Related papers: An Upper Bound for Signal Transmission Error Proba…
We consider the problem of lower bounding the error probability under the invariant causal prediction (ICP) framework. To this end, we examine and draw connections between ICP and the zero-rate Gaussian multiple access channel by first…
We present a new lower bound on the Bowen-Radin maximal density of radius-R ball packings in the m-dimensional hyperbolic space, improving on the basic covering bound by factor \Omega(m(R+\ln m)) as m tends to infinity. This is done by…
New upper and lower bounds for the error probability over an erasure channel are provided, making use of Wei's generalized weights, hierarchy and spectra. In many situations the upper and lower bounds coincide and this allows improvement of…
Embedding the data in hyperbolic spaces can preserve complex relationships in very few dimensions, thus enabling compact models and improving efficiency of machine learning (ML) algorithms. The underlying idea is that hyperbolic…
In this paper, we study the achievable performance of dirty paper coding for the Gaussian broadcast channel (BC) with finite blocklength and we propose two different achievability bounds for this problem. We present the broadcast adaptation…
In this paper we provide explicit upper bounds on some distances between the (law of the) output of a random Gaussian NN and (the law of) a random Gaussian vector. Our results concern both shallow random Gaussian neural networks with…
Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…
We introduce a definition of perfect and quasi-perfect codes for symmetric channels parametrized by an auxiliary output distribution. This notion generalizes previous definitions of perfect and quasi-perfect codes and encompasses maximum…
In this paper we analyse Belief Propagation over a Gaussian model in a dynamic environment. Recently, this has been proposed as a method to average local measurement values by a distributed protocol ("Consensus Propagation", Moallemi & Van…
We study non-relativistic propagation of Gaussian wave packets in one-dimensional Eckart potential, a barrier, or a well. In the picture used, the transmitted wave packet results from interference between the copies of the freely…
We provide accurate expressions for the $s$-wave scattering length for a Gaussian potential well in one, two and three spatial dimensions. The Gaussian potential is widely used as a pseudopotential in the theoretical description of…
Deep Learning Gaussian Processes (DL-GP) are proposed as a methodology for analyzing (approximating) computer models that produce heteroskedastic and high-dimensional output. Computer simulation models have many areas of applications,…
This paper adds to the understanding of the capacity region of the Gaussian interference channel. To this end, the capacity region of the one-sided Gaussian interference channel is first fully characterized. This is accomplished by…
We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (sub- or super-diffusion) at longer times. Using the standard non-Markovian diffusion equation…
For a conformally compact manifold that is hyperbolic near infinity and of dimension $n+1$, we complete the proof of the optimal $O(r^{n+1})$ upper bound on the resonance counting function, correcting a mistake in the existing literature.…
This paper deals with a situation of some importance for the analysis of experimental data via Neural Network (NN) or similar devices: Let $N$ data be given, such that $N=N_s+N_b$, where $N_s$ is the number of signals, $N_b$ the number of…
We consider here how to separate multidimensional signals into two categories, such that the binary decision transmits the maximum possible information transmitted about those signals. Our motivation comes from the nervous system, where…
For the additive white Gaussian noise channel with average codeword power constraint, sparse superposition codes are developed. These codes are based on the statistical high-dimensional regression framework. The paper [IEEE Trans. Inform.…
In this paper, we derive upper and lower bounds as well as a simple closed-form approximation for the capacity of the continuous-time, bandlimited, additive white Gaussian noise channel in a three-dimensional free-space electromagnetic…
The achievable rate of information transfer in optical communications is determined by the physical properties of the communication channel, such as the intrinsic channel noise. Bosonic phase-noise channels, a class of non-Gaussian…