Additive Noise Channel Research Articles

Classical capacity of quantum non-Gaussian attenuator and amplifier channels

We consider a quantum bosonic channel that couples the input mode via a beam splitter or two-mode squeezer to an environmental mode that is prepared in an arbitrary state. We investigate the classical capacity of this channel, which we call a non-Gaussian attenuator or amplifier channel. If the environment state is thermal, we of course recover a Gaussian phase-covariant channel whose classical capacity is well known. Otherwise, we derive both a lower and an upper bound to the classical capacity of the channel, drawing inspiration from the classical treatment of the capacity of non-Gaussian additive-noise channels. We show that the lower bound to the capacity is always achievable and give examples where the non-Gaussianity of the channel can be exploited so that the communication rate beats the capacity of the Gaussian-equivalent channel (i.e. the channel where the environment state is replaced by a Gaussian state with the same covariance matrix). Finally, our upper bound leads us to formulate and investigate conjectures on the input state that minimizes the output entropy of non-Gaussian attenuator or amplifier channels. Solving these conjectures would be a main step toward accessing the capacity of a large class of non-Gaussian bosonic channels.

Performance of Relaying System with NOMA over Symmetric a-Stable Noise Channels

Objectives: This paper investigates the performance of a candidate 5G transmission system technique that is Non-Orthogonal Multiple Access (NOMA) over α-stable channels. This type of channel gets more attention in the research community because of its ability to model new IoT scenarios. However, there is a research gap in applying this type of channel to different wireless communications scenarios. In this work, we envision a scenario where users employ NOMA communications in the presence of an obstacle. As our mathematical analysis and simulation results show, there is a significant difference in performance when considering α-stable channels. Methods: To characterize the performance of the proposed noise channel, performance metrics such as outage probability and achievable rate are discussed. More particularly, we derive expressions for both outage probability and achievable rate for three NOMA users, considering the near user as a relay. In this paper, we consider additive symmetric α-stable noise channels with alpha α ∈ (1, 2). We present expressions for achievable rate and outage probability for each user (near, middle, and far) and investigate its behavior for different values of alpha (α). Findings: Based on the simulation results, it is shown that the high achievable rate observed for low alpha values while reduced as alpha is increased. Also, due to the influence of alpha, the outage probability is highly affected by α for small rate thresholds (Ro). In an envisioned scenario of three users with only one user forwarding the transmission to the other two, our results show that the near and middle users’ outage probability decreases as alpha α increases. Novelty: Despite this extensive study of the NOMA on individual channels, transmission under α-stable channel is not considered to the best of the authors’ knowledge. Keywords: NOMA, relaying, Cooperative Non-Orthogonal Multiple Access, Symmetric α-Stable Noise Channels, Achievable rate

The entropic doubling constant and robustness of Gaussian codebooks for additive-noise channels

The entropic doubling constant and robustness of Gaussian codebooks for additive-noise channels

Identification Over Additive Noise Channels in the Presence of Feedback

We analyze deterministic message identification via channels with non-discrete additive white noise and with a noiseless feedback link under both average power and peak power constraints. The identification task is part of Post Shannon Theory. The consideration of communication systems beyond Shannon’s approach is useful in order to increase the efficiency of information transmission for certain applications. We propose a coding scheme that first generates infinite common randomness between the sender and the receiver. If the channel has a positive message transmission feedback capacity, for given error thresholds and sufficiently large blocklength this common randomness is then used to construct arbitrarily large deterministic identification codes. In particular, the deterministic identification feedback capacity is infinite regardless of the scaling (exponential, doubly exponential, etc.) chosen for the capacity definition. Clearly, if randomized encoding is allowed in addition to the use of feedback, these results continue to hold.

Capacity-Achieving Input Distributions of Additive Vector Gaussian Noise Channels: Even-Moment Constraints and Unbounded or Compact Support.

