non-Gaussian Channels Research Articles

Can corporate social performance mitigate the risk of extreme stock returns?

It is commonly believed that there exists a strong negative association between corporate social performance (CSP) and firm risk.11The authors would like to thank an anonymous reviewer for his careful reading of our manuscript and his many insightful comments and suggestions which have substantially improved the initial paper. The authors would alsolike to thank Lionel Tangy Malca and Alexandre Coureaud from HOMA Capital for fruitful and constructive discussions around the link between ESG and extremes stocks returns. To investigate the structure of this relationship, we decompose the dynamics of large U.S. company stock returns into two components: Gaussian and non-Gaussian innovations. Our findings indicate that CSP affects firm risk mainly through the non-Gaussian risk channel. In particular, it significantly reduces the magnitude of extreme returns. We find no consistent nor robust effect of CSP on the frequency of price boom and crash probability as it varies widely across industries. Last, we find no statistically significant impact of CSP on standard Gaussian volatility risk.

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.

Exact Quantum Sensing Limits for Bosonic Dephasing Channels

Dephasing is a prominent noise mechanism that afflicts quantum information carriers, and it is one of the main challenges toward realizing useful quantum computation, communication, and sensing. Here, we consider discrimination and estimation of bosonic dephasing channels, when using the most general adaptive strategies allowed by quantum mechanics. We reduce these difficult quantum problems to simple classical ones based on the probability densities defining the bosonic dephasing channels. By doing so, we rigorously establish the optimal performance of various distinguishability and estimation tasks and construct explicit strategies to achieve this performance. To the best of our knowledge, this is the first example of a non-Gaussian bosonic channel for which there are exact solutions for these tasks. Published by the American Physical Society 2024

Finite-size correction and variance of the mutual information of random linear estimation with non-Gaussian priors: A replica calculation.

Random linear vector channels have been known to increase the transmission of information in several communications systems. For Gaussian priors, the statistics of a key metric, namely, the mutual information, which is related to the free energy of the system, have been analyzed in great detail for various types of channel randomness. However, for the realistic case of non-Gaussian priors, only the average mutual information has been obtained in the asymptotic limit of large channel matrices. In this paper, we employ methods from statistical physics, namely, the replica approach, to calculate the finite-size correction and the variance of the mutual information with non-Gaussian priors, both for the case of correlated Gaussian and uncorrelated non-Gaussian channel matrices in the same asymptotic limit. Furthermore, using the same methodology, we show that higher order cumulants of the mutual information should vanish in the large-system-size limit. In addition, we obtain closed-form expressions for the minimum mean-square error finite-size corrections and variance for both Gaussian and non-Gaussian channels. Finally, we provide numerical verification of the results using numerical methods on finite-sized systems.

Breakdown of a concavity property of mutual information for non-Gaussian channels

Abstract Let $S$ and $\tilde S$ be two independent and identically distributed random variables, which we interpret as the signal, and let $P_{1}$ and $P_{2}$ be two communication channels. We can choose between two measurement scenarios: either we observe $S$ through $P_{1}$ and $P_{2}$, and also $\tilde S$ through $P_{1}$ and $P_{2}$; or we observe $S$ twice through $P_{1}$, and $\tilde{S}$ twice through $P_{2}$. In which of these two scenarios do we obtain the most information on the signal $(S, \tilde S)$? While the first scenario always yields more information when $P_{1}$ and $P_{2}$ are additive Gaussian channels, we give examples showing that this property does not extend to arbitrary channels. As a consequence of this result, we show that the continuous-time mutual information arising in the setting of community detection on sparse stochastic block models is not concave, even in the limit of large system size. This stands in contrast to the case of models with diverging average degree, and brings additional challenges to the analysis of the asymptotic behavior of this quantity.

