Related papers: Rotating Non-Uniform and High-Dimensional Constell…
We study the clustering task under anisotropic Gaussian Mixture Models where the covariance matrices from different clusters are unknown and are not necessarily the identical matrix. We characterize the dependence of signal-to-noise ratios…
We present a general method for the error analysis of spatial modulation (SM) systems over correlated and uncorrelated Rayleigh and Rician fading channels. The proposed method, making use of the properties of proper complex random variables…
This paper initiates a systematic development of a theory of non-commutative optimization. It aims to unify and generalize a growing body of work from the past few years which developed and analyzed algorithms for natural geodesically…
Weight sharing in convolutional neural networks (CNNs) ensures that their feature maps will be translation-equivariant. However, although conventional convolutions are equivariant to translation, they are not equivariant to other isometries…
We present a novel, generally applicable Monte Carlo algorithm for the simulation of fluid systems. Geometric transformations are used to identify clusters of particles in such a manner that every cluster move is accepted, irrespective of…
Flow Matching (FM) is a recent generative modelling technique: we aim to learn how to sample from distribution $\mathfrak{X}_1$ by flowing samples from some distribution $\mathfrak{X}_0$ that is easy to sample from. The key trick is that…
This article deals with approximating steady-state particle-resolved fluid flow around a fixed particle of interest under the influence of randomly distributed stationary particles in a dispersed multiphase setup using Convolutional Neural…
In recent years, LEO satellite constellations have become envisioned as a core component of the next-generation wireless communication networks. The successive establishment of mega satellite constellations has triggered further demands for…
Bit-interleaved coded modulation with iterative decoding (BICM-ID) offers very good error performance over additive white Gaussian noise (AWGN) and fading channels if it uses a wisely designed signal mapping. Further, error performance of…
We present a new class of stochastic, geometrically-driven optimization algorithms on the orthogonal group $O(d)$ and naturally reductive homogeneous manifolds obtained from the action of the rotation group $SO(d)$. We theoretically and…
Motivated by the fact that full diversity order is achieved using the "best-relay" selection technique, we consider opportunistic amplify-and-forward and decode-and-forward relaying systems. We focus on the outage probability of such a…
Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning. Both pursuits require knowledge of the underlying symmetries in data, yet discovering these symmetries…
Multi-dimensional (MD) mapping offers more flexibility in mapping design for bit-interleaved coded modulation with iterative decoding (BICM-ID) and potentially improves the bandwidth efficiency. However, for higher order signal…
Probabilistic constellation shaping enables easy rate adaption and has been proven to reduce the gap to Shannon capacity. Constellation point probabilities are optimized to maximize either the mutual information or the bit-wise mutual…
For many wiretap channel models asymptotically optimal coding schemes are known, but less effort has been put into actual realizations of wiretap codes for practical parameters. Bounds on the mutual information and error probability when…
We introduce a new methodology to design uniformly accurate methods for oscillatory evolution equations. The targeted models are envisaged in a wide spectrum of regimes, from non-stiff to highly-oscillatory. Thanks to an averaging…
We introduce a learning-based approach to optimize a joint constellation for a multi-user MIMO broadcast channel ($T$ Tx antennas, $K$ users, each with $R$ Rx antennas), with perfect channel knowledge. The aim of the optimizer (MAX-MIN) is…
We extend so-called slit-slide-sew bijections to constellations and quasiconstellations. We present an involution on the set of hypermaps given with an orientation, one distinguished corner, and one distinguished edge leading away from the…
We study the possible rotation of cluster galaxies, developing, testing and applying a novel algorithm which identifies rotation, if such does exist, as well as its rotational centre, its axis orientation, rotational velocity amplitude and,…
The popularity of data augmentation techniques in machine learning has increased in recent years, as they enable the creation of new samples from existing datasets. Rotational augmentation, in particular, has shown great promise by…