Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

In this paper, we provide for the first time a systematic comparison of distribution matching (DM) and sphere shaping (SpSh) algorithms for short blocklength probabilistic amplitude shaping. For asymptotically large blocklengths, constant composition distribution matching (CCDM) is known to generate the target capacity-achieving distribution. As the blocklength decreases, however, the resulting rate loss diminishes the efficiency of CCDM. We claim that for such short blocklengths and over the additive white Gaussian channel (AWGN), the objective of shaping should be reformulated as obtaining the most energy-efficient signal space for a given rate (rather than matching distributions). In light of this interpretation, multiset-partition DM (MPDM), enumerative sphere shaping (ESS) and shell mapping (SM), are reviewed as energy-efficient shaping techniques. Numerical results show that MPDM and SpSh have smaller rate losses than CCDM. SpSh--whose sole objective is to maximize the energy efficiency--is shown to have the minimum rate loss amongst all. We provide simulation results of the end-to-end decoding performance showing that up to 1 dB improvement in power efficiency over uniform signaling can be obtained with MPDM and SpSh at blocklengths around 200. Finally, we present a discussion on the complexity of these algorithms from the perspective of latency, storage and computations.Comment: 18 pages, 10 figure

Local ensemble transform Kalman filter, a fast non-stationary control law for adaptive optics on ELTs: theoretical aspects and first simulation results

We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs).Comment: This paper was published in Optics Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/oe/ . Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under la

The ESCAPE project : Energy-efficient Scalable Algorithms for Weather Prediction at Exascale

In the simulation of complex multi-scale flows arising in weather and climate modelling, one of the biggest challenges is to satisfy strict service requirements in terms of time to solution and to satisfy budgetary constraints in terms of energy to solution, without compromising the accuracy and stability of the application. These simulations require algorithms that minimise the energy footprint along with the time required to produce a solution, maintain the physically required level of accuracy, are numerically stable, and are resilient in case of hardware failure. The European Centre for Medium-Range Weather Forecasts (ECMWF) led the ESCAPE (Energy-efficient Scalable Algorithms for Weather Prediction at Exascale) project, funded by Horizon 2020 (H2020) under the FET-HPC (Future and Emerging Technologies in High Performance Computing) initiative. The goal of ESCAPE was to develop a sustainable strategy to evolve weather and climate prediction models to next-generation computing technologies. The project partners incorporate the expertise of leading European regional forecasting consortia, university research, experienced high-performance computing centres, and hardware vendors. This paper presents an overview of the ESCAPE strategy: (i) identify domain-specific key algorithmic motifs in weather prediction and climate models (which we term Weather & Climate Dwarfs), (ii) categorise them in terms of computational and communication patterns while (iii) adapting them to different hardware architectures with alternative programming models, (iv) analyse the challenges in optimising, and (v) find alternative algorithms for the same scheme. The participating weather prediction models are the following: IFS (Integrated Forecasting System); ALARO, a combination of AROME (Application de la Recherche a l'Operationnel a Meso-Echelle) and ALADIN (Aire Limitee Adaptation Dynamique Developpement International); and COSMO-EULAG, a combination of COSMO (Consortium for Small-scale Modeling) and EULAG (Eulerian and semi-Lagrangian fluid solver). For many of the weather and climate dwarfs ESCAPE provides prototype implementations on different hardware architectures (mainly Intel Skylake CPUs, NVIDIA GPUs, Intel Xeon Phi, Optalysys optical processor) with different programming models. The spectral transform dwarf represents a detailed example of the co-design cycle of an ESCAPE dwarf. The dwarf concept has proven to be extremely useful for the rapid prototyping of alternative algorithms and their interaction with hardware; e.g. the use of a domain-specific language (DSL). Manual adaptations have led to substantial accelerations of key algorithms in numerical weather prediction (NWP) but are not a general recipe for the performance portability of complex NWP models. Existing DSLs are found to require further evolution but are promising tools for achieving the latter. Measurements of energy and time to solution suggest that a future focus needs to be on exploiting the simultaneous use of all available resources in hybrid CPU-GPU arrangements

Apodized phase mask coronagraphs for arbitrary apertures

Phase masks coronagraphs can be seen as linear systems that spatially redistribute, in the pupil plane, the energy collected by the telescope. Most of the on-axis light must ideally be rejected outside the aperture to be blocked with a Lyot stop, while almost all off-axis light must go through it. The unobstructed circular apertures of off-axis telescopes make this possible but all major telescopes are however on-axis and the performance of these coronagraphs is dramatically reduced by the central obstruction. Their performance can be restored by using an additional optimally designed apodizer that changes the amplitude in the first pupil plane so that the on-axis light is rejected outside the obstructed aperture of the telescope. The numerical optimization model is built by maximizing the apodizer's transmission while setting constraints on the extremum values of the electric field that the Lyot stop does not block. The coronagraphic image is compared to what a non-apodized phase mask coronagraph provides and an analysis is made of the trade-offs that exist between the apodizer transmission and the Lyot stop properties. The existence of a solution and the mask transmission depend on the aperture and the Lyot stop geometries, and on the constraints that are set on the on-axis attenuation. The system throughput is a concave function of the Lyot stop transmission. In the case of a VLT-like aperture, apodizers with a transmission of 0.16 to 0.92 associated with a four-quadrant phase mask provide contrast as low as a few 1e-10 at 1 lambda/D from the star. The system's maximum throughput is 0.64, for an apodizer with an 0.88 transmission and a Lyot stop with a 0.69 transmission. Optimizing apodizers for a vortex phase mask requires computation times much longer than in the previous case, and no result is presented for this mask.Comment: 16 page

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature