James R. Wootton, Daniel Loss · Physical review. A/Physical review, A · 2018
The repetition code is an important primitive for the techniques of quantum error correction. Here we implement repetition codes of at most 15 qubits on the 16 qubit ibmqx3 device. Each experiment is run for a single round of syndrome measurements, achieved using the standard quantum technique of using ancilla qubits and controlled operations. The size of the final syndrome is small enough to allow for lookup table decoding using experimentally obtained data. The results show strong evidence that the logical error rate decays exponentially with code distance, as is expected and required for the development of fault-tolerant quantum computers. The results also give insight into the nature of noise in the device.
Cited by 64Open access
Matthew P. Stafford, Nicolas C. Menicucci · Physical review. A/Physical review, A · 2023
Continuous-variable quantum computing architectures based upon the Gottesman-Kitaev-Preskill (GKP) encoding have emerged as a promising candidate because one can achieve fault tolerance with a probabilistic supply of GKP states and Gaussian operations. Furthermore, by generalizing to rectangular-lattice GKP states, a bias can be introduced and exploited through concatenation with qubit codes that show improved performance under biasing. However, these codes (such as the XZZX surface code) still require weight-four stabilizer measurements and have complex decoding requirements to overcome. In this work, we study the code-capacity behavior of a rectangular-lattice GKP encoding concatenated with a repetition code under an isotropic Gaussian displacement channel. We find a numerical threshold of $\ensuremath{\sigma}=0.599$ for the noise's standard deviation, which outperforms the biased GKP planar surface code with a trade-off of increased biasing at the GKP level. This is all achieved with only weight-two stabilizer operators and simple decoding at the qubit level. Furthermore, with moderate levels of bias (aspect ratio $\ensuremath{\le}2.4$) and nine or fewer data modes, significant reductions in logical error rates can still be achieved for $\ensuremath{\sigma}\ensuremath{\le}0.3$, opening the possibility of using biased GKP repetition codes as a simple low-level qubit encoding for further concatenation.
Cited by 14Open access
Mingwei Liu, Juntao Li, Ying Wang et al. · ArXiv.org · 2025
Despite recent advances in Large Language Models (LLMs) for code generation, the quality of LLM-generated code still faces significant challenges. One significant issue is code repetition, which refers to the model's tendency to generate structurally redundant code, resulting in inefficiencies and reduced readability. To address this, we conduct the first empirical study to investigate the prevalence and nature of repetition across 19 state-of-the-art code LLMs using three widely-used benchmarks. Our study includes both quantitative and qualitative analyses, revealing that repetition is pervasive and manifests at various granularities and extents, including character, statement, and block levels. We further summarize a taxonomy of 20 repetition patterns. Building on our findings, we propose DeRep, a rule-based technique designed to detect and mitigate repetition in generated code. We evaluate DeRep using both open-source benchmarks and in an industrial setting. Our results demonstrate that DeRep significantly outperforms baselines in reducing repetition (with an average improvements of 91.3%, 93.5%, and 79.9% in rep-3, rep-line, and sim-line metrics) and enhancing code quality (with a Pass@1 increase of 208.3% over greedy search). Furthermore, integrating DeRep improves the performance of existing repetition mitigation methods, with Pass@1 improvements ranging from 53.7% to 215.7%.
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Brown, Rachel M., Koch, Iring · Psychology Archives · 2023
Code for accepted article titled: Repetition costs in sequence chunking
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Áron Rozgonyi, Gábor Széchenyi · arXiv (Cornell University) · 2023
Enhancing the lifetime of qubits with quantum code-based memories on different quantum hardware is a significant step towards fault-tolerant quantum computing. We theoretically show that the break-even point, i.e., preserving arbitrary quantum information longer than the lifetime of a single idle qubit, can be beaten even with the quantum phase-flip repetition code in a dephasing-time-limited system. Applying circuit-based analytical calculation, we determine the efficiency of the phase-flip code as a quantum memory in the presence of relaxation, dephasing, and faulty quantum gates. Considering current platforms for quantum computing, we identify the gate error probabilities and optimal repetition number of quantum error correction cycles to reach the break-even point.
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Association for Computational Linguistics 2025, Dong, Yihong, Jiang, Xue et al. · Underline Science Inc. · 2025
With the advent of neural language models, the performance of code generation has been significantly boosted. However, the problem of repetitions during the generation process continues to linger. Previous work has primarily focused on content repetition, which is merely a fraction of the broader repetition problem in code generation. A more prevalent and challenging problem is structural repetition. In structural repetition, the repeated code appears in various patterns but possesses a fixed structure, which can be inherently reflected in grammar. In this paper, we formally define structural repetition and propose an efficient decoding approach called RPG, which stands for Repetition Penalization based on Grammar, to alleviate the repetition problems in code generation for LLMs. Specifically, RPG first leverages grammar rules to identify repetition problems during code generation, and then strategically decays the likelihood of critical tokens that contribute to repetitions, thereby mitigating them in code generation. To facilitate this study, we construct a new dataset CodeRepetEval to comprehensively evaluate approaches for mitigating the repetition problems in code generation. Extensive experimental results demonstrate that RPG substantially outperforms the best-performing baselines on CodeRepetEval dataset as well as HumanEval and MBPP benchmarks, effectively reducing repetitions and enhancing the quality of generated code.
