Conditional Error Probability Research Articles

Improving Threshold for Fault-Tolerant Color-Code Quantum Computing by Flagged Weight Optimization

Color codes are promising quantum error-correction (QEC) codes because they have an advantage over surface codes in that all Clifford gates can be implemented transversally. However, the thresholds of color codes under circuit-level noise are relatively low, mainly because measurements of their high-weight stabilizer generators cause an increase in the circuit depth and, thus, substantial errors are introduced. This makes color codes not the best candidate for fault-tolerant quantum computing. Here, we propose a method to suppress the impact of such errors by optimizing weights of decoders using conditional error probabilities conditioned on the measurement outcomes of flag qubits. In numerical simulations, we improve the threshold of the (4.8.8) color code under circuit-level noise from 0.14% to around 0.27%, which is calculated by using an integer programming decoder. Furthermore, in the (6.6.6) color code, we achieve a circuit-level threshold of around 0.36%, which is almost the same value as the highest value in the previous studies employing the same noise model. In both cases, the effective code distance is also improved compared to a conventional method that uses a single ancilla qubit for each stabilizer measurement. Thereby, the achieved logical error rates at low physical error rates are almost one order of magnitude lower than those of the conventional method with the same code distance. Even when compared to the single-ancilla method with a higher code distance, considering the increased number of qubits used in our method, we achieve lower logical error rates in most cases. This method can also be applied to other weight-based decoders, making the color codes more promising as candidates for the experimental implementation of QEC. Furthermore, one can utilize this approach to improve a threshold of wider classes of QEC codes, such as high-rate quantum low-density parity-check codes. Published by the American Physical Society 2024

Model of Satellite Communication Channel Functioning under Conditions of Episodic Synchronization with Pulse Interference Flows

The article investigates the effect of pulse interference on information reception in conditions of episodic synchronization of frames of the physical level of a satellite communication channel with streams of radio pulses of unintended interference. An analytical model of the influence of pulse interference on the reception of information in a satellite communication channel under conditions of episodic synchronization of physical-level frames with pulse interference streams is proposed. Using the example of the DVB family of standards, the combined effect of noise and unintended impulse interference on the conditional error probabilities when receiving a synchro group, the service part of the header and the information part of the frame is shown. Estimates of the average number of frames of the physical level for the duration of the interval of episodic synchronization, the number of intervals of episodic synchronization and the proportion of elementary parcels in the frame exposed to interference, depending on the duration of the pulse interference, are given. It is shown that there are such relations between the duration of the interference pulse and the continuity of the sequence, in which the phenomenon of the episodic synchronization of physical-level frames with the flow of pulse interference has a significant impact on the functioning of the satellite communication channel. The dependences of the probability of erroneous reception of a frame of the physical level of a satellite communication channel on the signal-to-interference ratio at the fixed signal-to-noise ratio and on the duration of the interference pulse are obtained. It has been found that at high signal-to-noise ratios and the duration of the interference correlated with the duration of the service part of the frame, but significantly less than the duration of the frame, the probability of erroneous reception of the frame may be higher than at lower signal-to-noise ratios due to errors when receiving the service part of the frames.

A New Approach to Deriving Closed-Form Bit Error Probability Expressions of MPSK Signals

In conventional approach, the bit error probability (BEP) expressions of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary phase-shift keying (MPSK) signals over additive white Gaussian noise (AWGN) channel are derived by averaging error probabilities for all bits of MPSK symbol. The closed-form BEP expressions of MPSK signals over AWGN channel can also be derived by using the weighted conditional symbol error probability (SEP) expressions, which has not been reported. In this paper, we derive the conditional SEP expressions of MPSK signals in terms of Gaussian <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> and Owen’s <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> functions by changing the domain of integration from a plane bounded by two rays into a quadrant. By weighting the conditional SEP expressions according to average distance spectrum, the closed-form BEP expressions of MPSK signals over AWGN channel are obtained. Only two summations involving two parameters are required. The closed-form BEP expressions of MPSK signals over Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading channel are derived by using the BEP expressions over AWGN channel and the moment generating function-based approach. The approximate BEP expressions of MPSK signals over Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading channel are obtained by using elementary functions-based approximations of Gaussian <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> and Owen’s <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> functions. The conciseness and computational complexity of our BEP expressions are verified by the comparison with existing results.