We investigate the support of a capacity-achieving input to a vector-valued Gaussian noise channel. The input is subjected to a radial even-moment constraint and is either allowed to take any value in Rn or is restricted to a given compact subset of Rn. It is shown that the support of the capacity-achieving distribution is composed of a countable union of submanifolds, each with a dimension of n-1 or less. When the input is restricted to a compact subset of Rn, this union is finite. Finally, the support of the capacity-achieving distribution is shown to have Lebesgue measure 0 and to be nowhere dense in Rn.

Learning Maximum Margin Channel Decoders

The problem of learning a channel decoder is considered for two channel models. The first model is an additive noise channel whose noise distribution is unknown and nonparametric. The learner is provided with a fixed codebook and a dataset comprised of independent samples of the noise, and is required to select a precision matrix for a nearest neighbor decoder in terms of the Mahalanobis distance. The second model is a non-linear channel with additive white Gaussian noise and unknown channel transformation. The learner is provided with a fixed codebook and a dataset comprised of independent input-output samples of the channel, and is required to select a matrix for a nearest neighbor decoder with a linear kernel. For both models, the objective of maximizing the margin of the decoder is addressed. Accordingly, for each channel model, a regularized loss minimization problem with a codebook-related regularization term and hinge-like loss function is developed, which is inspired by the support vector machine paradigm for classification problems. Expected generalization error bounds for the error probability loss function are provided for both models, under optimal choice of the regularization parameter. For the additive noise channel, a theoretical guidance for choosing the training signal-to-noise ratio is proposed based on this bound. In addition, for the non-linear channel, a high probability uniform generalization error bound is provided for the hypothesis class. For each channel, a stochastic sub-gradient descent algorithm for solving the regularized loss minimization problem is proposed, and an optimization error bound is stated. The performance of the proposed algorithms is demonstrated through several examples.

Implementation on SDR platform of algorithms for noncoherent reception of optimal signals built on the basis of eigenfunctions

Formulation of the problem. When transmitting data at speeds above the Nyquist barrier, the algorithmic and computational complexity of radio modems increases significantly, especially with incoherent signal reception. Non-coherent reception algorithms can be implemented on a software-defined radio platform, on which optimal signals are formed and received. The ability to programmatically change the radio frequency parameters of signals without making structural changes to the transmit-receive path can significantly reduce the computing resources of radio modems. The goal is to determine the possibility of practical implementation on the SDR platform (Software Defined Radio) of noncoherent processing algorithms with decision feedback with the choice of optimal values of the observation interval for symbol rates R>1/T using optimal signals built on the basis of eigenfunctions. Results. The possibility of using differential modulation of optimal signals, the forms of which are obtained as a result of solving an optimization problem in accordance with the criterion of the maximum decay rate of the spectrum level outside the occupied frequency band, is shown for packet data transmission protocols and the use of an incoherent processing algorithm in channels with additive Gaussian noise. It is shown that when using algorithms of incoherent element-by-element processing with optimization of the observation interval, it is possible to ensure stable reception of binary optimal signals up to transmission rates exceeding the Nyquist barrier by 1.66 times and for an error probability of 10–3, the energy loss is about 18 dB relative to potential noise immunity. The digital modem of optimal spectrally efficient signals, built on the basis of the SDR platform, makes it possible to conduct spectral and energy efficiency studies in real time in the presence of additive channel noise, and the influence of clock synchronization inaccuracies during packet messaging leads to energy losses of no more than 1 dB. Practical significance. The use of differential modulation of optimal signals can be used in digital television and radio broadcasting systems in the European digital television standards DVB-S2 (Digital Video Broadcasting Satellite Second Generation), DVB-T2 (Digital Video Broadcasting Terrestrial Second Generation).

Batch-Based Learning Consensus of Multiagent Systems With Faded Neighborhood Information.

