This paper proves that a family of number field lattice codes simultaneously achieves a constant gap to capacity in Rayleigh fast fading and Gaussian channels.
The key property in the proof is the existence of infinite towers of Hilbert class fields with bounded root discriminant. The gap to capacity of the proposed families is determined by the root discriminant.
The comparison between the Gaussian and fading case reveals that in Rayleigh fading channels the normalized minimum product distance plays an analogous role to the Hermite invariant in Gaussian channels.
The covert capacity is characterized for a non-coherent fast Rayleigh-fading wireless channel, in which a legitimate user wishes to communicate reliably with a legitimate receiver while escaping detection from a warden. It is shown that the covert capacity is achieved with an amplitude-constrained input distribution that consists of a finite number of mass points including one at zero and numerically tractable bounds are provided. It is also conjectured that distributions with two mass points in fixed locations are optimal.
We investigate the problem of message transmission over time-varying single-user multiple-input multiple-output (MIMO) Rayleigh fading channels with average power constraint and with complete channel state information available at the receiver side (CSIR). To describe the channel variations over the time, we consider a first-order Gauss-Markov model. We completely solve the problem by giving a single-letter characterization of the channel capacity in closed form and by providing a rigorous proof of it.
The proposed research performs the capacity analysis of the wireless channel described by the fluctuating double-Rayleigh with the line-of-sight model. The closed-form analytical expressions for the conditional capacity (in the case of arbitrary noninteger fading parameter) and the ergodic capacity (in the case of the integer fading parameter) are derived in terms of the extended generalized bivariate Meijer G-function. The exact solutions are succeeded by the approximating expressions deduced for the cases of small and large ratios between the Rician K-factor and the fading parameter. The per…
Over the past decades, the problem of communication over finite-state Markov channels (FSMCs) has been investigated in many researches and the capacity of FSMCs has been studied in closed form under the assumption of the availability of partial/complete channel state information at the sender and/or the receiver. In our work, we focus on infinite-state Markov channels by investigating the problem of message transmission over time-varying single-user multiple-input multiple-output (MIMO) Gauss-Markov Rayleigh fading channels with average power constraint and with complete channel state informat…
We analyze the channel capacity of a system with a large number of one-bit transceivers in a classical Rayleigh environment with perfect channel information at the receiver. With $M$ transmitters and $N=αM$ receivers, we derive an expression of the capacity per transmitter $\mathcal{C}$, where $\mathcal{C}\leq\min(1,α)$, as a function of $α$ and signal-to-noise ratio (SNR) $ρ$, when $M\to\infty$. We show that our expression is a good approximation for small $M$, and provide simple approximations of $\mathcal{C}$ for various ranges of $α$ and SNR $ρ$. We conclude that at high SNR, $\mathcal{C}$…
Multimode/multicore fibers are expected to provide an attractive solution to overcome the capacity limit of the current optical communication system. In the presence of high cross-talk between modes/cores, the squared singular values of the input/output transfer matrix follow the law of the Jacobi ensemble of random matrices. Assuming that the channel state information is only available at the receiver, we derive a new expression for the ergodic capacity of the MIMO Jacobi fading channel. This expression involves double integrals which can be evaluated easily and efficiently. Moreover, the met…
This paper considers the cooperative device-to-device (D2D) systems with non-orthogonal multiple access (NOMA). We assume that the base station (BS) can communicate simultaneously with all users to satisfy the full information transmission. In order to characterize the impact of the weak channel and different decoding schemes, two kinds of decoding strategies are proposed: \emph{single signal decoding scheme} and \emph{MRC decoding scheme}, respectively. For the \emph{single signal decoding scheme}, the users immediately decode the received signals after receptions from the BS. Meanwhile, for …
This paper considers the distributed information bottleneck (D-IB) problem for a primitive Gaussian diamond channel with two relays and Rayleigh fading. Due to the bottleneck constraint, it is impossible for the relays to inform the destination node of the perfect channel state information (CSI) in each realization. To evaluate the bottleneck rate, we provide an upper bound by assuming that the destination node knows the CSI and the relays can cooperate with each other, and also three achievable schemes with simple symbol-by-symbol relay processing and compression. Numerical results show that …