Dependence assessment in human reliability analysis using the 2-tuple linguistic information and DEMATEL method

Human reliability analysis (HRA), which is to analyze human contribution to system risk, is an effective way to model and assess human errors. Dependence assessment among human errors is an essential part of HRA, which often depends on the judgments of experts. As real-world problems often involve many complex factors, the judgments provided by the experts are often linguistic terms, even under uncertainty. To this end, by integrating 2-tuple linguistic variables and DEMATEL method, this paper presents a novel way to assess the dependence among human actions in HRA. In the proposed method, the linguistic judgments of the experts are modeled using 2-tuple linguistic variables, and the weights of the influential factors are determined using DEMATEL method, furthermore, the conditional human error probability is calculated by aggregating the 2-tuples of different influential factors based on the 2-tuple weighted average operator, where a novel weight calculation method is developed to determine the weights of different experts. Finally, a case study is presented to demonstrate the effectiveness and reliability of the proposed method. By adopting 2-tuple linguistic variables and DEMATEL method, the proposed method could effectively address the uncertainty in the dependence assessment while capturing the relationship among the influential factors.

The Conditional Probability for Human Error Caused by Fatigue, Stress and Anxiety in Seafaring

Human error caused by the interaction and effect of fatigue, stress and anxiety in seafarers is the subject of this research. The human element is a major part of the maritime system. We used Bayesian networks to predict human error in maritime affairs by analysing interactions between people, technology, organisational and environmental factors which make up the specificity of the maritime system. Bayesian networks are graphical structures developed to represent the conditional dependencies among a number of variables and to make conditional conclusions related to the selected variables. Through the analysis of psychic causes such as stress, fatigue, anxiety and so on, the model can produce graphic diagrams indicating which rank on which type of vessel at which seafarers age contributes to an increase in conditional probability of human error. The contribution of the paper is to find the worst combinations of influencing variables that can lead to an increase in the risk of human error. The results show a significant level of fatigue and stress in all officers (engine and nautical), regardless of the type of vessel they serve. A strong presence of anxiety is also reported in all surveyed officers, with a higher degree between engine officers.

Assessing dependence in human reliability analysis using probabilistic linguistic term sets

Dependence assessment is an important part in human reliability analysis (HRA). Normally, the judgments provided by the experts for dependence assessment are linguistic terms, and uncertainty could exist in the judgments. In this paper, a novel dependence assessment method based on the probabilistic linguistic term set (PLTS) is proposed to assess dependence among human actions. Firstly, the influential factors of the dependence assessment are identified, and their weights are determined using the analytical hierarchy process (AHP). Then, judgments provided by the analysts are presented using PLTSs. Next, the PLTSs from different analysts on a specific factor are combined, where their weights are determined using a new PLTS weight calculation method. Finally, the dependence level and the conditional human error probability (CHEP) are obtained by combining PLTSs of all influential factors. The proposed method can address the uncertainty in the dependence assessment in HRA, which inherently is a linguistic assessment process.

Dependence assessment in human reliability analysis under uncertain and dynamic situations

Since reliability and security of man-machine system increasingly depend on reliability of human, human reliability analysis (HRA) has attracted a lot of attention in many fields especially in nuclear engineering. Dependence assessment among human tasks is a important part in HRA which contributes to an appropriate evaluation result. Most of methods in HRA are based on experts’ opinions which are subjective and uncertain. Also, the dependence influencing factors are usually considered to be constant, which is unrealistic. In this paper, a new model based on Dempster–Shafer evidence theory (DSET) and fuzzy number is proposed to handle the dependence between two tasks in HRA under uncertain and dynamic situations. First, the dependence influencing factors are identified and the judgments on the factors are represented as basic belief assignments (BBAs). Second, the BBAs of the factors that varying with time are reconstructed based on the correction BBA derived from time value. Then, BBAs of all factors are combined to gain the fused BBA. Finally, conditional human error probability (CHEP) is derived based on the fused BBA. The proposed method can deal with uncertainties in the judgments and dynamics of the dependence influencing factors. A case study is illustrated to show the effectiveness and the flexibility of the proposed method.

Free Space Optics, Channel Models and Hybrid Modulation Schemes: A Review

Free space optical (FSO) communication system is a wireless communication technology which possess advantages such as huge license free bandwidth and high data carrying capacity among others. It has proved to be a viable solution towards the radio frequency spectrum crunch and hence has been applied in cellular back haul, earth to satellite links, deep space and defense among others. However, FSO performance is adversely affected by atmospheric turbulence and weather conditions. Different channel models are used to estimate the performance of FSO communication system. Meanwhile, different mitigation techniques have been proposed and analyzed over the years for improvement of FSO communication. Of late, hybrid modulation schemes have proved to be another research direction. In this article, we review the FSO channel models as well as hybrid modulation schemes that have been recently introduced to further improve the FSO performance. The conditional probability of error for the commonly used FSO modulation schemes are presented. Finally, the expressions for the bit error for the hybrid modulation schemes are also given.