A multi-user cognitive radio full-duplex channel under imperfect spectrum sensing: Achievable rates and energy efficiency

In this work, the achievable rates and energy efficiency of a multi-user cognitive radio (CR) uplink channel with full-duplex (FD) are studied. For this multi-user CR channel, secondary users can work in FD mode to simultaneously transmit and listen to the channel. We consider a realistic scenario in which both FD operation and spectrum sensing are imperfect. At first, we examine the sensing performance and the rate region through the evaluation of the probability of miss-detection and the probability of false alarm when the primary user (PU) activity is assumed to be non-time-slotted. Due to an imperfect sensing operation, the cognitive radio channel is modeled as a non-Gaussian channel impacted by a Gaussian-mixture (GM) noise plus PU interference. Under this practical assumption, it is not possible to calculate the achievable rates and the rate region directly. Instead, we derive simple approximations of these metrics which can be easily calculated with arbitrarily small errors. In the second part of the paper, we further evaluate the derivatives of these achievable rates at low-power regimes. This calculation helps us evaluate the energy efficiency and obtain the minimum energy per bit Eb/N0min when Gaussian and discrete input signals are used.

Investigation of NOMA 5G Systems Under Non-Gaussian Channels

Investigation of NOMA 5G Systems Under Non-Gaussian Channels

Blind receiver design-based multi-dimensional stable distribution model using the EM algorithm

Multi-antenna receivers are a key technology for modern communication systems. Signal attenuation in the very low frequency (VLF) channel is a serious problem. In addition to high signal attenuation, the resulting noise on the VLF channel is non-Gaussian. Hence, to analyze and address the issue of the normal operation of the multi-antenna receiver in the VLF channel, we must study the signal detection problem in a multi-dimensional non-Gaussian fading channel. Motivated by the existing blind receiver in an underwater submarine single-antenna receiver, we study the signal detection and estimation algorithm under the fading channel for a multi-dimensional non-Gaussian noise model. In this study, we propose a blind receiver based on the expectation-maximization (EM) algorithm. The proposed blind receiver can reduce non-Gaussian noise. In addition, we propose a nonlinear receiver that can accurately receive the transmitted signal over the high-attenuation VLF communication systems. Numerical and simulation results over uncorrelated and correlated non-Gaussian channels confirm that the design of the proposed blind receiver is close to optimal, with low computation complexity.

Filtering Over Non-Gaussian Channels: The Role of Anytime Capacity

Filtering over noisy channels is of interest in many network applications, in which a node infers a time-varying state by using messages received from another node that can observe such a state. This letter explores filtering with general models for state disturbance and communication channels by deriving a sufficient condition for which the estimation error is bounded. Specifically, the sufficient condition is expressed in terms of anytime capacity, a notion that characterizes the maximum sequential communication rate. The joint design of encoder and estimator with bounded estimation error is also presented.

Bias for the Trace of the Resolvent and Its Application on Non-Gaussian and Non-Centered MIMO Channels

The mutual information (MI) of Gaussian multi-input multi-output (MIMO) channels has been evaluated by utilizing random matrix theory (RMT) and shown to asymptotically follow Gaussian distribution, where the ergodic mutual information (EMI) converges to a deterministic quantity. However, with non-Gaussian channels, there is a bias between the EMI and its deterministic equivalent (DE), whose evaluation is not available in the literature. This bias of the EMI is related to the bias for the trace of the resolvent in large RMT. In this paper, we first derive the bias for the trace of the resolvent, which is further extended to compute the bias for the linear spectral statistics (LSS). Then, we apply the above results on non-Gaussian MIMO channels to determine the bias for the EMI. It is also proved that the bias for the EMI is $-0.5$ times of that for the variance of the MI. Finally, the derived bias is utilized to modify the central limit theory (CLT) and calculate the outage probability. Numerical results show that the modified CLT significantly outperforms previous methods in approximating the distribution of the MI and improves the accuracy for the outage probability evaluation.