Many-access channel (MnAC) model allows the number of users in the system and the number of active users to scale as a function of the blocklength and as such is suited for dynamic communication systems with massive number of users such as the Internet of Things. Existing MnAC models assume a priori knowledge of channel gains which is impractical since acquiring Channel State Information (CSI) for massive number of users can overwhelm the available radio resources. This paper incorporates Rayleigh fading effects to the MnAC model and derives an upper bound on the symmetric message-length capac…
In this paper, we consider unmanned aerial vehicle (UAV) assisted communication systems where a number of UAVs are utilized as multi-tier relays between a number of users and a base-transceiver station (BTS). We model the wireless propagation channel between the users and the BTS as a Rayleigh product channel, which is a product of a series of independent and identically distributed (i.i.d.) Rayleigh multi-input multi-output (MIMO) channels. We put a special interested in optimizing the number of tiers in such UAV-assisted systems for a given total number of UAVs to maximize the ergodic capaci…
In this paper, the blocklength-limited performance of a relaying system is studied, where channels are assumed to experience quasi-static Rayleigh fading while at the same time only the average channel state information (CSI) is available at the source. Both the physical-layer performance (blocklength-limited throughput) and the link-layer performance (effective capacity) of the relaying system are investigated. We propose a simple system operation by introducing a factor based on which we weight the average CSI and let the source determine the coding rate accordingly. In particular, we prove …
We study a hierarchical heterogeneous Rayleigh fading wireless sensor network (WSN) in which sensor nodes surveil a region of interest (RoI) and use access points (APs) as relays to transmit their sensed information to base stations (BSs). By considering both large-scale path-loss signal attenuation and small-scale signal variation due to Rayleigh fading, we formulate the node deployment problem as an optimization problem intended to minimize the network's wireless communication power consumption. Given ergodic capacity constraints on all wireless links, we study the necessary conditions for a…
The high-SNR capacity of the noncoherent MIMO channel has been derived for the case of independent and identically distributed (IID) Rayleigh block fading by exploiting the Gaussianity of the channel matrix. This implies the optimal degrees of freedom (DoF), i.e., the capacity pre-log factor. Nevertheless, as far as the optimal DoF is concerned, IID Rayleigh fading is apparently a sufficient but not necessary condition. In this paper, we show that the optimal DoF for the IID Rayleigh block fading channel is also the optimal DoF for a more general class of generic block fading channels, in whic…
Motivated by the current interest in ultra-reliable, low-latency, machine-type communication systems, we investigate the tradeoff between reliability, throughput, and latency in the transmission of information over multiple-antenna Rayleigh block-fading channels. Specifically, we obtain finite-blocklength, finite-SNR upper and lower bounds on the maximum coding rate achievable over such channels for a given constraint on the packet error probability. Numerical evidence suggests that our bounds delimit tightly the maximum coding rate already for short blocklengths (packets of about 100 symbols)…
We develop a characterization of fading models, which assigns a number called logarithmic Jensen's gap to a given fading model. We show that as a consequence of a finite logarithmic Jensen's gap, approximate capacity region can be obtained for fast fading interference channels (FF-IC) for several scenarios. We illustrate three instances where a constant capacity gap can be obtained as a function of the logarithmic Jensen's gap. Firstly for an FF-IC with neither feedback nor instantaneous channel state information at transmitter (CSIT), if the fading distribution has finite logarithmic Jensen's…
The correspondence cited in the title [1] derived ergodic capacity of the coherent multiple-input multiple-output (MIMO) channel in independent and identically distributed (IID) Rayleigh fading. While the theoretical results are correct, several plots in the paper are incorrect. In this correspondence, we correct the plots. More importantly, the corrected plots present an interesting and compelling contrast between performances of the coherent MIMO systems with and without channel state information at the transmitter; whereas this view is somewhat limited in [1] because of flaws in the capacit…
Polar codes have been shown to approach capacity of symmetric binary erasure channels and also have low encoding and decoding complexity. Wireless channels are bursty in nature and a method to apply polar codes over wireless channels is proposed. This paper investigates the performance of polar codes over typical urban fading wireless channels. The wireless channel is modeled as a degraded erasure channel by using an inner convolution code and interleaving. When the convolution code fails to correct any errors, the corresponding bits are discarded and treated as erasures. We present the perfor…
The capacity of multiple-input multiple-output additive white Gaussian noise channels is investigated under peak amplitude constraints on the norm of the input vector. New insights on the capacity-achieving input distribution are presented. Furthermore, it is provided an iterative algorithm to numerically evaluate both the information capacity and the optimal input distribution of such channel.