Priority-Aware Secure Precoding Based on Multi-Objective Symbol Error Ratio Optimization

The secrecy capacity based on the assumption of having continuous distributions for the input signals constitutes one of the fundamental metrics for the existing physical layer security (PHYS) solutions. However, the input signals of real-world communication systems obey discrete distributions. Furthermore, apart from the capacity, another ultimate performance metric of a communication system is its symbol error ratio (SER). In this article, we pursue a radically new approach to PHYS by considering rigorous direct SER optimization exploiting the discrete nature of practical modulated signals. Specifically, we propose a secure precoding technique based on a multi-objective SER criterion, which aims for minimizing the confidential messages' SER at their legitimate user, while maximizing the SER of the confidential messages leaked to the illegitimate user. The key to this challenging multi-objective optimization problem is to introduce a priority factor that controls the priority of directly minimizing the SER of the legitimate user against directly maximizing the SER of the leaked confidential messages. Furthermore, we define a new metric termed as the security-level, which is related to the conditional symbol error probability of the confidential messages leaked to the illegitimate user. Additionally, we also introduce the secure discrete-input continuous-output memoryless channel (DCMC) capacity referred to as secure-DCMC-capacity, which serves as a classical security metric of the confidential messages, given a specific discrete modulation scheme. The impacts of both the channel's Rician factor and the correlation factor of antennas on the security-level and the secure-DCMC-capacity are investigated. Our simulation results demonstrate that the proposed priority-aware secure precoding based on the direct SER metric is capable of securing transmissions, even in the challenging scenario, where the eavesdropper has three receive antennas, while the legitimate user only has a single one.

A Generalized Dimming Control Scheme for Visible Light Communications

A novel dimming control scheme, termed as generalized dimming control (GDC), is proposed for visible light communication (VLC) systems. The basic idea of GDC is to exploit adaptively time, spatial and signal domain resources for enhancing communication performance under practical illumination constraints. In particular, to satisfy the illumination constraints, an incremental algorithm for index mapping is first proposed to achieve target optical power and uniform illumination. Next, GDC having the optimal activation pattern is investigated to improve the bit-error rate (BER) performance of VLC. In particular, the BER performance of GDC is analyzed using the union bound technique. Based on the analytical BER bound, the optimal activation pattern of GDC scheme having the minimum BER criterion (GDC-MBER) is obtained by exhaustively searching all conditional pairwise error probabilities. However, since GDC-MBER requires high search complexity, two low-complexity GDC schemes having the maximum free distance criterion (GDC-MFD) are proposed. The first low-complexity GDC-MFD scheme, termed as GDC-MFD1, is derived by a lower bound of the free distance using the Rayleigh-Ritz theorem. The second low-complexity GDC-MFD scheme, termed as GDC-MFD2, is proposed to reduce further the computation by exploiting the time-invariance characteristics of the VLC channel. Simulation and numerical results show that GDC-MBER, GDC-MFD1 and GDC-MFD2 have similar BER performance, and they can achieve more than 3 dB SNR gains compared with conventional dimming control schemes for a BER of ${10^{ - 4}}$ and a dimming level of 50%.

Down-Link NOMA Networks in the Presence of IQI and Imperfect SIC: Receiver Design and Performance Analysis

This article addresses the practical aspects that may affect the performance of down-link non-orthogonal multiple access (NOMA) systems. The system performance of two down-link NOMA users, where both users suffer from the effects of in-phase/quadrature-phase imbalance (IQI), while the first user also experiences imperfect successive interference cancellation (SIC) is examined. In order to mitigate the effects of IQI, an optimal maximum likelihood (ML) receiver is designed and analyzed, and the performance of the proposed receiver is compared with the traditional ML one. Moreover, closed-form mathematical expressions of the conditional pairwise error probability (PEP) for each user are derived. The simulation results validate the analysis and demonstrate that the proposed receiver outperforms the traditional one, with the ability to reduce the effects of IQI for both users.