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Yihong Dong, Yuchen Liu, Xue Jiang et al. · 2025
With the advent of neural language models, the performance of code generation has been significantly boosted.However, the problem of repetitions during the generation process continues to linger.Previous work has primarily focused on content repetition, which is merely a fraction of the broader repetition problem in code generation.A more prevalent and challenging problem is structural repetition.In structural repetition, the repeated code appears in various patterns but possesses a fixed structure, which can be inherently reflected in grammar.In this paper, we formally define structural repetition and propose an efficient decoding approach called RPG, which stands for Repetition Penalization based on Grammar, to alleviate the repetition problems in code generation for LLMs.Specifically, RPG first leverages grammar rules to identify repetition problems during code generation, and then strategically decays the likelihood of critical tokens that contribute to repetitions, thereby mitigating them in code generation.To facilitate this study, we construct a new dataset CodeRepetEval to comprehensively evaluate approaches for mitigating the repetition problems in code generation.Extensive experimental results demonstrate that RPG substantially outperforms the best-performing baselines on CodeRepetEval dataset as well as HumanEval and MBPP benchmarks, effectively reducing repetitions and enhancing the quality of generated code. 1
Cited by 1Open access
Maxim Tarnawsky · Kyiv-Mohyla Humanities Journal · 2014
Traditional and modernist comments on the mechanics of Nechui’s prose style are largely critical, focusing on what are assumed to be errors or infelicities in writing. This article examines these presumed errors and proceeds to focus on three central qualities of Nechui’s writing: repetition, pacing, and the absence of purposeful construction. The intention here is not to make judgments about the strengths and weaknesses of his writing but rather to point out its essential features. Two central features of Nechui’s writing that are explored are deliberate repetition and non-purposeful plot structure.
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Yu, Quan, Sung, Chi Wan, Chan, Terence H. · arXiv (Cornell University) · 2014
This paper presents a flexible irregular model for heterogeneous cloud storage systems and investigates how the cost of repairing failed nodes can be minimized. The fractional repetition code, originally designed for minimizing repair bandwidth for homogeneous storage systems, is generalized to the irregular fractional repetition code, which is adaptable to heterogeneous environments. The code structure and the associated storage allocation can be obtained by solving an integer linear programming problem. For moderate sized networks, a heuristic algorithm is proposed and shown to be near-optimal by computer simulations.
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Mulder, Jasper (author) · Research Repository (Delft University of Technology) · 2022
In this thesis, the repetition code for bit flip errors is examined. Based the stabilizer measurements outcome of a run of the repetition code, one does not know exactly which errors have occurred. Statistics can be used to estimate the probability of all possible error events. This probability estimation is investigated for simulated data assuming phenomenological and circuit level noise. Experiments on the repetition code are performed by the DiCarlo group at the Delft University of Technology on a superconducting quantum computer. For this data, some error probabilities are estimated to be nonphysical. The goal of this thesis is to investigate these nonphysical probabilities and to determine whether they result from sampling noise or a problem with the assumed error model that determines the estimation of the probabilities. By estimating the standard deviation using the bootstrap method it is shown that the nonphysical probabilities are not due to sampling noise. Therefore, it is possible that non-conventional errors, such as leakage or crosstalk, are affecting these estimates.<br/><br/>In a further analysis on the error probabilities and their standard deviation, it is shown that the standard error for space and time edges in the experiment is consistent with the standard error from phenomenological noise initialised with the average error data and ancilla error probabilities, even when<br/>these may be affected by non-conventional errors.
Cited by 0
Hikari Matsuoka, Yoshihito Doi, Yabe Tatsuro et al. · IEICE Transactions on Communications · 2014
This paper investigates the performance of an overloaded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system with a repetition code. It has been demonstrated that diversity with block coding prevents the performance degradation induced by signal multiplexing. However, the computational complexity of a joint decoding scheme increases exponentially with the number of multiplexed signal streams. Thus, this paper proposes the use of a repetition code in the overloaded MIMO-OFDM system. In addition, QR decomposition with M-algorithm (QRM) maximum likelihood decoding (MLD) is applied to the decoding of the repetition code. QRM-MLD significantly reduces the amount of joint decoding complexity. In addition, virtual antennas are employed in order to increase the throughput that is reduced by the repetition code. It is shown that the proposed scheme reduces the complexity by about 1/48 for 6 signal streams with QPSK modulation while the BER degradation is less than 0.1dB at the BER of 10-3.