This article addresses the batch-based learning consensus for linear and nonlinear multiagent systems (MASs) with faded neighborhood information. The motivation comes from the observation that agents exchange information via wireless networks, which inevitably introduces random fading effect and channel additive noise to the transmitted signals. It is therefore of great significance to investigate how to ensure the precise consensus tracking to a given reference leader using heavily contaminated information. To this end, a novel distributed learning consensus scheme is proposed, which consists of a classic distributed control structure, a preliminary correction mechanism, and a separated design of learning gain and regulation matrix. The influence of biased and unbiased randomness is discussed in detail according to the convergence rate and consensus performance. The iterationwise asymptotic consensus tracking is strictly established for linear MAS first to demonstrate the inherent principles for the effectiveness of the proposed scheme. Then, the results are extended to nonlinear systems with nonidentical initialization condition and diverse gain design. The obtained results show that the distributed learning consensus scheme can achieve high-precision tracking performance for an MAS under unreliable communications. The theoretical results are verified by two illustrative simulations.

The road to achieve the capacity of the three-way degraded broadcast channel

In this paper, we consider the discrete memory-less three-way degraded broadcast channel (3WDBC). The main contribution of this paper is in characterizing the capacity region of the discrete memoryless 3WDBC. To end up with this goal, we first develop the achievable region. Then, an outer bound to the capacity region is also derived. Next, the achievable region is shown to meet the outer bound such that the capacity is achieved. After that, the 3WDBC is shown to encompass many well-known multi-user networks such as (i) broadcast channel, (ii) multiple access channel, (iii) two-way channel, and (iv) relay channel. Further, the achievable capacity region is then extended to the additive Gaussian noise channel. Specifically, superposition encoding is employed at each user such that a given user can appropriately allocate its power to broadcast to the other two users. In this direction, two design criteria are theoretically presented and numerically investigated to show the range that the power allocation factor at each user may have.

Costa’s concavity inequality for dependent variables based on the multivariate Gaussian copula

AbstractAn extension of Shannon’s entropy power inequality when one of the summands is Gaussian was provided by Costa in 1985, known as Costa’s concavity inequality. We consider the additive Gaussian noise channel with a more realistic assumption, i.e. the input and noise components are not independent and their dependence structure follows the well-known multivariate Gaussian copula. Two generalizations for the first- and second-order derivatives of the differential entropy of the output signal for dependent multivariate random variables are derived. It is shown that some previous results in the literature are particular versions of our results. Using these derivatives, concavity of the entropy power, under certain mild conditions, is proved. Finally, special one-dimensional versions of our general results are described which indeed reveal an extension of the one-dimensional case of Costa’s concavity inequality to the dependent case. An illustrative example is also presented.

Design and Analysis of a Multi−Carrier Orthogonal Double Bit Rate Differential Chaotic Shift Keying Communication System

A new multi−carrier orthogonal double bit rate differential chaotic shift keying (MC−ODBR−DCSK) communication system is presented in this paper. With two composite signals generated by an orthogonal chaotic signal generator as reference signals, 2M bits of information data are transmitted on M−channel subcarriers, improving transmission speed and energy efficiency. In addition, the receiver does not require a radio frequency (RF) delay circuit to demodulate the received data, which makes the system easier to implement. This paper analyzes Data−energy−to−Bit−energy Ratio (DBR) of the system. The bit error rate performance of the system is simulated to verify the impact of parameters such as chaotic maps, semi-spread spectrum factor, and sub-carrier number. At the same time, the bit error rate performance of the MC−ODBR−DCSK system is compared with traditional DCSK systems in Rician fading and additive Gaussian white noise (AWGN) channels.

