Capacity and Modulations with Peak Power Constraint

A practical communication channel often suffers from constraints on input other than the average power, such as the peak power constraint. In order to compare achievable rates with different constellations as well as the channel capacity under such constraints, it is crucial to take these constraints into consideration properly. In this paper, we propose a direct approach to compare the achievable rates of practical input constellations and the capacity under such constraints. As an example, we study the discrete-time complex-valued additive white Gaussian noise (AWGN) channel and compare the capacity under the peak power constraint with the achievable rates of phase shift keying (PSK) and quadrature amplitude modulation (QAM) input constellations.Comment: 9 pages with 12 figures. Preparing for submissio

Neural style transfer of weak lensing mass maps

We propose a new generative model of projected cosmic mass density maps inferred from weak gravitational lensing observations of distant galaxies (weak lensing mass maps). We construct the model based on a neural style transfer so that it can transform Gaussian weak lensing mass maps into deeply non-Gaussian counterparts as predicted in ray-tracing lensing simulations. We develop an unpaired image-to-image translation method with Cycle-Consistent Generative Adversarial Networks (Cycle GAN), which learn efficient mapping from an input domain to a target domain. Our model is designed to enjoy important advantages; it is trainable with no need for paired simulation data, flexible to make the input domain visually meaningful, and expandable to rapidly-produce a map with a larger sky coverage than training data without additional learning. Using 10,000 lensing simulations, we find that appropriate labeling of training data based on field variance requires the model to exhibit a desired diversity of various summary statistics for weak lensing mass maps. Compared with a popular log-normal model, our model improves in predicting the statistical natures of three-point correlations and local properties of rare high-density regions. We also demonstrate that our model enables us to produce a continuous map with a sky coverage of $\sim166\, \mathrm{deg}^2$ but similar non-Gaussian features to training data covering $\sim12\, \mathrm{deg}^2$ in a GPU minute. Hence, our model can be beneficial to massive productions of synthetic weak lensing mass maps, which is of great importance in future precise real-world analyses.Comment: 20 pages, 11 figures, 3 tables. A trial dataset of fake weak lensing mass maps generated by our GANs is available at https://www.dropbox.com/scl/fo/hq1o41e8jwsfm4gqtkmnu/h?rlkey=0ymsucz2nzoju3gew8tsyz7qw&dl=