Although this study is done for classical linear codes, it has implications for designing quantum codes which are built using classical codes. This part of the thesis defines the beginning of a significant area of interest encompassing efficiently testing important properties of classical and quantum codes.
Cited by 0Open access
B. Baumgartner, M. Reinhardt, G. Richter et al. · 2008
Abstract — In this paper the broadband wireless access system provided by the IEEE 802.16 wireless MAN air interface with its amendment to mobile users (IEEE 802.16e) is addressed. We exclusively consider data transmission in the uplink based on scalable OFDMA. We provide performance results for the most important forward error correcting (FEC) schemes intended for IEEE 802.16e, namely convolutional codes (CC), convolutional turbo codes (CTC) and low-density parity-check (LDPC) codes. Index Terms — low-density parity-check codes, convolutional turbo codes, convolutional codes, IEEE 802.16e I.
Cited by 0
Eric Huang, Andrew C. Doherty, Steven T. Flammia · Physical review. A/Physical review, A · 2019
We compare the performance of quantum error correcting codes when memory errors are unitary with the more familiar case of dephasing noise. For a wide range of codes, we analytically compute the effective logical channel that results when the error correction steps are performed noiselessly. Our examples include the entire family of repetition codes, the five-qubit, Steane, Shor, and surface codes. When errors are measured in terms of the diamond norm, we find that the error correction is typically much more effective for unitary errors than for dephasing. We observe this behavior for a wide range of codes after a single level of encoding, and in the thresholds of concatenated codes using hard decoders. We show that this holds with great generality by proving a bound on the performance of any stabilizer code when the noise at the physical level is unitary. By comparing the diamond norm error ${D}_{\ensuremath{\diamond}}^{\ensuremath{'}}$ of the logical qubit with the same quantity at the physical level ${D}_{\ensuremath{\diamond}}$, we show that ${D}_{\ensuremath{\diamond}}^{\ensuremath{'}}\ensuremath{\le}c{D}_{\ensuremath{\diamond}}^{d}$ where $d$ is the distance of the code and $c$ is a constant that depends on the code but not on the error. This bound compares very favorably to the performance of error correction for dephasing noise and other Pauli channels, where an error correcting code of odd distance $d$ will exhibit a scaling ${D}_{\ensuremath{\diamond}}^{\ensuremath{'}}\ensuremath{\sim}{D}_{\ensuremath{\diamond}}^{(d+1)/2}$.
Cited by 77Open access
Fern H. E. Watson · Spiral (Imperial College London) · 2015
In this thesis we present three main contributions to the field of topological quantum error correcting codes. We focus on some of the properties of such codes required for fault-tolerant quantum computation. Prior work has concentrated on determining error rate thresholds of particular models, but increasingly other parameters are gaining prominence. One of these is the overhead -- the quantity of a named resource required to achieve a desired level of performance from the code. We characterise the qubit overhead of the toric code in a fault-tolerant setting. These results provide a general framework for determining the overhead for other code constructions with more complicated noise models. Next we introduce a decoding algorithm, applicable to topological codes in a qudit architecture, specifically those where fault-tolerance is achieved through repeated syndrome measurements. It is computationally light and capable of decoding qudits of arbitrarily high dimension with negligible increase in its run time. The threshold of the decoder is limited by the percolation of the syndromes. Using local matching techniques we are able to overcome this limitation, increasing the threshold by almost a factor of two for high qudit dimensions. Finally, we turn our attention to a second family of topological quantum codes: the colour codes. In three and higher spatial dimensions such codes can support transversal non-Clifford gates. We show, using a technique that we call a star-bipartition of the vertices of the lattice, that any existing qubit colour code lattice can be used to define a qudit colour code. By generalising the notion of triorthogonal matrices we derive analogous transversality properties in the qudit codes.
Cited by 2Open access
Henning Zörlein, Dejan E. Lazich, Martin Bossert · 2011
In this paper, the real-valued Compressed Sensing (CS)-based error correction scheme which was proposed by Candes and Tao is evaluated against the background of channel coding theory. Substantial differences to conventional linear block codes over Galois fields are reviewed and interpreted. A unified channel model is introduced. It enables performance evaluation of more realistic almost sparse channels, which are of interest for communication applications. It is shown by simulations that certain variations of the CS based error correction scheme are suitable for special channels. Additionally, explanations for the noise sensitivity of CS based error correction schemes are given.
