Terms Of Error Probability Research Articles

Performance Analysis of Classical Data Transmission Over a Quantum Channel in the Presence of Atmospheric Turbulence

This paper presents the performance analysis of classical data transmission over a quantum channel in the presence of atmospheric turbulence. To transmit classical data, quantum coherent states are modulated over a log-normal turbulent channel for satellite-to-ground applications. The expression for the number of photons in the turbulent coherent state is approximated. Performance analysis is done in terms of error probability, channel capacity, and quantum bit error rate (QBER). The simulation results are presented using the Monte-Carlo simulation method. Numerical results show that the error performance improves with increasing the number of signal photons. However, for turbulence strength greater than 0.8, QBER increases more rapidly with a higher number of signal photons. Hence, a trade-off is essential between an achievable QBER and the number of signal photons.

Landauer Bound and Continuous Phase Transitions.

In this review, we establish a relation between information erasure and continuous phase transitions. The order parameter, which characterizes these transitions, measures the order of the systems. It varies between 0, when the system is completely disordered, and 1, when the system is completely ordered. This ordering process can be seen as information erasure by resetting a certain number of bits to a standard value. The thermodynamic entropy in the partially ordered phase is given by the information-theoretic expression for the generalized Landauer bound in terms of error probability. We will demonstrate this for the Hopfield neural network model of associative memory, where the Landauer bound sets a lower limit for the work associated with 'remembering' rather than 'forgetting'. Using the relation between the Landauer bound and continuous phase transition, we will be able to extend the bound to analog computing systems. In the case of the erasure of an analog variable, the entropy production per degree of freedom is given by the logarithm of the configurational volume measured in units of its minimal quantum.

Анализ и оптимизация схем кодирования для каналов с рэлеевскими замираниями

Conventional approach to perform error-correcting decoding in channels with memory is an adoption of interleaving, which increases the receiver complexity and delay. In order to avoid these limitations, approaches for adapting an error-correcting scheme for memory channels may be used. One approach is to use error-correcting codes with modified design and decoding procedure, taking into account the presence of error bursts in the channel. Another approach to adapting the coding scheme for burst error correction is to use product codes with iterative decoding algorithms. Component codes of product codes themselves may not be able to correct error bursts, but a two-dimensional structure of product codes operating as an artificial interleaver and iterative decoding allow for correction of grouping errors. Purpose: The purpose of the study is to analyze the methods of error-correcting code adaptation to burst error correction in channels with memory in order to reduce the probability of error. Results: The study considered methods of error-correcting code scheme adaptation for low-density parity-check codes, polar codes, and product codes for burst error correction in Gilbert-Elliott channel (GE) and correlated Rayleigh fading channel with different correlation coefficients. Degree distribution of low-density parity-check code was optimized for GE channel. The influence of selected parameters of product code component codes on burst error correction in the GE channel was analyzed. The structure of the polar code has been optimized using a genetic algorithm for the correlated Rayleigh channel, which outperforms the 5G polar code design in terms of error probability. Discussion: Existing error-correcting code schemes do not provide theoretically possible limits, so the question remains of developing coding and decoding schemes capable of reaching theoretical limits.

Perfect and Quasi-Perfect Codes for the Bosonic Classical-Quantum Channel

We explore perfect and quasi-perfect codes for the Bosonic channel, where information is generated by a laser and conveyed in the form of coherent states. In particular, we consider the phase-modulation codebook for coherent states in a Bosonic channel. We show that these phase-modulation codes are quasi-perfect as long as the cardinality of the code is the same as the dimension of the coherent states. These codes feature the smallest error probability among all codes of the same cardinality and the same dimension of the channel Hilbert space. We study the performance of these codes in terms of error probability, incorporating the degradation caused by a depolarizing or an erasure quantum channel.