On the performance of digital systems in α-[formula omitted] fading and non-Gaussian noise channels

In this paper, a closed-form expression is derived for the bit error probability (BEP) under several digital modulation schemes, considering the channel subject to α-F fading and non-Gaussian noise, characterized by the additive generalized Gaussian noise (AWGGN) distribution. An asymptotic BEP analysis is carried out in this work. A closed-form and unified BEP expression is derived for a wide range of modulation schemes, under α-F fading and AWGGN for the maximal-ratio combining (MRC), equal gain combining (EGC), and selection combining (SC) based receivers. Comments are provided on the special cases encompassed by the α-F fading and AWGGN noise, as well as on the convergence and complexity analysis of the BEP expressions derived. BEP curves are shown for different parameters that characterize the channel and are corroborated by simulations performed with the Monte-Carlo method.

Generalized sparse codes for non-Gaussian channels: Code design, algorithms, and applications

In this paper, generalized sparse (GS) codes are proposed to support reliable and efficient transmission over non-Gaussian channels. Specifically, by expanding the single-parity check (SPC) code constraints with powerful algebraic codes, GS codes generalize conventional sparse codes with enhanced error-correcting capability, as well as better code design flexibility by covering a wide range of block-lengths and coding rates with reduced encoding/decoding complexity. Moreover, by introducing a universal communication channel model, a general framework for performance analysis and code design of GS codes is formulated, by which the coding parameters can be optimized for different target channel conditions. Finally, example codes are constructed for several critical application scenarios with non-Gaussian channels. Numerical simulations are performed to demonstrate the superiority of the proposed GS coding scheme to traditional channel coding schemes.

Accuracy Analysis of Feature-Based Automatic Modulation Classification via Deep Neural Network.

A feature-based automatic modulation classification (FB-AMC) algorithm has been widely investigated because of its better performance and lower complexity. In this study, a deep learning model was designed to analyze the classification performance of FB-AMC among the most commonly used features, including higher-order cumulants (HOC), features-based fuzzy c-means clustering (FCM), grid-like constellation diagram (GCD), cumulative distribution function (CDF), and raw IQ data. A novel end-to-end modulation classifier based on deep learning, named CCT classifier, which can automatically identify unknown modulation schemes from extracted features using a general architecture, was proposed. Features except GCD are first converted into two-dimensional representations. Then, each feature is fed into the CCT classifier for modulation classification. In addition, Gaussian channel, phase offset, frequency offset, non-Gaussian channel, and flat-fading channel are also introduced to compare the performance of different features. Additionally, transfer learning is introduced to reduce training time. Experimental results showed that the features HOC, raw IQ data, and GCD obtained better classification performance than CDF and FCM under Gaussian channel, while CDF and FCM were less sensitive to the given phase offset and frequency offset. Moreover, CDF was an effective feature for AMC under non-Gaussian and flat-fading channels, and the raw IQ data can be applied to different channels’ conditions. Finally, it showed that compared with the existing CNN and K-S classifiers, the proposed CCT classifier significantly improved the classification performance for MQAM at N = 512, reaching about 3.2% and 2.1% under Gaussian channel, respectively.

Abating Jamming in Free Space Optical Systems—A Game-Theoretic Solution

Free space optical (FSO) channel provides a significantly large transmission capacity. However, in the presence of random jamming attacks, the efficacy of FSO communication channel can be affected critically. In this paper, the discrete-input continuous-output memoryless channel (DCMC) capacity of a single-input single-output FSO communication system is investigated under the random jamming effects. The ergodic channel capacity analysis is performed over additive non-Gaussian noise channel (jamming noise channel). The derived closed-form expression of DCMC capacity for the considered FSO system and also, the effects of partial-band jamming and broadband jamming over the FSO channel capacity are verified through simulation results. It is observed that the FSO channel capacity is very sensitive to the degree of jamming and the ergodic channel capacity alters crucially even for small change in jamming probability. The derived results are utilized to study the considered network in the presence of a rational jammer whose ability to jam is limited by its battery capacity. The presence of a rational jammer is addressed by modelling the interaction between the FSO transmitter and the jammer as a non-cooperative game. The closed-form expressions of the equilibrium of the proposed game are derived and verified through simulation. The game-theoretic solution provides a performance improvement of 74% in comparison to uniform power allocation.

Effects of magnetic fields on stochastic resonance in Hodgkin-Huxley neuronal network driven by Gaussian noise and non-Gaussian noise.

