On the capacity of channels with Gaussian and non-Gaussian noise

We evaluate the information capacity of channels for which the noise process is a Gaussian measure on a quasi-complete locally convex space. The coding capacity is calculated in this setting and for time-continuous Gaussian channels using the information capacity result. The coding capacity of channels with non-Gaussian noise having finite entropy with respect to Gaussian noise of the same covariance is shown not to exceed the coding capacity of the Gaussian channel. The sensitivity of the information capacity to deviations from normality in the noise process is also investigated

Optimization of capacity in non-Gaussian noise models with and without fading channels for sustainable communication systems

The highest rate at which information may be reliably sent via a communication link is known as its capacity. In the case of non-Gaussian noise, the capacity of the channel depends on the specific characteristics of the noise, which can cause severe errors and reduce the reliability of communication systems over a fading channel. The Gaussian mixture impulsive noise model (GMINM), which is a more general and flexible non-Gaussian model for impulsive noise, has been compared in this paper with the Middleton Class-A impulsive noise model (MCAINM) in terms of derived channel capacity normalized by channel bandwidth (C/BW) with and without Rayleigh fading (Rf) channels. It also investigated the trade-off between complexity and accuracy in modeling the impulsive noise using two simplified Middleton Class-A impulsive noise models based on derived C/BW. The derived C/BW of these models under various conditions, such as different signal-to-noise ratios and impulsive noise parameters and models, have been performed and evaluated using two different scenarios: the exact method and the semi-analytical method. When the impulsive noise parameters  and A are both near 0 in GMINM and MCAINM, respectively, the capacity of the impulsive noise channel is found to be equivalent to that of the Gaussian channel sustainable, as shown by the findings based on Monte-Carlo simulations. We have shown that when the impulsive noise decreases, the capacity increases in all models; however, the capacity of Gaussian noise is higher than the capacity of non-Gaussian noise, which in turn is higher than the capacity of non-Gaussian noise over the Rf channel overall values of SNR in dB. Moreover, multi-channel configuration introduces spatial diversity and multiplexing gains that have been proposed to sustainably optimize the ergodic capacity for the challenge case when the channel state information (CSI) is unknown at the transmitter in non-Gaussian noise over Rf channel. In today's rapidly evolving world, sustainable communication systems play a crucial role in ensuring efficient and responsible utilization of resources. As the demand for wireless communication continues to rise, it becomes imperative to optimize the capacity of communication channels, especially in scenarios involving non-Gaussian noise models and fading channels.

Quantum communication with photon-number entangled states and realistic photodetection

We address the effects of realistic photodetection, with nonunit quantum efficiency and background noise (dark counts), on the performances of quantum communication schemes based on photon-number entangled states. We consider channels based on Gaussian twin-beam states and non-Gaussian two-mode coherent states and evaluate the channel capacity by optimizing the bit discrimination threshold. We found that TWB-based channels are more robust against noise than TMC-based ones and that this result is almost independent on the statistics of dark counts.Comment: 8 pages, 2 figures, to appear in Phys. Lett.

Characterization of Information Channels for Asymptotic Mean Stationarity and Stochastic Stability of Non-stationary/Unstable Linear Systems

Stabilization of non-stationary linear systems over noisy communication channels is considered. Stochastically stable sources, and unstable but noise-free or bounded-noise systems have been extensively studied in information theory and control theory literature since 1970s, with a renewed interest in the past decade. There have also been studies on non-causal and causal coding of unstable/non-stationary linear Gaussian sources. In this paper, tight necessary and sufficient conditions for stochastic stabilizability of unstable (non-stationary) possibly multi-dimensional linear systems driven by Gaussian noise over discrete channels (possibly with memory and feedback) are presented. Stochastic stability notions include recurrence, asymptotic mean stationarity and sample path ergodicity, and the existence of finite second moments. Our constructive proof uses random-time state-dependent stochastic drift criteria for stabilization of Markov chains. For asymptotic mean stationarity (and thus sample path ergodicity), it is sufficient that the capacity of a channel is (strictly) greater than the sum of the logarithms of the unstable pole magnitudes for memoryless channels and a class of channels with memory. This condition is also necessary under a mild technical condition. Sufficient conditions for the existence of finite average second moments for such systems driven by unbounded noise are provided.Comment: To appear in IEEE Transactions on Information Theor

Multi-mode bosonic Gaussian channels

A complete analysis of multi-mode bosonic Gaussian channels is proposed. We clarify the structure of unitary dilations of general Gaussian channels involving any number of bosonic modes and present a normal form. The maximum number of auxiliary modes that is needed is identified, including all rank deficient cases, and the specific role of additive classical noise is highlighted. By using this analysis, we derive a canonical matrix form of the noisy evolution of n-mode bosonic Gaussian channels and of their weak complementary counterparts, based on a recent generalization of the normal mode decomposition for non-symmetric or locality constrained situations. It allows us to simplify the weak-degradability classification. Moreover, we investigate the structure of some singular multi-mode channels, like the additive classical noise channel that can be used to decompose a noisy channel in terms of a less noisy one in order to find new sets of maps with zero quantum capacity. Finally, the two-mode case is analyzed in detail. By exploiting the composition rules of two-mode maps and the fact that anti-degradable channels cannot be used to transfer quantum information, we identify sets of two-mode bosonic channels with zero capacity.Comment: 37 pages, 3 figures (minor editing), accepted for publication in New Journal of Physic