Rate Compatible Gaussian Modulation

This letter proposes a rate compatible Gaussian modulation (RCGM) for wireless channels. RCGM constructs a high-density non-uniformly spaced Gaussian constellation, and optimizes the mapping schemes by maximizing the Harmonic mean. The information bits are randomly sampled by a sparse matrix whose weights are all powers of 2, then the sampled bits are modulated to the high-density constellation following the mapping scheme. The number of the modulated symbols can be adjusted at a fine granularity according to the channel condition so as to achieve seamless rate adaptation. Both numerical and simulation results show that RCGM outperforms other rate adaptive modulations, such as rate compatible modulation and analog fountain code, in terms of error probability and throughput. RCGM can provide a capacity approaching modulation scheme in a wide range of signal-to-noise ratio even without channel coding.

Unsourced Random Massive Access With Beam-Space Tree Decoding

The core requirement of massive Machine-Type Communication (mMTC) is to support reliable and fast access for an enormous number of machine-type devices (MTDs). In many practical applications, the base station (BS) only concerns the list of received messages instead of the source information, introducing the emerging concept of unsourced random access (URA). Although some massive multiple-input multiple-output (MIMO) URA schemes have been proposed recently, the unique propagation properties of millimeter-wave (mmWave) massive MIMO systems are not fully exploited in conventional URA schemes. In grant-free random access, the BS cannot perform receive beamforming independently as the identities of active users are unknown to the BS. Therefore, only the intrinsic beam division property can be exploited to improve the decoding performance. In this paper, a URA scheme based on beam-space tree decoding is proposed for mmWave massive MIMO system. Specifically, two beam-space tree decoders are designed based on hard decision and soft decision, respectively, to utilize the beam division property. They both leverage the beam division property to assist in discriminating the sub-blocks transmitted from different users. Besides, the first decoder can reduce the searching space, enjoying a low complexity. The second decoder exploits the advantage of list decoding to recover the miss-detected packets. Simulation results verify the superiority of the proposed URA schemes compared to the conventional URA schemes in terms of error probability.

Design and Implementation of Optimum LSD Coded Signal Processing Algorithm in the Multiple-Antenna System for the 5G Wireless Technology

The 5G system requires an optimum coding technique to achieve the high diversity gain, low bit error rate (BER), and low detection complexity. Various coding techniques were developed in recent times for improving the diversity performance of the MIMO systems. Space-time-coding (STC) is used to fulfill the requirement of handling large data flow in the 5G wireless communications. It is highly required to optimize the orthogonal nature of STC. The paper proposed a novel design of the optimum linearly scalable dispersion code (O-LSDC). In this paper, an optimum coefficient-based O-LSDC is designed based on the elementary matrix operations, unitary matrix normalization technique, and coefficient mapping strategy. Mapped coefficients are linearly solved for optimum value estimation. To find the optimum solution of the LSDC codes, five cases of LSDC are defined based on the scaling coefficients and then performance is evaluated against the BER vs. SNR. Evaluating the simulation results in terms of error probabilities for the five different orthonormal LSDC, this work simulates the system for multiple antennas using the Rayleigh fading MIMO system model. Also, evaluating the impact of the proposed LSDC over the BER performance for the varied number of Monte Carlo iterations, then the performance graph is plotted for multiple-antennas system. The proposed O-LSDC under Rayleigh fading channel using the M-PSK modulation enhances the performance of the 5G and beyond communication system in terms of BER and SNR.

Modeling Molecular Communication Channel in the Biological Sphere With Arbitrary Homogeneous Boundary Conditions

Diffusion-based molecular communication (DMC) is envisioned to realize nanonetworks for health applications. Inspired by sphere-like entities in the body, modeling diffusion channel in the biological sphere is motivated. The boundary condition in such biological environments is considered as homogeneous boundary conditions (HBC) that can simply model the molecular processes over biological barriers, e.g., carrier-mediated transport and transcytosis over the blood vessel walls. In this letter, we model the diffusive communication channel between a point source transmitter and a transparent receiver arbitrarily located inside a spherical environment with HBC. To this end, the concentration Green’s function (CGF) is analytically derived in the Fourier domain. Statistics of the signal received at the receiver is computed based on the derived CGF to obtain the analytical results. The analytical results are accurately confirmed with particle-based simulation (PBS). The performance of a simple on-off keying modulation scheme is also examined in terms of error probability.