Stochastic resonance is a remarkable phenomenon that can enhance signal processing by the addition of random noise. However, the effect of magnetic fields on stochastic resonance under channel noises has been inadequately studied. In this paper, the stochastic resonance in Hodgkin-Huxley neuronal network under Gaussian channel noises and non-Gaussian channel noise were studied, and the effects of electromagnetic field stimulation on stochastic resonance were considered. The results indicate that stochastic resonance in neuronal networks can be induced by Gaussian channel noise and non-Gaussian Levy channel noise, and stochastic resonance may occur more easily under Levy channel noise. The resonance amplitude was significantly improved by selecting appropriate parameters of the magnetic field, while, a too strong magnetic field can be detrimental to the resonance amplitude. Magnetic fields may induce the enhancement of the resonance amplitude by increasing the firing frequency and spiking regularity.

Non-binary QC-LDPC codes for non-Gaussian optical channels

Non-binary QC-LDPC codes for non-Gaussian optical channels

A Novel Hybrid Code-Domain Index Modulation Scheme

In this letter, a novel hybrid code-domain index modulation (CDIM) scheme is proposed for future multi-domain communications, where the indices of the interleaving and spreading codes are exploited for information transmission. Specifically, we first provide a general design framework for CDIM, including the bit-to-symbol mapping rule and the detector. Then, we propose a code optimization method to select the utilized interleaver sequence and spreading code, with the objective of significantly improving the bit error ratio (BER) performance. Moreover, an intelligent detector is also proposed for CDIM in complicated wireless communication scenarios, e.g., non-Gaussian wireless channels. Simulation results show that the proposed CDIM is capable of substantially improving the system error performance compared with the conventional coded wireless communication systems.

Quantum capacity of a bosonic dephasing channel

We study the quantum capacity of continuous variable dephasing channel, which is a notable example of non-Gaussian quantum channel. We prove that a single letter formula applies. We then consider input energy restriction and show that by increasing it, the capacity saturates to a finite value. The optimal input state is found to be diagonal in the Fock basis and with a distribution that is a discrete version of a Gaussian. Relations between its mean/variance and dephasing rate/input energy are put forward. We also show that quantum capacity decays exponentially for large values of dephasing rates.

Large-System Analysis of AF Full-Duplex Massive MIMO Two-Way MRC/MRT Relaying

The massive multiple-input multiple-output (MIMO) full-duplex two-way relaying (FD-TWR) literature has extensively investigated power scaling for rate guarantees by considering a fixed number of users. We investigate the pairwise error probability (PEP) and the per-user rate of a FD-TWR with $N_{r}$ relay antennas that employs maximal ratio combining/transmission to enable two-way communication between $K$ FD users. We propose novel relay and user powers scalings, with both $N_{r}$ and $K$ tending to infinity, and show that the PEP of each user converges almost surely to its AWGN counterpart. These power scalings are different from the existing ones, which are derived by fixing $K$ and by assuming that only $N_{r}$ tends to large values. We show that the analysis developed herein applies to both Gaussian and non-Gaussian complex channels with finite number of moments. We numerically show that when both $K$ and $N_{r}$ increase concurrently to large values, the proposed power scaling schemes not only have better per-user PEP and rate than the existing schemes, but they are also robust to the FD self loop-interference power.

ʅ1-Norm Constrained Minimum Eror Entropy Algorithm

This work proposes a linear phase sparse minimum error entropy adaptive filtering algorithm. The linear phase condition is obtained by considering symmetry or anti symmetry condition onto the system coefficients. The proposed work integrates linear constraint based on linear phase of the system and -norm for sparseness into minimum error entropy adaptive algorithm. The proposed -norm linear constrained minimum error entropy criterion ( -CMEE) algorithm makes use of high-order statistics, hence worthy for non-Gaussian channel noise. The experimental results obtained for linear phase sparse system identification in the presence of non-Gaussian channel noise reveal that the proposed algorithm has lower steady state error and higher convergence rate than other existing MEE variants.