Cited by 7
Randy L. Buckner, Mark E. Wheeler, Luigi Maccotta et al. · NeuroImage · 2001
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Bing Zhu · IEEE Communications Letters · 2015
Modern storage systems are increasingly employing erasure codes to protect data against disk failures. Various codes have been elaborately constructed to achieve the desirable storage performance. In this letter, we consider fractional repetition (FR) codes, which provide uncoded exact repairs with minimum repair bandwidth. We present a novel code construction framework that is built on existing codes to generate new FR codes. The proposed framework extends the construction of FR codes to a larger set of parameters, and is applicable to heterogeneous storage networks. Moreover, we characterize a general expression for the minimum distance of FR codes, which is derived from a simple analysis and depends on the size of stored file. We further present closed-form expressions on the minimum distance for some special scenarios.
Cited by 11
Data-Bukowska, Ewa · Homo Politicus (Academy of Humanities and Economics in Lodz) · 2016
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Sang‐Rok Moon, Sunghyun Bae · Optics Communications · 2024
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Mingqing Wang, Sheng Liang, Shuqin Lou · IEEE Photonics Technology Letters · 2018
We propose a tunable repetition rate multiplier for optical phase code sequences consisting of a temporal grating and a temporal 4-F system. The temporal 4-F imaging preserves the input code words at the output, while the temporal grating multiplies the code rate by an integer being programed via an arbitrary wave generator. A lower bound and an upper bound are, respectively, set for aperture width of involved active elements and dispersion deviation of involved dispersion elements to control output phase distortion. By numerical simulation, an 8-period-long input sequence of individual phase Barker code with 10 ns code chip width and 2-rad peak phase is multiplied from 4 to 16 MHz corresponding to multiplication factor tuned from one to four. The expected phase preserving feature and tunable capacity are validated. Degradations including leaked ripples and envelop fluctuation are successfully controlled by the aperture-width bound and the dispersion-deviation bound, respectively. The proposed multiplier provides a promising potential for multifunctional photonic-aided continuous-wave radars with enhanced agility and adaptability.
Cited by 2
Sixue Wu, Gerrit Blacquière, Gert-Jan Adriaan van Groenestijn · Geophysics · 2018
In blended seismic acquisition, or simultaneous source seismic acquisition, source encoding is essential at the acquisition stage to allow for separation of the blended sources at the processing stage. In land seismic surveys, the vibroseis sources may be encoded with near-orthogonal sweeps for blending. In marine seismic surveys, the sweep type of source encoding is difficult because the main source type in marine seismic exploration is the air-gun array, which has an impulsive character. Another issue in marine streamer seismic data acquisition is that the spatial source sampling is generally coarse. This hinders the deblending performance of algorithms based on the random time delay blending code that inherently requires a dense source sampling because they exploit the signal coherency in the common-receiver domain. We have developed an alternative source code called shot repetition that exploits the impulsive character of the marine seismic source in blending. This source code consists of repeated spikes of ones and can be realized physically by activating a broadband impulsive source more than once at (nearly) the same location. Optimization of the shot-repetition type of blending code was done to improve the deblending performance. As a result of using shot repetition, the deblending process can be carried out in individual shot gathers. Therefore, our method has no need for a regular dense source sampling: It can cope with irregular sparse source sampling; it can help with real-time data quality control. In addition, the use of shot repetition is beneficial for reducing the background noise in the deblended data. We determine the feasibility of our method on numerical examples.
Cited by 7Open access
Dejin Kong, X. Zheng, Yukang Tian et al. · Digital Communications and Networks · 2021
In this paper, we address the Alamouti code in Filter-Bank Multicarrier with Offset Quadrature Amplitude Modulation (FBMC/OQAM) and propose a novel block-wise Alamouti code, in which a repeated block is designed to eliminate the imaginary interference among FBMC/OQAM symbols. The proposed approach exhibits a higher spectral efficiency than the conventional block-wise Alamouti scheme, as only one column of zero symbols is used as a guard interval instead of two. Furthermore, compared to the conventional scheme, the bit error ratio is improved in the proposed block-wise Alamouti, as the assumption on channel invariance at two adjacent subcarriers is not required. Simulation results indicate that, with a significantly reduced overhead, the proposed Alamouti scheme achieves better performance over the conventional block-wise Alamouti scheme.
Cited by 6Open access
Claudio Viecelli (5784458), David Graf (1776046), David Aguayo (2218423) et al. · Figshare · 2020
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Chella Pandian P · Malaya Journal of Matematik · 2022
In this paper, the covering radius of codes over \(R = \mathbb{Z}_2\mathbb{Z}_6\) with different weight are discussed. The block repetition codes over \(R\) is defined and the covering radius for block repetition codes R are obtained.
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