Information-theoretic analysis of a family of additive energy channels

This dissertation studies a new family of channel models for non-coherent com- munications, the additive energy channels. By construction, the additive en- ergy channels occupy an intermediate region between two widely used channel models: the discrete-time Gaussian channel, used to represent coherent com- munication systems operating at radio and microwave frequencies, and the discrete-time Poisson channel, which often appears in the analysis of intensity- modulated systems working at optical frequencies. The additive energy chan- nels share with the Gaussian channel the additivity between a useful signal and a noise component. However, the signal and noise components are not complex- valued quadrature amplitudes but, as in the Poisson channel, non-negative real numbers, the energy or squared modulus of the complex amplitude. The additive energy channels come in two variants, depending on whether the channel output is discrete or continuous. In the former case, the energy is a multiple of a fundamental unit, the quantum of energy, whereas in the second the value of the energy can take on any non-negative real number. For con- tinuous output the additive noise has an exponential density, as for the energy of a sample of complex Gaussian noise. For discrete, or quantized, energy the signal component is randomly distributed according to a Poisson distribution whose mean is the signal energy of the corresponding Gaussian channel; part of the total noise at the channel output is thus a signal-dependent, Poisson noise component. Moreover, the additive noise has a geometric distribution, the discrete counterpart of the exponential density. Contrary to the common engineering wisdom that not using the quadrature amplitude incurs in a signi¯cant performance penalty, it is shown in this dis- sertation that the capacity of the additive energy channels essentially coincides with that of a coherent Gaussian model under a broad set of circumstances. Moreover, common modulation and coding techniques for the Gaussian chan- nel often admit a natural extension to the additive energy channels, and their performance frequently parallels those of the Gaussian channel methods. Four information-theoretic quantities, covering both theoretical and practi- cal aspects of the reliable transmission of information, are studied: the channel capacity, the minimum energy per bit, the constrained capacity when a given digital modulation format is used, and the pairwise error probability. Of these quantities, the channel capacity sets a fundamental limit on the transmission capabilities of the channel but is sometimes di±cult to determine. The min- imum energy per bit (or its inverse, the capacity per unit cost), on the other hand, turns out to be easier to determine, and may be used to analyze the performance of systems operating at low levels of signal energy. Closer to a practical ¯gure of merit is the constrained capacity, which estimates the largest amount of information which can be transmitted by using a speci¯c digital modulation format. Its study is complemented by the computation of the pairwise error probability, an e®ective tool to estimate the performance of practical coded communication systems. Regarding the channel capacity, the capacity of the continuous additive energy channel is found to coincide with that of a Gaussian channel with iden- tical signal-to-noise ratio. Also, an upper bound |the tightest known| to the capacity of the discrete-time Poisson channel is derived. The capacity of the quantized additive energy channel is shown to have two distinct functional forms: if additive noise is dominant, the capacity is close to that of the continu- ous channel with the same energy and noise levels; when Poisson noise prevails, the capacity is similar to that of a discrete-time Poisson channel, with no ad- ditive noise. An analogy with radiation channels of an arbitrary frequency, for which the quanta of energy are photons, is presented. Additive noise is found to be dominant when frequency is low and, simultaneously, the signal-to-noise ratio lies below a threshold; the value of this threshold is well approximated by the expected number of quanta of additive noise. As for the minimum energy per nat (1 nat is log2 e bits, or about 1.4427 bits), it equals the average energy of the additive noise component for all the stud- ied channel models. A similar result was previously known to hold for two particular cases, namely the discrete-time Gaussian and Poisson channels. An extension of digital modulation methods from the Gaussian channels to the additive energy channel is presented, and their constrained capacity determined. Special attention is paid to their asymptotic form of the capacity at low and high levels of signal energy. In contrast to the behaviour in the vi Gaussian channel, arbitrary modulation formats do not achieve the minimum energy per bit at low signal energy. Analytic expressions for the constrained capacity at low signal energy levels are provided. In the high-energy limit simple pulse-energy modulations, which achieve a larger constrained capacity than their counterparts for the Gaussian channel, are presented. As a ¯nal element, the error probability of binary channel codes in the ad- ditive energy channels is studied by analyzing the pairwise error probability, the probability of wrong decision between two alternative binary codewords. Saddlepoint approximations to the pairwise error probability are given, both for binary modulation and for bit-interleaved coded modulation, a simple and e±cient method to use binary codes with non-binary modulations. The meth- ods yield new simple approximations to the error probability in the fading Gaussian channel. The error rates in the continuous additive energy channel are close to those of coherent transmission at identical signal-to-noise ratio. Constellations minimizing the pairwise error probability in the additive energy channels are presented, and their form compared to that of the constellations which maximize the constrained capacity at high signal energy levels