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

Nitrogen oxides and PAN in plumes from boreal fires during ARCTAS-B and their impact on ozone: an integrated analysis of aircraft and satellite observations

We determine enhancement ratios for NO_x, PAN, and other NO_y species from boreal biomass burning using aircraft data obtained during the ARCTAS-B campaign and examine the impact of these emissions on tropospheric ozone in the Arctic. We find an initial emission factor for NO_x of 1.06 g NO per kg dry matter (DM) burned, much lower than previous observations of boreal plumes, and also one third the value recommended for extratropical fires. Our analysis provides the first observational confirmation of rapid PAN formation in a boreal smoke plume, with 40% of the initial NO_x emissions being converted to PAN in the first few hours after emission. We find little clear evidence for ozone formation in the boreal smoke plumes during ARCTAS-B in either aircraft or satellite observations, or in model simulations. Only a third of the smoke plumes observed by the NASA DC8 showed a correlation between ozone and CO, and ozone was depleted in the plumes as often as it was enhanced. Special observations from the Tropospheric Emission Spectrometer (TES) also show little evidence for enhanced ozone in boreal smoke plumes between 15 June and 15 July 2008. Of the 22 plumes observed by TES, only 4 showed ozone increasing within the smoke plumes, and even in those cases it was unclear that the increase was caused by fire emissions. Using the GEOS-Chem atmospheric chemistry model, we show that boreal fires during ARCTAS-B had little impact on the median ozone profile measured over Canada, and had little impact on ozone within the smoke plumes observed by TES