Dependence Assessment in Human Reliability Analysis Based on the Interval Evidential Reasoning Algorithm Under Interval Uncertainty

Dependence assessment, which is to assess the influence of the operator’s failure of a task on the failure probability of subsequent tasks, is an important part in Human reliability analysis (HRA). The technique for human error rate prediction (THERP) has been widely applied to assess the dependence in HRA. However, due to the complexity of the real world, various kinds of uncertainty could occur in dependence assessment problem, and how to properly express and deal with uncertainty especially interval uncertainty remains a pressing issue. In this article, a novel method based on the interval evidential reasoning (IER) algorithm is proposed to assess dependence in HRA under interval uncertainty. First, dependence influential factors are identified and their functional relationship is determined. Then, judgments on these factors provided by the analysts are represented using interval belief distributions. Next, the interval evidential reasoning algorithm is employed to aggregate interval belief distributions of different factors according to their functional relationship while considering the credibility of the interval belief distribution. Finally, the conditional human error probability (CHEP) is calculated based on the fused interval belief distribution, where the upper and lower values are determined by assigning belief degree to the highest and lowest grade of the corresponding grade interval, respectively. Two numerical examples demonstrate that the proposed method not only properly deals with interval uncertainty using interval belief distribution and IER algorithm, but also provides a novel and effective way for dependence assessment in HRA.

Channel Magnitude-Based MIMO With Energy Detection for Internet of Things Applications

In this article, three low complexity multiple-input multiple-output (MIMO) receivers using energy detection and multilevel amplitude-shift keying (ASK) for Internet of Things (IoT) applications are described. To circumvent the inherent nonlinearity of the noncoherent MIMO system, an equivalent linear system model for the channel is introduced. This allows the proposed receivers to be configured analogously to coherent-based approaches. The tradeoff is that increased numbers of receive antennas need to be used but the overall complexity is decreased compared to existing noncoherent approaches. The receivers can also easily be integrated with energy harvesting systems. The three receiver structures considered are zero forcing (ZF), ZF with ordered successive interference cancellation (ZF-OSIC), and weighted envelope detection (WENVD), and their performance in flat Rayleigh fading channels with multilevel ASK is investigated. For the WENVD receiver, the error performance under the condition of high signal-to-noise ratio is also analyzed, and closed form approximations of the conditional (conditioned on the channel matrix) symbol vector error probability (SEP) and the average of the conditional SEP are derived. It is found that the ZF receiver has the lowest complexity and the WENVD receiver the highest; however, error performance comparison through numerical results reveals that the WENVD receiver has the best performance and the ZF-OSIC receiver has the next best. When combined with multiport energy harvesting technology the receivers have significant potential for use in IoT.

Performer selection in Human Reliability analysis: D numbers approach

Dependence assessment among human errors in human reliability analysis (HRA) is an significant issue. Many previous works discussed the factors influencing the dependence level but failed to discuss how these factors like "similarity of performers" determine the final result. In this paper, the influence of performers on HRA is focused, in addition, a new way of D numbers which is usually used to handle with the multiple criteria decision making (MCDM) problems is introduced as well to determine the optimal performer. Experimental result demonstrates the validity of proposed methods in choosing the best performers with lowest the conditional human error probability (CHEP) under the same circumstance.

The parameterized Gallager’s first bounds based on conditional triplet-wise error probability

In this paper, the conditional triplet-wise error probability is proposed to improve Gallager’s first bounds based on the general framework of parameterized Gallager’s first bounding technique (GFBT) of binary linear block codes over additive white Gaussian noise (AWGN) channels, which can alleviate the repeated accumulations caused by the use of the pair-wise error probability. Within the recently proposed bounding framework based on nested Gallager regions, three well-known upper bounds, namely, the sphere bound (SB) of Herzberg and Poltyrev, the tangential bound (TB) of Berlekamp, and the tangential-sphere bound (TSB) of Poltyrev, are visited. Within the proposed bounding framework based on conditional triplet-wise error probability, the three well-known bounds can be improved by exploring more detailed geometrical structure of the code when upper bounding the error probabilities. Numerical results show that the proposed bounding framework is useful since the proposed bounds can even improve the TSB, which is considered as one of the tightest upper bounds.

A Restricted Bayes Approach to Joint Detection and Estimation Under Prior Uncertainty

The problem of joint detection and estimation under prior uncertainty is considered within the framework of restricted Bayes theory, which covers the classical Bayes and minimax frameworks as special cases. A linear combination of the average estimation risk with respect to some guessed prior probability and the maximum conditional estimation risk is minimized for generic convex estimation cost functions subject to a constraint on a linear combination of the average detection error probability with respect to the assumed prior and the maximum conditional detection error probability. Unknown random parameters common to different hypotheses as well as parameters unique to each hypothesis are assumed. The jointly optimal estimators and detector that minimize the resulting estimation performance metric under the detection error constraint are derived. With the proposed framework, it is possible to strike any desired balance between a fully minimax framework (where the worst case performance metrics appear in both the objective and the constraint functions of the optimization problem) and the standard Bayesian setting where exact knowledge of the prior distribution is assumed to be available. Unlike the previous studies in the literature, which deal with special cases of the problem studied in this work, the solution to the most general problem indicates that the optimal estimators are coupled with the optimal detector through a least favorable prior.

