Minimum Error Probability Research Articles

CURATE: Scaling-Up Differentially Private Causal Graph Discovery

Causal graph discovery (CGD) is the process of estimating the underlying probabilistic graphical model that represents the joint distribution of features of a dataset. CGD algorithms are broadly classified into two categories: (i) constraint-based algorithms, where the outcome depends on conditional independence (CI) tests, and (ii) score-based algorithms, where the outcome depends on optimized score function. Because sensitive features of observational data are prone to privacy leakage, differential privacy (DP) has been adopted to ensure user privacy in CGD. Adding the same amount of noise in this sequential-type estimation process affects the predictive performance of algorithms. Initial CI tests in constraint-based algorithms and later iterations of the optimization process of score-based algorithms are crucial; thus, they need to be more accurate and less noisy. Based on this key observation, we present CURATE (CaUsal gRaph AdapTivE privacy), a DP-CGD framework with adaptive privacy budgeting. In contrast to existing DP-CGD algorithms with uniform privacy budgeting across all iterations, CURATE allows for adaptive privacy budgeting by minimizing error probability (constraint-based), maximizing iterations of the optimization problem (score-based) while keeping the cumulative leakage bounded. To validate our framework, we present a comprehensive set of experiments on several datasets and show that CURATE achieves higher utility compared to existing DP-CGD algorithms with less privacy leakage.

Covert throughput maximization for NOMA based visible light covert communication networks

Covert throughput maximization for a non-orthogonal multiple access (NOMA)-based visible light covert communication (VLCC) network is investigated. The network consists of a light emitting diode (LED) transmitter, two NOMA users (one public, one covert), and a monitor tasked with detecting any covert transmissions between the LED and the covert user. The transmitter leverages its interaction with the public user to mask the covert communication with the covert user, adopting a random power transmission scheme. This strategy serves to amplify the monitor’s detection uncertainty and significantly enhance the covertness of the VLCC network. Two VLCC scenarios are covered: For the indoor static VLCC scenario where the LED is fixed, subject to the minimum detection error probability of the monitor (covertness constraint) and the outage probability of NOMA users (reliability constraint), the covert throughput is maximized by optimizing the ratio of the LED’s power allocation factor (PAF). For the mobile VLCC scenario where the LED is mounted on an unmanned aerial vehicle (UAV), subject to the constraints of the covertness, reliability and UAV’s flight region, the optimal LED’s PAF ratio and UAV’s location are jointly obtained via a graphical approach. Finally, simulations are carried out to analyze the influence of VLCC parameters on the maximum covert throughput, and results show that compared with benchmark schemes, the proposed scheme can greatly improve the covert throughput.

Минимизация вероятности ошибки при взвешенном приеме сообщения с двухпозиционной импульсно-кодовой манипуляцией в условиях межсимвольной интерференции

In order to increase the noise immunity of data transmission systems, it is proposed to reduce the level of intersymbol interference by means of orthogonalizing the channel symbols. Orthogonalization is done through determining the orthogonality weight. Presented below is a calculation of the E-criterion for assessing the level of intersymbol interference for the proposed data transmission systems using the pulse-code modulation. For both systems, it was assumed that normalized Butterworth low-pass filters would be used as the shaping filter. It is shown that when signal-to-noise ratios exceed a certain critical value, weighted signal processing provides a lower bit error probability compared to the conventional processing technique. A general analytical expression for the orthogonality weight of channel symbols is given, which ensures a minimum bit error probability.

Derivation of standard quantum theory via state discrimination

It is a key issue to characterize the model of standard quantum theory out of general models by an operational condition. The framework of general probabilistic theories (GPTs) is a new information theoretical approach to single out standard quantum theory. It is known that traditional properties, for example, Bell-CHSH inequality, are not sufficient to single out standard quantum theory among possible models in GPTs. As a more precise property, we focus on the bound of the performance for an information task called state discrimination in general models. We give an equivalent condition for outperforming the minimum discrimination error probability under the standard quantum theory given by the trace norm. Besides, by applying the equivalent condition, we characterize standard quantum theory out of general models in GPTs by the bound of the performance for state discrimination.

Performance Comparison of Relay-Based Covert Communications: DF, CF and AF.

In this paper, we investigate the performance of covert communications in different types of a relay system: decode-and-forward (DF), compress-and-forward (CF) and amplify-and-forward (AF). We consider a source node that attempts to send both public and covert messages to a destination node through a relay on which a covert message detector is embedded. By taking the minimum detection error probability (DEP) at the relay into account, we optimize the power distribution between the public and covert messages to achieve the maximum covert rate. We further make a delay-aware comparison among DF, CF and AF relay systems with the obtained closed-form covert rates and conduct an extensive examination on the asymptotic behaviors in different limits. Our analyses reveal that CF or AF tend to outperform DF for high source transmit power or low relay transmit power, while various system parameters such as the processing delay, minimum required quality of service for public messages and DEP threshold lead to different performance relationships among DF, CF and AF for high relay transmit power. Numerical results verify our investigation into the performance comparison in various channel models.

