Related papers: On approximating Gaussian relay networks by determ…
We consider the N-relay Gaussian diamond network where a source node communicates to a destination node via N parallel relays through a cascade of a Gaussian broadcast (BC) and a multiple access (MAC) channel. Introduced in 2000 by Schein…
We consider an arbitrary layered Gaussian relay network with $L$ layers of $N$ relays each, from which we select subnetworks with $K$ relays per layer. We prove that: (i) For arbitrary $L, N$ and $K = 1$, there always exists a subnetwork…
When a hybrid Bayesian network has conditionally deterministic variables with continuous parents, the joint density function for the continuous variables does not exist. Conditional linear Gaussian distributions can handle such cases when…
Bayesian neural networks are theoretically well-understood only in the infinite-width limit, where Gaussian priors over network weights yield Gaussian priors over network outputs. Recent work has suggested that finite Bayesian networks may…
A full-duplex wireless network with three users that want to establish full message-exchange via a relay is considered. Thus, the network known as the Y-channel has a total of 6 messages, 2 outgoing and 2 incoming at each user. The users…
Multilayer (or deep) networks are powerful probabilistic models based on multiple stages of a linear transform followed by a non-linear (possibly random) function. In general, the linear transforms are defined by matrices and the non-linear…
In this paper, the Gaussian relay channel with linear time-invariant relay filtering is considered. Based on spectral theory for stationary processes, the maximum achievable rate for this subclass of linear Gaussian relay operation is…
Infinitely wide or deep neural networks (NNs) with independent and identically distributed (i.i.d.) parameters have been shown to be equivalent to Gaussian processes. Because of the favorable properties of Gaussian processes, this…
In a recently published paper [1], it is shown that deep neural networks (DNNs) with random Gaussian weights preserve the metric structure of the data, with the property that the distance shrinks more when the angle between the two data…
Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…
This paper revisits the Gaussian degraded relay channel, where the link that carries information from the source to the destination is a physically degraded version of the link that carries information from the source to the relay. The…
We present a framework to study linear deterministic interference networks over finite fields. Unlike the popular linear deterministic models introduced to study Gaussian networks, we consider networks where the channel coefficients are…
We prove large and moderate deviations for the output of Gaussian fully connected neural networks. The main achievements concern deep neural networks (i.e., when the model has more than one hidden layer) and hold for bounded and continuous…
In this paper, we investigate the optimal precoding scheme for relay networks with finite-alphabet constraints. We show that the previous work utilizing various design criteria to maximize either the diversity order or the transmission rate…
We consider a three-terminal state-dependent relay channel with the channel state noncausally available at only the relay. Such a model may be useful for designing cooperative wireless networks with some terminals equipped with cognition…
Noisy network coding, which elegantly combines the conventional compress-and-forward relaying strategy and ideas from network coding, has recently drawn much attention for its simplicity and optimality in achieving to within constant gap of…
We study the efficacy and efficiency of deep generative networks for approximating probability distributions. We prove that neural networks can transform a low-dimensional source distribution to a distribution that is arbitrarily close to a…
In this paper, we show that the capacity of the three-node Gaussian relay channel can be achieved to within 1 and 2 bit/sec/Hz using compress-and-forward and amplify-and-forward relaying, respectively.
Standard upper and lower bounds on the capacity of relay channels are cut-set (CS), decode-forward (DF), and quantize-forward (QF) rates. For real additive white Gaussian noise (AWGN) multicast relay channels with one source node and one…
The ability of overparameterized deep networks to generalize well has been linked to the fact that stochastic gradient descent (SGD) finds solutions that lie in flat, wide minima in the training loss -- minima where the output of the…