Performance analysis of SPAD-based optical wireless communication with OFDM

In recent years, there has been a growing interest in the use of a single-photon avalanche diode (SPAD) in optical wireless communication (OWC). The SPAD operates in the Geiger mode and can act as a photon counting receiver obviating the need for a transimpedance amplifier. Although a SPAD receiver can provide higher sensitivity compared to traditional linear photodetectors, it suffers from dead-time-induced nonlinearity. To improve the data rates of SPAD-based OWC systems, optical orthogonal frequency division multiplexing (OFDM) can be employed. This paper provides a comprehensive theoretical analysis of the SPAD-based OWC systems using direct-current-biased optical OFDM signaling considering the effects of signal clipping, SPAD nonlinearity, and signal-dependent shot noise. An equivalent additive Gaussian noise channel model is proposed to describe the performance of the SPAD-based OFDM system. The statistics of the proposed channel model and the analytical expressions of the signal-to-noise ratio and bit error rate are derived in closed forms. By means of extensive numerical results, the impact of the unique receiver nonlinearity on the system performance is investigated. The results demonstrate new insights into different optical power regimes of reliable operation for SPAD-based OFDM systems even well beyond the SPAD saturation level.

ИССЛЕДОВАНИЕ ВЛИЯНИЯ ФАЗОВЫХ ШУМОВ МОДУЛЯТОРОВ ЦИФРОВЫХ СИГНАЛОВ НА ВЕРОЯТНОСТНЫЕ ХАРАКТЕРИСТИК ПРИ ИХ ПРИЕМЕ

The results of studies of the distorting effect for phase noise of digital signal modulators, generated by short-term instability of clock generators, on the degradation of probabilistic characteristics (bit error probability) when receiving digital signals with two-dimensional "constellations" (signals with multi-position phase shift keying and signals with amplitude-phase shift keying) are presented. Research is carried out for two models of phase noises with parameters of their power with uniform and normal laws of phase density distribution. Numerical estimates of energy losses are given, obtained by theoretical calculation and computer simulation of the algorithm for receiving digital signals using the considered models of phase noise with respect to additive white Gaussian channel noise. It is shown that the energy losses calculated using the analytical relation for these signals are fairly approximate estimates in relation to the simulation results. It is also shown that for signals with 2-position phase shift keying and for amplitude-phase keying with a keying order equal to 8, in the presence of phase noise with specified powers and distribution density laws, the bit error probabilities are practically equivalent to the theoretical values of the bit error probabilities for channel with additive white Gaussian noise - in this case, the energy loss is almost equal to 0. Signals with 8-position phase-shift keying are most susceptible to the distorting effect of phase noise - for the considered phase noise power parameter, the energy loss exceeds 1.5 dB. The method of reducing energy losses when receiving the considered series of digital signals is based on the use of clock generators with a decrease in the power of phase noise

ПІДВИЩЕННЯ ЕФЕКТИВНОСТІ ІНТЕЛЕКТУАЛЬНИХ МЕРЕЖ MIMO НА ОСНОВІ 6G

Methods of increasing the efficiency of 6G radio access networks due to new design principles and optimization criteria of the MIMO structure have been determined. A flexible and versatile network with the possibility of expansion not only due to advances in existing technologies, but also due to numerous new technologies, such as ELAA, RIS, artificial intelligence, scanning, new materials, as well as new designs and structures of antennas, has been studied. The considered technologies will provide a universal set of tools for increasing network bandwidth. Advances in RF components, signal processing, and antenna communications that will affect various aspects of MIMO systems, including modulators, waveforms, and receiver designs, are explored. Functional parameters of transceivers based on electronic, photonic and combined technologies are considered. The use of intelligent radio channels, which significantly improve the quality of communication, system productivity, cell coverage, and the quality of communication at the cell boundary in wireless networks, was investigated, which was proven by numerous simulation results in various scenarios. A promising direction of research for super-massive MIMO 6G, which is relevant when using lattices with an extra-large aperture (ELAA), has been determined. The goal of ELAA is defined, which is that all users use mutually orthogonal channels with a per-user bandwidth similar to an additive Gaussian white noise channel. Intelligent massive MIMO in the 6G network based on AI has been studied, which facilitates learning and increases its efficiency. The OAM technology for high-speed transmission based on multiplexing access with mode separation is considered. The practical application of OAM technology in transit transmission between base stations, device-to-device (D2D) transmission, and communication between artificial satellites, where it is relatively easy to obtain the necessary axis alignment, has been studied. An analysis of the development of MIMO technology was carried out, taking into account the characteristics of the THz channel, in particular, a study of reconfigurable intelligent surfaces, which are characterized by the simplicity of the hardware architecture, low hardware complexity, low energy consumption and high efficiency of spectrum use, was carried out. The peculiarities of creating antenna arrays with an ultra-large aperture when applying new multiplexing schemes, using spatial depth information to separate streams or equipment using pre-coding, are determined. MIMO efficiency has been improved using artificial intelligence, which is capable of minimizing BER and increasing the spectral efficiency of massive MIMO of the millimeter range and significantly reducing computational complexity. A study of alternative MIMO technologies was carried out.