On Scheduling Performance of Multi-User Full-Duplex Two-Way Relaying System With Rician Distributed RSI

In this paper, a multi-user full-duplex (FD) two-way relaying system with decode-and-forward protocol is considered where all the nodes are assumed to be mobile and to have FD abilities. The residual self-interference (RSI) at each node is modeled as a Rician distributed random variable and the effect of mobility is incorporated by adopting the first order auto-regressive (AR) model. Then, the signal-to-interference-plus-noise-ratio (SINR) based scheduling schemes namely random scheduling, absolute channel power-based (CPB) scheduling, hybrid scheduling, and normalized CPB scheduling, are modified and the user pair selection is carried out on the basis of instantaneous channel statistics. The performance of the considered framework is analyzed for the modified scheduling schemes in terms of error probability and average rate. Next, the closed-form expressions for the symbol error probability (SEP) and average rate are derived for independent and non-identically distributed Rayleigh fading channels. Also, the numerical analysis highlighting the impact of user mobility and imperfect channel estimation on the scheduling strategies, fairness is presented. Furthermore, the impacts of the degree of traffic asymmetry, scheduling fairness, user mobility, channel estimation errors and RSI on the system performance are investigated. Numerical results are validated through the Monte Carlo simulations.

A Novel Extension to Craig’s Q-Function Formula and Its Application in Dual-Branch EGC Performance Analysis

A novel identity for the Gaussian Q-function of the sum of two non-negative variables is introduced as an extension of Craig’s Q-function formula. It is shown that this new identity provides a unified framework in the performance analysis of dual-branch equal-gain combining (EGC) diversity, similar to that of Craig’s Q-function formula for maximum ratio combining diversity. Then, the performance of dual correlated branch EGC in Nakagami- $m$ fading is studied using this novel approach. For coherent modulations with error probabilities in terms of the Gaussian Q-function, it is shown that the average error probability of the dual correlated branch EGC in Nakagami- $m$ fading is the same as the average error probability of a modeled single-channel receiver in the same fading environment. Using this fact, simple exact and approximate closed-form expressions for this average error probability are derived. The analytical results are verified and illustrated by numerical results and computer simulations.

Pulse parity modulation for impulse radio UWB transmission based on non-coherent detection

To enhance the error performance of impulse radio UWB transceivers, we introduce in this manuscript a novel modulation scheme based on exploiting the symmetry properties of transmitted waveforms. Parity Modulation utilizes odd versus even pulses to represent binary data, while the detector relies on a time reverser and non-coherent cross correlator. The analytical expression of power spectral density has been derived; then, considering different orders of Gaussian derivatives as pulse waveforms, the spectral characteristics have been optimized to comply with the UWB emission regulation. The bit error rate formula in an AWGN channel has been developed, while our simulation measurements showed a significant performance gain for 2 Gbps Parity over 1 Gbps Pulse Position Modulation and 2 Gbps On Off Keying. A reference-based parity scheme has been eventually proposed to enhance robustness against multi-path effects, interesting results have been achieved in terms of error probability in a realistic channel, with a compromise between data rate and complexity.

Optimization of distributed detection in energy harvesting wireless sensor networks with multiple antenna fusion center

AbstractThis paper addresses the detection improvement using multiple antenna fusion center (FC) and optimal collaboration among sensors with energy harvesting (EH) capability in WSNs. Using multiple antennas at FC, we benefit from the available fundamental spatial diversity in distributed WSN. We formulate to maximize the probability of collaborative detection based on parameters of collaboration among sensors and the energy of each sensor for the different scenarios as the optimization problem. In particular, we consider several practical constraints for EH and battery energy storage to maintain network connectivity. The objective function is the nonconvex function so the optimization problem is obtained as the nonconvex problem. To resolve this issue, the objective function is converted to a convex function using a relaxation method, and an optimum solution is obtained for this problem using local optimum values. The numerical results show the impact of the different parameters on the performance of the collaborative decision. These results also demonstrate that using distributed spatial diversity at FC by multiple antennas leads to a better decision in terms of error probability, and distributed wireless sensor‐enabled with EH capability results to more robust network connectivity in practice.