Trade-off relations of geometric coherence

Quantum coherence is an important quantum resource and it is intimately related to various research fields. The geometric coherence is a coherence measure both operationally and geometrically. We study the trade-off relation of geometric coherence in qubit systems. We first derive an upper bound for the geometric coherence by the purity of quantum states. Based on this, a complementarity relation between the quantum coherence and the mixedness is established. We then derive the quantum uncertainty relations of the geometric coherence on two and three general measurement bases in terms of the incompatibility respectively, which turn out to be state-independent for pure states. These trade-off relations provide the limit to the amount of quantum coherence. As a byproduct, the complementarity relation between the minimum error probability for discriminating a pure-states ensemble and the mixedness of quantum states is established.

A Game-Theoretic Approach to Achieve Covert Communication in Cognitive Radio Systems

In this paper, we investigate a covert cooperative cognitive radio (CCCR) system, where multiple primary transmitters (PTs) transmit information with the aid of multiple secondary transmitters (STs) in order to conserve power consumption. In return, by opportunistically accessing PT's spectrum, STs send confidential information to a secondary receiver (SR) in the presence of external eavesdropper (Eve). Aiming to maximize covert rate, we model our CCCR framework as an evolutionary game in which each PT and ST make decisions based on their utility histories. By introducing the evolutionary game, we propose a game-oriented secondary user scheduling (G-SUS) scheme to find when multiple STs determine to access PTs' spectrum. Moreover, we analyze covert performance of the proposed scheme and obtain a closed-form expression for Eve's detection error probability. Numerical results show that, the minimal detection error probability at Eve can be effectively impacted by creating channel uncertainty and noise uncertainty. Furthermore, the results also demonstrate the proposed scheme can converge quickly, which stimulates its practical implementation.

ANALYSIS OF ROUTING PROTOCOLS EFFECTIVENESS IN COMPUTER NETWORKS

The main task of networks is to transport information from the sending computer to the receiving computer. In most cases, you need to make several transfers to do this. The problem of choosing a path is solved by routing algorithms. The routing algorithm must have well-defined properties: reliability, correctness, stability, simplicity and optimality. The latter property is not as transparent as it may seem at first glance, it all depends on which or which parameters are optimized. This task is sometimes not at all easy even for relatively simple local networks. Optimization parameters may include minimum delivery delay, maximum throughput, minimum price, maximum reliability, or minimum error probability. In this paper, reactive, proactive and hybrid routing protocols are considered. When making their choice, we relied on the method of hierarchy analysis. Based on the results obtained during the simulation of a network with video conference traffic, a matrix was constructed for each of the criteria studied. The protocols were compared in terms of the possibility of information loss. The results of the research can be useful in the course of building modern computer networks.

Covert communications in a compress-and-forward relay system

In this paper, we study covert communications strategies in a compress-and-forward (CF) relay system. Along with a public message to a destination node via a CF relay, a source node attempts to transmit a covert message while evading the surveillance of the CF relay. We identify the optimal power distribution between the public and covert messages and the optimal amount of compression that maximize the covert rate subject to the minimum detection error probability requirement. Our provided solutions also reveal that both the power distribution and the achievable covert rate are identical to that of an equivalent amplify-and-forward (AF) relay system if an adequate quantization codebook with the optimal compression is employed. The numerical results verify the effectiveness of the optimal solutions and confirm our analyses.

Utilizing double-shadowed Rician fading over energy detector-based spectrum sensing with diversity reception

This study explores the capabilities of an Energy Detector (ED)-based Cognitive Radio (CR) device in a double shadowed (DS) Rician distribution environment for spectrum sensing. The effectiveness of the ED is evaluated using metrics such as average probability of detection (PD) and average area under the receiver operating characteristics curve (AUC). The investigation extends to single-input-multiple-output (SIMO) channel conditions, considering maximal ratio combining (MRC) and square-law selection (SLS) diversity techniques. To provide a comprehensive understanding of the system, the study also includes the asymptotic performance analysis of diversity techniques, including MRC, equal gain combining (EGC), and selection combining (SC). The findings indicated a notable enhancement in detection performance through the application of diversity combining techniques. Among the evaluated schemes, MRC demonstrated the most favorable results, followed EGC, while SC yielded comparatively weaker outcomes. To further minimize error probability, the detection threshold is optimized, resulting in improved energy detection statistics, even in scenarios involving diversity. The formulations are additionally applied to cooperative spectrum sensing (CSS). It further noted that fading parameter directly influence the array gain, while diversity gain only depends on the number of diversity branches. The accuracy and validity of the proposed results are confirmed through Monte-Carlo simulation.