A Probabilistically Quantized Learning Control Framework for Networked Linear Systems.

In this article, we consider quantized learning control for linear networked systems with additive channel noise. Our objective is to achieve high tracking performance while reducing the communication burden on the communication network. To address this problem, we propose an integrated framework consisting of two modules: a probabilistic quantizer and a learning scheme. The employed probabilistic quantizer is developed by employing a Bernoulli distribution driven by the quantization errors. Three learning control schemes are studied, namely, a constant gain, a decreasing gain sequence satisfying certain conditions, and an optimal gain sequence that is recursively generated based on a performance index. We show that the control with a constant gain can only ensure the input error sequence to converge to a bounded sphere in a mean-square sense, where the radius of this sphere is proportional to the constant gain. On the contrary, we show that the control that employs any of the two proposed gain sequences drives the input error to zero in the mean-square sense. In addition, we show that the convergence rate associated with the constant gain is exponential, whereas the rate associated with the proposed gain sequences is not faster than a specific exponential trend. Illustrative simulations are provided to demonstrate the convergence rate properties and steady-state tracking performance associated with each gain, and their robustness against modeling uncertainties.

Zero-Error Feedback Capacity for Bounded Stabilization and Finite-State Additive Noise Channels

This article studies the zero-error feedback capacity of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">causal</i> discrete channels with memory. First, by extending the classical zero-error feedback capacity concept, a new notion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">uniform zero-error feedback capacity</i> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{0f} $ </tex-math></inline-formula> for such channels is introduced. Using this notion a tight condition for bounded stabilization of unstable noisy linear systems via causal channels is obtained, assuming no channel state information at either end of the channel. Furthermore, the zero-error feedback capacity of a class of additive noise channels is investigated. It is known that for a discrete channel with correlated additive noise, the ordinary capacity with or without feedback is equal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\log q-\mathcal {H}_{ch} $ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{ch} $ </tex-math></inline-formula> is the entropy rate of the noise process and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q $ </tex-math></inline-formula> is the input alphabet size. In this paper, for a class of finite-state additive noise channels (FSANCs), it is shown that the zero-error feedback capacity is either zero or <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$C_{0f} =\log q -h_{ch} $ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$h_{ch} $ </tex-math></inline-formula> is the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">topological entropy</i> of the noise process. A condition is given to determine when the zero-error capacity with or without feedback is zero. This, in conjunction with the stabilization result, leads to a “Small-Entropy Theorem”, stating that stabilization over FSANCs can be achieved if the sum of the topological entropies of the linear system and the channel is smaller than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\log q$ </tex-math></inline-formula> .

Speech quality assessment with WARP‐Q: From similarity to subsequence dynamic time warp cost

Speech coding has been shown to achieve good speech quality using either waveform matching or parametric reconstruction. For very low bit rate streams, recently developed generative speech models can reconstruct high-quality wideband speech from the bit streams of standard parametric encoders at less than 3 kb/s. Generative codecs produce high-quality speech based on synthesising speech from a DNN and the parametric input. Existing objective speech quality models (e.g., ViSQOL and POLQA) cannot be used to accurately evaluate the quality of coded speech from generative models as they penalise based on signal differences not apparent in subjective listening test results. This paper presents WARP-Q, a full-reference objective speech quality metric that uses a dynamic time warping cost for MFCC representations of the signals. It is robust to low perceptual signal changes introduced by low bit rate neural vocoders. An evaluation using waveform matching, parametric, and generative neural vocoder-based codecs as well as channel and environmental noise shows that WARP-Q has better correlation and codec quality ranking for novel codecs compared to traditional metrics as well as the versatility of capturing other types of degradations, such as additive noise and transmission channel degradations.

