Additive non-Gaussian Noise Channel Research Articles

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.

The Dispersion of Nearest-Neighbor Decoding for Additive Non-Gaussian Channels

We study the second-order asymptotics of information transmission using random Gaussian codebooks and nearest neighbor decoding over a power-limited stationary memoryless additive non-Gaussian noise channel. We show that the dispersion term depends on the non-Gaussian noise only through its second and fourth moments, thus complementing the capacity result (Lapidoth, 1996), which depends only on the second moment. Furthermore, we characterize the second-order asymptotics of point-to-point codes over $K$ -sender interference networks with non-Gaussian additive noise. Specifically, we assume that each user’s codebook is Gaussian and that NN decoding is employed, i.e., that interference from the $K-1$ unintended users (Gaussian interfering signals) is treated as noise at each decoder. We show that while the first-order term in the asymptotic expansion of the maximum number of messages depends on the power of the interfering codewords only through their sum, this does not hold for the second-order term.

Robust Signal-to-Noise Ratio Estimation in Non-Gaussian Noise Channel

Signal-to-noise ratio (SNR) estimation available in the literature are designed based on the assumption of Gaussian noise models. These estimators may produce misleading results when the distribution of the noise deviates from Gaussian. This paper investigates the performance of existing SNR estimators in an additive non-Gaussian noise channel based on a Gaussian mixture model. An expectation---maximization (EM) based approach is proposed for optimum SNR estimation in the non-Gaussian noise channel. In addition, the Cramer---Rao bound is derived and used as a benchmark to assess the performance of the SNR estimators. Simulation results confirm the optimality and robustness of the proposed EM-based estimator in Gaussian and non-Gaussian noise channels.

Extension of de Bruijn's identity to dependent non-Gaussian noise channels

Abstract De Bruijn's identity relates two important concepts in information theory: Fisher information and differential entropy. Unlike the common practice in the literature, in this paper we consider general additive non-Gaussian noise channels where more realistically, the input signal and additive noise are not independently distributed. It is shown that, for general dependent signal and noise, the first derivative of the differential entropy is directly related to the conditional mean estimate of the input. Then, by using Gaussian and Farlie–Gumbel–Morgenstern copulas, special versions of the result are given in the respective case of additive normally distributed noise. The previous result on independent Gaussian noise channels is included as a special case. Illustrative examples are also provided.

New Bounds on the Capacity of Certain Infinite-Dimensional Additive Non-Gaussian Channels

An additive non-Gaussian noise channel with a generalized average input energy constraint is considered. New bounds on the channel capacity are found for the case that the divergence of the probability measure induced in function space by the noise process, with respect to the measure induced by the Gaussian process with the same covariance as that of the noise process, is finite. Upper and lower bounds that depend on the noise process only via the divergence are given for large signal-to-noise energy ratio S. It is also shown that the increase in the capacity of an infinite-dimensional non-Gaussian channel, relative to the infinite-dimensional Gaussian channel capacity S/2, could be significant

Multilevel code design for multistage and parallel decoding schemes for rayleigh fading channels

The objective is to design efficient coded modulation systems with sub-optimum but practical decoding schemes for Rayleigh fading channels. The well-known rate design rule is conventionally used for additive white Gaussian noise (AWGN) channels. In this paper its application is extended to the Rayleigh fading case by modelling the channel as a time-invariant additive non-Gaussian noise channel, and the equivalent channel capacity equations are evaluated. The sub-optimumbut practical decoding schemes of multistage decoding and parallel decoding on levels are considered. The fading channel is modelled as a time-invariant additive non-Gaussian noise channel by assuming that the channel state information is available at the receiver. The equivalent channel capacity equations for both decoding schemes and a code design example are presented. It is demonstrated that very good coding gains can be achieved if code rates are selected correctly.

Nearest neighbor decoding for additive non-Gaussian noise channels

We study the performance of a transmission scheme employing random Gaussian codebooks and nearest neighbor decoding over a power limited additive non-Gaussian noise channel. We show that the achievable rates depend on the noise distribution only via its power and thus coincide with the capacity region of a white Gaussian noise channel with signal and noise power equal to those of the original channel. The results are presented for single-user channels as well as multiple-access channels, and are extended to fading channels with side information at the receiver.

On the capacity of certain additive non-Gaussian channels

A model of an additive non-Gaussian noise channel with generalized average input energy constraint is considered. The asymptotic channel capacity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C_{\zeta}(S)</tex> , for large signal-to-noise ratio <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</tex> , is found under certain conditions on the entropy <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H_{ \tilde{ \zeta}}( \zeta)</tex> of the measure induced in function space by the noise process <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\zeta</tex> , relative to the measure induced by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\tilde{\zeta}</tex> , where is a Gaussian process with the same covariance as that of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\zeta</tex> . If <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H_{ \tilde{zeta}}( \zeta) &lt; \infty</tex> and the channel input signal is of dimension <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M&lt; \infty</tex> , then <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C_{ \zeta}(S)= \frac{1}{2}M \ln(1 + S/M) + Q_{\zeta}( M ) + {o}(1)</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0 \leq Q_{ \zeta}( M ) \leq H_{ \tilde{ \zeta}}( \zeta)</tex> . If the channel input signal is of infinite dimension and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H_{ \tilde{ \zeta}}( \zeta) \rightarrow 0</tex> for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S \rightarrow \infty</tex> , then <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C_{ \zeta}(S) = \frac{1}{2}S+{o}(1)</tex> .

On the Calculation of Mutual Information

Abstract : Calculating the amount of information about a random function contained in another random function has important uses in communication theory. An expression for the mutual information for continuous time random processes has been given by Gelfand and Yaglom, Chiang, and Perez by generalizing Shannon's result in a natural way. Under a condition of absolute continuity of measures the continuous time expression has the same form as Shannon's result. For two Gaussian processes Gelfand and Yaglom express the mutual information in terms of a mean square estimation error. We generalize this result to diffusion processes and express the solution in a different form which is more naturally related to a corresponding filtering problem. We also use these results to calculate some information rates.