SYSTEM ANALYSIS OF MAINTENANCE OF THE ELECTRICAL COMPLEX

Modern electronic devices are characterized by complex circuit design solutions, which requires performing their design using high-performance circuit design computer-aided design systems. The development of such computer-aided design systems is associated with significant expenditure of time and labor resources and should be based on new approaches to the construction of mathematical and software, taking into account the specific features of the subject area and the nature of the tasks to be solved. In this paper, the problems associated with the modeling of maintenance of electrical complex are considered. A methodology for predicting components based on a single attribute within an experiment is demonstrated. The criterion in terms of risk assessment for the consumer is considered. The results of modeling the main parameters characterizing the quality of electrolytic capacitors are presented. After the tests are completed, the value of the predicted parameter is determined for each realization. The optimum value of leakage current, providing the minimum probability of error, for tantalum electrolytic capacitors with nominal capacity is shown. The results of the research can be useful for specialists working on electrical engineering complexes.

Geometric discord of tripartite quantum systems

We study the quantification of geometric discord for tripartite quantum systems. Firstly, we obtain the analytic formula of geometric discord for tripartite pure states. It is already known that the geometric discord of pure states reduces to the geometric entanglement in bipartite systems, the results presented here show that this property is no longer true in tripartite systems. Furthermore, we provide an operational meaning for tripartite geometric discord by linking it to quantum state discrimination, that is, we prove that the geometric discord of tripartite states is equal to the minimum error probability to discriminate a set of quantum states with von Neumann measurement. Lastly, we calculate the geometric discord of three-qubit Bell diagonal states and then investigate the dynamic behavior of tripartite geometric discord under local decoherence. It is interesting that the frozen phenomenon exists for geometric discord in this scenario.

M-Ary Direct Modulation Chirp Spread Spectrum for Spectrally Efficient Communications

Spread spectrum techniques, such as the Chirp Spread Spectrum (CSS) used by LoRa technology, are important for machine-to-machine communication in the context of the Internet of Things. They offer high processing gain, reliable communication over long ranges, robustness to interference and noise in harsh environments, etc. However, these features are compromised by their poor spectral efficiency, resulting in a very low data transmission rate. This paper deals with a spectrally efficient variant of CSS. The system uses M-ary phase keying to modulate the data and exploits CSS’s properties to transmit the modulated symbols as overlapping chirps. The overlapping of chirp signals may affect the system performance due to inter-symbol interference. Therefore, we analyse the relationship between the number of overlaps and the effect of inter-symbol interference (ISI), and we also determine the BER expression as a function of the number of overlaps. Finally, we derive the optimal number of overlapping symbols that corresponds to the minimum error probability.

Multi-antenna Jammer assisted covert communications in data collected IoT with NOMA

In this paper, we investigate covert communications in data collected IoT with NOMA, where the paired sensor nodes S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> and S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> transmit covert messages to a legitimate receiver (Bob) in the presence of a Warden (Willie). To confuse the detection at Willie, an extra multi-antenna friendly jammer (Jammer) has been employed to transmit artificial noise (AN) with random power. Based on the CSI of Willie is available or not at Jammer, three AN transmission schemes, including null-space artificial noise (NAN), transmit antenna selection (TAS), and zero-forcing beamforming (ZFB), are proposed. Furthermore, the closed-form expressions of expected minimum detection error probability (EMDEP) and joint connection outage probability (JCOP) are derived to measure covertness and reliability, respectively. Finally, the maximum effective covert rate (ECR) is obtained with a given covertness constraint. The numerical results show that ZFB scheme has the best maximum ECR in the case of the number of antennas satisfies N > 2, and the same maximum ECR can be achieved in ZFB and NAN schemes with N =3D 2. Moreover, TAS scheme also can improve the maximum ECR compared with the benchmark scheme (i.e., signal-antenna jammer). In addition, a proper NOMA node pairing can further improve the maximum ECR.

Joint Trajectory and Resource Optimization for Covert Communication in UAV-Enabled Relaying Systems

A novel covert communication framework is proposed to enhance the privacy of the unmanned aerial vehicle (UAV)-enabled relaying systems. Specifically, the full-duplex (FD) UAV covertly relays data from each ground sensor to remote base station (BS) against a warden (Willie). Considering a noise uncertainty model, the minimum detection error probability (DEP) of Willie is first derived. Under the constraint of the derived DEP, the minimum average covert transmission rate (ACTR) is then maximized by jointly designing the sensor association, the UAV transmit power, and the UAV trajectory. A low-complexity algorithm based on the penalty successive convex approximation (P-SCA) is further invoked to achieve the locally optimal solution. Finally, numerical results show the effectiveness of the proposed framework and reveal some insights, i.e., increasing uncertainty at Willie can improve the covertness performance.