Remote State Estimation of Nonlinear Systems Over Fading Channels via Recurrent Neural Networks

In this article, we consider the remote state estimation for nonlinear dynamic systems with known linear dynamics and unknown nonlinear perturbations. The nonlinear dynamic plant is monitored by multiple distributed sensors over a random access wireless network with shared common radio channel. We focus on the communication strategy and remote state estimation algorithm design so as to achieve a remote state estimation stability subject to unknown nonlinearities in plant and various wireless impairments, such as multisensor interference, wireless fading, and additive channel noise. By exploiting the additive properties of the physical wireless channels, we propose a novel information fusion over-the-air mechanism to address the signal collision and interference among the sensors. Utilizing the partial knowledge on the linear dynamics of the plant, we also propose a novel recurrent neural network (RNN)-based remote state estimator aided by a virtual state estimation mean-square-error (MSE) process. We further propose a novel online training algorithm such that the RNN at the remote estimator can effectively learn the unknown plant nonlinearities. Using the Lyapunov drift analysis approach, we establish closed-form sufficient requirements on the communication resources needed to achieve almost sure stability of both state estimation and RNN online training in high signal-to-noise ratio (SNR) regime. As a result, our proposed scheme is asymptomatic optimal for large SNR in the sense that both the plant state and the unknown plant nonlinearities can be perfectly recovered at the remote estimator. The proposed scheme is also compared with various baselines and we show that significant performance gains can be achieved.

Bounded Estimation Over Finite-State Channels: Relating Topological Entropy and Zero-Error Capacity

We investigate state estimation of linear systems over channels having a finite state not known by the transmitter or receiver. We show that similar to memoryless channels, zero-error capacity is the right figure of merit for achieving bounded estimation errors. We then consider finite-state, worst-case versions of the common erasure, and additive noise channels models, in which the noise is governed by a finite-state machine without any statistical structure. Upper and lower bounds on their zero-error capacities are derived, revealing a connection with the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">topological entropy</i> of the channel dynamics. Separate necessary and sufficient conditions for bounded linear state estimation errors via such channels are obtained. These estimation conditions bring together the topological entropies of the linear system and the discrete channel.

GNPy model of the physical layer for open and disaggregated optical networking [Invited

Networking technologies are fast evolving to support the request for ubiquitous Internet access that is becoming a fundamental need for the modern and inclusive society, with a dramatic speed-up caused by the COVID-19 emergency. Such evolution needs the development of networks into disaggregated and programmable systems according to the software-defined networking (SDN) paradigm. Wavelength-division multiplexed (WDM) optical transmission and networking is expanding as physical layer technology from core and metro networks to 5G x -hauling and inter- and intra-data-center connections requiring the application of the SDN paradigm at the optical layer based on the WDM optical data transport virtualization. We present the fundamental principles of the open-source project Gaussian Noise in Python (GNPy) for the optical transport virtualization in modeling the WDM optical transmission for open and disaggregated networking. GNPy approximates transparent lightpaths as additive white and Gaussian noise channels and can be used as a vendor-agnostic digital twin for open network planning and management. The quality-of-transmission degradation of each network element is independently modeled to allow disaggregated network management. We describe the GNPy models for fiber propagation, optical amplifiers, and reconfigurable add/drop multiplexers together with modeling of coherent transceivers from the back-to-back characterization. We address the use of GNPy as a vendor-agnostic design and planning tool and as physical layer virtualization in software-defined optical networking.