Cited by 5
Shih-Ting Lin · PLoS ONE · 2024
Large language models (LLMs) have recently exhibited significant capabilities in various English NLP tasks. However, their performance in Chinese grammatical error correction (CGEC) remains unexplored. This study evaluates the abilities of state-of-the-art LLMs in correcting learner Chinese errors from a corpus linguistic perspective. The performance of LLMs is assessed using standard evaluation metrics of MaxMatch score. Keyword and key n-gram analyses are conducted to quantitatively explore linguistic features that differentiate LLM outputs from those of human annotators. LLMs' performance in syntactic and semantic dimensions is further qualitatively analyzed based on these probes of keywords and key n-grams. Results show that LLMs achieve a relatively higher performance in test datasets with multiple annotators and low performance in those with a single annotator. LLMs tend to overcorrect wrong sentences, under the explicit prompt of the "minimal edit" strategy, by using more linguistic devices to generate fluent and grammatical sentences. Furthermore, they struggle with under-correction and hallucination in reasoning-dependent situations. These findings highlight the strengths and limitations of LLMs in CGEC, suggesting that future efforts should focus on refining overcorrection tendencies and improving the handling of complex semantic contexts.
Cited by 6Open access
Paul G. Baity, Anuj K. Nayak, Lav R. Varshney et al. · arXiv (Cornell University) · 2026
Radiation impacts are a current challenge with computing on superconducting-based quantum devices because they can lead to widespread correlated errors across the device. Such errors can be problematic for quantum error correction (QEC) codes, which are generally designed to correct independent errors. To address this, we have developed a computational model to simulate the effects of radiation impacts on QEC performance. This is achieved by building from recently developed models of quasiparticle density, mapping radiation-induced qubit error rates onto a quantum error channel and simulation of a simple surface code. We also provide a performance metric to quantify the resilience of a QEC code to radiation impacts. Additionally, we sweep various parameters of chip design to test mitigation strategies for improved QEC performance. Our model approach is holistic, allowing for modular performance testing of error mitigation strategies and chip and code designs.
Cited by 0Open access
Paul G. Baity, Anuj K. Nayak, Lav R. Varshney et al. · ArXiv.org · 2026
Radiation impacts are a current challenge with computing on superconducting-based quantum devices because they can lead to widespread correlated errors across the device. Such errors can be problematic for quantum error correction (QEC) codes, which are generally designed to correct independent errors. To address this, we have developed a computational model to simulate the effects of radiation impacts on QEC performance. This is achieved by building from recently developed models of quasiparticle density, mapping radiation-induced qubit error rates onto a quantum error channel and simulation of a simple surface code. We also provide a performance metric to quantify the resilience of a QEC code to radiation impacts. Additionally, we sweep various parameters of chip design to test mitigation strategies for improved QEC performance. Our model approach is holistic, allowing for modular performance testing of error mitigation strategies and chip and code designs.
Cited by 0Open access
Edward Chandler, George R. Cooper · 1982
This study was motivated by a desire to minimize the required input signal-to-noise ratio at the receiver as a first step in optimizing the anti-intercept (AI) performance of a spread spectrum system. In the absence of error correction coding, specification of the message bit rate, the transmitted signal bandwidth, and the required bit error probability can yield a required signal-to-noise ratio for each type of SS system. Error correction coding can be used to reduce the required signal-to-noise ratio. When coding is employed, lower and upper bounds on the reduction of required signal-to-noise ratio can be determined in terms of the required bit error probability and code complexity. These performance bounds are evaluated as functions of the restricted code complexity.
Cited by 1
Reetu Tripathi, Neha Vaishampayan, Kalpana Chaturvedi · 2016
Cited by 0
Falah Ali (4460566), S Soysa (16077578) · Figshare · 2001
The complex-Valued Collaborative Coding Multiple Access (CV_CCMA) scheme has been proposed as a viable method, for enabling simultaneous transmission by multiple users over a common radio channel, without the use of orthogonal codes nor sub division in time or frequency [1]. This paper investigates the use of forward error correction to improve the performance of CV-CCMA in Rayleigh fading channels. T-user M-PSK CV-CCMA schemes employing block coding are described. The simulation results show the significant gains achieved using linear block codes and dual space diversity.
Cited by 0Open access
Paulo Henrique da Silva Franco · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2013
One of the most used physical properties to implement quantum technology is the polarization of the light. However, since the polarization of the light is fragile, it is essential that a quantum error correction system is used to make quantum information feasible in the polarization of a photon. A method of correction of polarization proposed for isolated photons divides the channel into sub-channels in such a way that only the variation in those sub-channels destroys the information. Therefore, rapid changes must occur in the moment that two optical pulses pass through the sub-channel. This work analyses a statistical model that uses the degree of depolarization of the light as a probability for the sub-channel to undergo minute variations in the time between the passage of two pulses. To model the variations of the parameters of the channel, it is used the probabilistic method of Poisson, applied to rare events. An estimate can be done using numerical methods which measures the degree of polarization of the light to predict how would be the behavior in the practice of the quantum error correction system studied.
Cited by 0Open access