A New Classification Algorithm With Guaranteed Sensitivity and Specificity for Medical Applications

We propose a novel algorithm to construct binary classifiers, in the spirit of the recently proposed guaranteed error machine (GEM) but with a-posteriori assessment of the “support” instances and without the need for a ternary output. We provide rigorous guarantees on the probability of misclassification; differently from GEM, such guarantees aim to bound the conditional probability of error given the true value of the classified instance. The proposed classifier can be tuned in order to give more importance to one of the two kinds of error, and to balance their ratio also in the presence of unbalanced training sets. Guaranteeing the conditional probabilities of error is crucial in many classification problems, in particular medical diagnoses, where being able to push the tradeoff between sensitivity (conditional probability of detecting a “true positive”) and specificity (conditional probability of detecting a “true negative”) toward higher sensitivity is of paramount importance. The application that first motivated our study is the classification of ventricular fibrillation (VF) into cases where restoration of an organized electrical activity is achieved immediately after a defibrillatory shock (“positive”), and cases where prompt resuscitation does not happen (“negative”). We provide experimental evidence that our approach is promising by testing it against three well-known medical datasets, against some data on VF that are available to the authors, and with Monte Carlo simulations.

On the performance of asymmetric SIM‐based RF/FSO system with MIMO DF relaying

AbstractIn this paper, we consider the asymmetric dual‐hop radio frequency (RF) and free‐space optical (FSO) wireless communication system with a decode‐and‐forward–based multiple‐input–multiple‐output relay over the Nakagami‐m/Generalized‐K( ) distribution. The distribution is a generic statistical model, which has been used for a wide range of atmospheric turbulence–induced fading in FSO communication. The coefficients of the RF hop are considered to be independent and nonidentically distributed with the Nakagami‐m distribution, and the coefficients of FSO hop are considered to be independent and identically distributed. We also consider the path loss and misalignment error effect in FSO hop. We derive the approximate closed‐form expression of the symbol error probability and outage probability in terms of the Meijer G function for the considered mixed decode‐and‐forward RF/FSO system. The closed‐form expressions of the conditional symbol error probability and outage probability are also derived for the considered system while taking into account the effect of a misalignment error. We have also analyzed the considered system for high signal‐to‐noise ratio conditions. In addition, the diversity order of the considered system is also obtained analytically.

Estimating the Influence of Improper Workplace Environment on Human Error: Posterior Predictive Analysis

A model for identifying, analyzing, and quantifying the mechanisms for the influence of improper workplace environment on human error in elevator installation is proposed in this study. By combining a modification of a human error model with real‐world inspection data collected by an elevator installation company, the influence paths of improper workplace environment on the conditional probability of human error were quantified using a Bayesian network parameter‐learning estimation method and posterior predictive simulation. Under the condition of an improper workplace environment, the probability of human error increased by 80% of its original value, a factor much higher than that resulting from improper management. The most probable influence was found to be improper workmanship and changes in the information required by the worker, thus triggering cognitive failure and consequent unsafe actions by workers. The proposed methodology (posterior predictive simulation) provides a new approach in construction studies for quantifying the probabilistic levels of various causal paths, and the results show the key mechanism for the influence of improper workplace environment on human error using real‐world mechanical installation data.

Performance analysis of spatially modulated differential chaos shift keying modulation

A high-data-rate differential chaos shift keying (DCSK) scheme based on spatial modulation (SM), spatially modulated DCSK (SM-DCSK), is proposed. By employing multiple transmit antennas and using transmit antenna index as information-carrying unit, the proposed scheme offers a higher data rate compared with the conventional DCSK scheme. In particular, with two transmit antennas, the proposed scheme transmits a DCSK modulated bit from a selected antenna and hence can double the data rate. At the receiver, the maximum received signal is used to retrieve the block of transmitted bits. Mathematical expression for the conditional error probability of the proposed system is derived based on Gaussian approximation. The error probability of the antenna number estimation and the error probability of the transmitted bit estimation are evaluated numerically. Symbol error rate of the proposed scheme is compared with that of the quadrature chaos shift keying scheme. Numerical and simulation results are presented as a function of system parameters.