Optimal Position and Target Rate for Covert Communication in UAV-Assisted Uplink RSMA Systems

With the explosive increase in demand for wireless communication, the issue of wireless communication security has also become a growing concern. In this paper, we investigate a novel covert communication for unmanned aerial vehicle (UAV)-assisted uplink rate-splitting multiple access (RSMA) systems, where a UAV adopts the rate-splitting (RS) strategy to increase the total transmission rate while avoiding deteriorating the covert transmission of a ground user. In the proposed system, a ground user and a UAV adopt the RSMA scheme to simultaneously communicate with a base station surveilled by an evil monitor. The UAV acts as both the transmitter and the friendly jammer to cover the ground user’s transmission with random power. To maximize the expected sum rate (ESR), we first study the RS strategy and obtain the optimal power allocation factor. Then, the closed-form of minimum detection error probability (DEP), ESR, and optimal target rate of the UAV are derived. Constrained by the minimum DEP and expected covert rate (ECR), we maximize the ESR by optimizing the position and target rate of the UAV. Numerical results show that the proposed scheme outperforms the traditional NOMA systems in terms of ESR with the same DEP and ECR.

Minimum probability of error of list M-ary hypothesis testing

Abstract We study a variation of Bayesian $M$-ary hypothesis testing in which the test outputs a list of $L$ candidates out of the $M$ possible upon processing the observation. We study the minimum error probability of list hypothesis testing, where an error is defined as the event where the true hypothesis is not in the list output by the test. We derive two exact expressions of the minimum probability or error. The first is expressed as the error probability of a certain non-Bayesian binary hypothesis test and is reminiscent of the meta-converse bound by Polyanskiy, Poor and Verdú (2010). The second, is expressed as the tail probability of the likelihood ratio between the two distributions involved in the aforementioned non-Bayesian binary hypothesis test. Hypothesis testing, error probability, information theory.

Novel Fano type lower bounds on the minimum error probability of list $M$-ary hypothesis testing

he problem of list $M$-ary hypothesis testing with fixed list size $L< M$ is considered. Based on some random observation, the test outputs a list of $L$ candidates out of $M$ possible hypotheses. The probability of list error is defined as the probability of the event that the list output by the test does not contain the true hypothesis that has generated the observation. An identity is derived that relates the minimum average probability of error of the optimal list hypothesis test to the minimum average probability of error of an optimal maximum a posteriori probability decision rule. The latter decides among an alternative set of hypotheses corresponding to all possible $L$-component mixtures of the distributions that characterize the observation under the original $M$ candidate hypotheses. As an application, the proposed identity is employed to obtain novel Fano type lower bounds on the minimum error probability of list $M$-ary hypothesis testing.

Zero-forcing Beamforming for Jamming Aided Covert Communication in MIMO Systems

This paper investigates covert wireless communication in a multi-input multi-output (MIMO) system, where a multi-antenna transmitter transmits covert signal to a multi-antenna receiver with the assistance of a multi-antenna jammer employing zero-forcing (ZF) beamforming to avoid detection by a warden equipped with single antenna. For the given scenario, we first provide theoretical modeling for the minimum detection error probability at warden and covert rate from transmitter to receiver. We then explore the optimal beamformer design of the jammer to maximize the covert rate, subjecting to the constraints of covertness, upper bounds of transmitter and jammer transmit power, and beamformer on jammer. We further devise an iterative algorithm to determine the related optimal precoding matrix for covert rate maximization. Finally, we provide extensive numerical results to illustrate the impact of system parameters on covert performance.

HybNet: A Hybrid Deep Learning-Matched Filter Approach for IoT Signal Detection

Random access schemes are widely used in IoT wireless access networks. They enable a reduced complexity and overcome power consumption constraints. Nevertheless, random access results in high packet losses which are caused by overlapping transmissions. Signal detection methods for digital modulation techniques are typically based on the well-established <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">matched filter</i> , which is proven as the optimal filter under additive white Gaussian noise for minimizing error probability. However, with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">colored</i> interference arising from the overlapping IoT transmissions, deep learning approaches are being considered a suitable alternative. In this paper, we present a hybrid framework, dubbed as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">HybNet</i> , that alternates between deep learning and match filter pathways based on the perceived interference level. This helps the detector to work in a broader range of conditions, optimally leveraging both the matched filter and deep learning advantages. We compare the performance of several possible data modalities and detection architectures concerning the interference-to-noise ratio, demonstrating that leveraging domain knowledge by pre-processing the input data in conjunction with the proposed HybNet surpasses the complex conjugate matched filter performance under interference-limited scenarios.