Cube-Split: A Structured Grassmannian Constellation for Non-Coherent SIMO Communications

In this paper, we propose a practical structured constellation for non-coherent communication with a single transmit antenna over Rayleigh flat and block fading channel without instantaneous channel state information. The constellation symbols belong to the Grassmannian of lines and are defined up to a complex scaling. The constellation is generated by partitioning the Grassmannian of lines into a collection of bent hypercubes and defining a mapping onto each of these bent hypercubes such that the resulting symbols are approximately uniformly distributed on the Grassmannian. With a reasonable choice of parameters, this so-called cube-split constellation has higher packing efficiency, represented by the minimum distance, than the existing structured constellations. Furthermore, exploiting the constellation structure, we propose low-complexity greedy symbol decoder and log-likelihood ratio computation, as well as an efficient way to associate it to a multilevel code with multistage decoding. Numerical results show that the performance of the cube-split constellation is close to that of a numerically optimized constellation and better than other structured constellations. It also outperforms a coherent pilot-based scheme in terms of error probability and achievable data rate in the regime of short coherence time and large constellation size.

Dependence of Error Probability on the telegraph Distortion Value

The transmission of messages via non-stationary communication channels is made in conditions of adapting the receiving and transmitting equipment to the communication conditions. Mode of adaptation to communication conditions requires rapid assessment of the communication channel quality. The most obvious criterion for assessing the quality of a non-stationary communication channel is the constantly changing value of the elements error probability in the transmitted message. However, assessing the error probability of message elements requires significant time intervals, which may exceed the time of stationary state of the communication channel. It is known that the error probability of message elements is uniquely related to the value of telegraph distortions. The estimation of the telegraph distortion value requires much less time compared to the time required to estimate the probability of errors. In this case, the indirect estimation of the error probability by the value of the telegraph distortion can be made relatively quickly at an interval that is many times less than the stationary state interval of the communication channel. In this regard, the possibility of indirect estimation of error probability in terms of telegraph distortion is relevant for receiving and transmitting equipment with adaptation to communication conditions.

On the Performance of QPSK Modulation Over Downlink NOMA: From Error Probability Derivation to SDR-Based Validation

In this paper, we study the performance of QPSK modulation in the context of multi-user downlink NOMA with a successive interference canceller (SIC) at the receiver side. The first objective is to evaluate the benefit of such a technique in terms of error probability, regardless of the number of involved users. Analytical derivations on its closed-form have been verified by both simulation and experimental validation. The article uses numerical simulations not only to corroborate the tightness of our theoretical expressions, but also to analyze the problem of power allocation in the two and three users cases. Finally, this paper provides an interplay between NOMA and software radio by building an experimental validation testbed.

Robust image watermarking using sample area quantization

Digital watermarking is a way to protect the intellectual property of digital media. Among different algorithms, Quantization Index Modulation (QIM) is one of the popular methods in designing a watermark system. In this paper, a sample area quantization method is proposed for robust watermarking of digital images. First, the samples of the host signal form a polygon and low frequency wavelet coefficients of the carrier image is considered as the host sample. A watermark digit is embedded by quantizing the area of the polygon. Then, in order to minimize the distortion, the watermarked samples are obtained as close as possible to the host samples by solving an optimization problem while maintaining the quantized area at its fixed value. The optimization problem is solved using the gradient descend method. Finally, a maximum likelihood detector is designed to extract the watermark digits, assuming a Gaussian distribution for the host signal samples. The performance of the proposed method is theoretically obtained in terms of error probability in the presence of additive white Gaussian noise. Theoretical results are verified using simulation with artificial signals. The proposed method is compared to the state-of-the-art method under different attacks including: noise addition, JPEG compression, filtering, and geometrical attacks. The results confirm that the proposed method outperforms the other ones in terms of error probability against different attacks. The results also show that in the trade-off between robustness, distortion and capacity, by decreasing capacity the two other factors could be improved simultaneously.

