6,064 research outputs found
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
X-ray Reflection Spectroscopy of the Black Hole GX 339-4: Exploring the Hard State with Unprecedented Sensitivity
We analyze {\it simultaneously} six composite {\it RXTE} spectra of GX 339--4
in the hard state comprising 77 million counts collected over 196 ks. The
source spectra are ordered by luminosity and spanthe range 1.6\% to 17\% of the
Eddington luminosity. Crucially, using our new tool {\tt pcacorr}, we
re-calibrate the data to a precision of 0.1\%, an order of magnitude
improvement over all earlier work. Using our advanced reflection model {\tt
relxill}, we target the strong features in the component of emission reflected
from the disk, namely, the relativistically-broadened Fe K emission line, the
Fe K edge and the Compton hump. We report results for two joint fits to the six
spectra: For the first fit, we fix the spin parameter to its maximal value
() and allow the inner disk radius to vary. Results
include (i) precise measurements of , with evidence that the disk
becomes slightly truncated at a few percent of Eddington; and (ii) an
order-of-magnitude swing with luminosity in the high energy cutoff, which
reaches keV at our lowest luminosity. For the second fit, we make the
standard assumption in estimating spin that the inner edge of the accretion
disk is located at the innermost stable circular orbit () and find (90\% confidence,
statistical). For both fits, and at the same level of statistical confidence,
we estimate that the disk inclination is deg and that the Fe
abundance is super-solar, .Comment: Accepted for publication in ApJ, 20 pages, 13 figure
Protograph-Based LDPC Code Design for Shaped Bit-Metric Decoding
A protograph-based low-density parity-check (LDPC) code design technique for
bandwidth-efficient coded modulation is presented. The approach jointly
optimizes the LDPC code node degrees and the mapping of the coded bits to the
bit-interleaved coded modulation (BICM) bit-channels. For BICM with uniform
input and for BICM with probabilistic shaping, binary-input symmetric-output
surrogate channels for the code design are used. The constructed codes for
uniform inputs perform as good as the multi-edge type codes of Zhang and
Kschischang (2013). For 8-ASK and 64-ASK with probabilistic shaping, codes of
rates 2/3 and 5/6 with blocklength 64800 are designed, which operate within
0.63dB and 0.69dB of continuous AWGN capacity for a target frame error rate of
1e-3 at spectral efficiencies of 1.38 and 4.25 bits/channel use, respectively.Comment: 9 pages, 10 figures. arXiv admin note: substantial text overlap with
arXiv:1501.0559
Two are better than one: Fundamental parameters of frame coherence
This paper investigates two parameters that measure the coherence of a frame:
worst-case and average coherence. We first use worst-case and average coherence
to derive near-optimal probabilistic guarantees on both sparse signal detection
and reconstruction in the presence of noise. Next, we provide a catalog of
nearly tight frames with small worst-case and average coherence. Later, we find
a new lower bound on worst-case coherence; we compare it to the Welch bound and
use it to interpret recently reported signal reconstruction results. Finally,
we give an algorithm that transforms frames in a way that decreases average
coherence without changing the spectral norm or worst-case coherence
Performance Prediction of Nonbinary Forward Error Correction in Optical Transmission Experiments
In this paper, we compare different metrics to predict the error rate of
optical systems based on nonbinary forward error correction (FEC). It is shown
that the correct metric to predict the performance of coded modulation based on
nonbinary FEC is the mutual information. The accuracy of the prediction is
verified in a detailed example with multiple constellation formats, FEC
overheads in both simulations and optical transmission experiments over a
recirculating loop. It is shown that the employed FEC codes must be universal
if performance prediction based on thresholds is used. A tutorial introduction
into the computation of the threshold from optical transmission measurements is
also given.Comment: submitted to IEEE/OSA Journal of Lightwave Technolog
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