Classification using sequential order statistics

Whereas discrimination methods and their error probabilities were broadly investigated for common data distributions such as the multivariate normal or t-distributions, this paper considers the case when the recorded data are assumed to be observations from sequential order statistics. Random vectors of sequential order statistics describe, e.g., successive failures in a k-out-of-n system or in other coherent and load sharing systems allowing for changes of underlying lifetime distributions caused by component failures. Within this framework, the Bayesian two-class discrimination approach with known prior probabilities and class parameters is considered, and exact and asymptotic formulas for the error probabilities in terms of Erlang and hypoexponential distributions are derived. Since the Bayesian classifier is closely related to Kullback–Leibler’s information distance, this approach is extended by invoking other divergence measures such as Jeffreys and Renyi’s distance. While exact formulas for the misclassification rates of the resulting distance-based classifiers are not available, inequalities among the corresponding error probabilities are derived. The performance of the applied classifiers is illustrated by some simulation results.

Wireless Powered Communications With Finite Battery and Finite Blocklength

We analyze a wireless communication system with finite block length and finite battery energy, under quasi-static Nakagami-m fading. Wireless energy transfer is carried out in the downlink while information transfer occurs in the uplink. Transmission strategies for scenarios with/without energy accumulation between transmission rounds are characterized in terms of error probability and energy consumption. A power control protocol for the energy accumulation scenario is proposed and results show the enormous impact on improving the system performance, in terms of error probability and energy consumption. The numerical results corroborate the existence and uniqueness of an optimum target error probability, while showing that a relatively small battery could be a limiting factor for some setups, specially when using the energy accumulation strategy.

Base Station Ordering for Emergency Call Localization in Ultra-Dense Cellular Networks

This paper proposes the base station ordering localization technique (BoLT) for emergency call localization in cellular networks. Exploiting the foreseen ultra-densification of the next-generation (5G and beyond) cellular networks, we utilize higher order Voronoi tessellations to provide ubiquitous localization services that are in compliance to the public safety standards in cellular networks. The proposed localization algorithm runs at the base stations (BSs) and requires minimal operation from agents (i.e., mobile users). Particularly, BoLT requires each agent to feedback a neighbor cell list that contains the order of neighboring BSs based on the received signal power in the pilots sent from these BSs. Moreover, this paper utilizes stochastic geometry to develop a tractable mathematical model to assess the performance of BoLT in a general network setting. The goal of this paper is to answer the following two fundamental questions: 1) how many BSs should be ordered and reported by the agent to achieve a desirable localization accuracy? and 2) what is the localization error probability given that the pilot signals are subject to shadowing? Assuming that the BSs are deployed according to a Poisson point process, we answer these two questions via characterizing the tradeoff between the area of location region and the localization error probability in terms of the number of BSs ordered by the agent. The results show that reporting the order of six neighboring BSs is sufficient to localize the agent within 10% of the cell area. Increasing the number of reported BSs to ten confines the location region to 1% of the cell area. This would translate to the range of a few meters to decimeters in the foreseen ultra-dense 5G networks.

Quick Performance Assessment of Improved Nyquist Pulses

An explanation is proposed for the improved behavior of the improved Nyquist pulses with an asymptotic decay rate of t-2 when sampled with a timing offset. Three figures of merit that indicate the energy distribution into the sidelobes of the time response and allow a quick assessment of their performance in terms of error probability when the impulse response is sampled with a timing error have been proposed and verified on several improved Nyquist pulses reported in the literature. In order to check the validity of the proposed figures of merit a novel family of Nyquist pulses denoted as power sine was introduced. Using the proposed approach the design process was expedited as the volume of necessary calculations was significantly decreased. To explain the difference in close pulse performance a figure of merit based on limited ISI distortion was introduced.