27 research outputs found
Enumerative Sphere Shaping for Rate Adaptation and Reach Increase in WDM Transmission Systems
The performance of enumerative sphere shaping (ESS), constant composition
distribution matching (CCDM), and uniform signalling are compared at the same
forward error correction rate. ESS is shown to offer a reach increase of
approximately 10% and 22% compared to CCDM and uniform signalling,
respectively.Comment: 4 Pages, 4 figure
Temporal Properties of Enumerative Shaping:Autocorrelation and Energy Dispersion Index
We study the effective SNR behavior of various enumerative amplitude shaping algorithms. We show that their relative behavior can be explained via the temporal autocorrelation function or via the energy dispersion index
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
On the Nonlinear Shaping Gain with Probabilistic Shaping and Carrier Phase Recovery
The performance of different probabilistic amplitude shaping (PAS)techniques in the nonlinear regime is investigated, highlighting its dependence on the PAS block length and the interaction with carrier phase recovery (CPR). Different PAS implementations are considered, based on different distribution matching (DM) techniques—namely, sphere shaping, shell mapping with different number of shells, and constant composition DM—and amplitude-to-symbol maps. When CPR is not included, PAS with optimal block length provides a nonlinear shaping gain with respect to a linearly optimized PAS (with infinite block length); among the considered DM techniques, the largest gain is obtained with sphere shaping. On the other hand, the nonlinear shaping gain becomes smaller, or completely vanishes, when CPR is included, meaning that in this case all the considered implementations achieve a similar performance for a sufficiently long block length. Similar results are obtained in different link configurations ( km, km, and km single-mode-fiber links), and also including laser phase noise, except when in-line dispersion compensation is used. Furthermore, we define a new metric, the nonlinear phase noise (NPN) metric, which is based on the frequency resolved logarithmic perturbation models and explains the interaction of CPR and PAS. We show that the NPN metric is highly correlated with the performance of the system. Our results suggest that, in general, the optimization of PAS in the nonlinear regime should always account for the presence of a CPR algorithm. In this case, the reduction of the rate loss (obtained by using sphere shaping and increasing the DM block length) turns out to be more important than the mitigation of the nonlinear phase noise (obtained by using constant-energy DMs and reducing the block length), the latter being already granted by the CPR algorithm
Polarization-ring-switching for nonlinearity-tolerant geometrically-shaped four-dimensional formats maximizing generalized mutual information
In this paper, a new four-dimensional 64-ary polarization ring switching
(4D-64PRS) modulation format with a spectral efficiency of 6 bit/4D-sym is
introduced. The format is designed by maximizing the generalized mutual
information (GMI) and by imposing a constant-modulus on the 4D structure. The
proposed format yields an improved performance with respect to state-of-the-art
geometrically shaped modulation formats for bit-interleaved coded modulation
systems at the same spectral efficiency. Unlike previously published results,
the coordinates of the constellation points and the binary labeling of the
constellation are jointly optimized. When compared with
polarization-multiplexed 8-ary quadrature-amplitude modulation (PM-8QAM), gains
of up to 0.7 dB in signal-to-noise ratio are observed in the additive white
Gaussian noise (AWGN) channel. For a long-haul nonlinear optical fiber system
of 8,000 km, gains of up to 0.27 bit/4D-sym (5.5% data capacity increase) are
observed. These gains translate into a reach increase of approximately 16%
(1,100 km). The proposed modulation format is also shown to be more tolerant to
nonlinearities than PM-8QAM. Results with LDPC codes are also presented, which
confirm the gains predicted by the GMI.Comment: 12 pages, 12 figure
On the Nonlinear Shaping Gain with Probabilistic Shaping and Carrier Phase Recovery
The performance of different probabilistic amplitude shaping (PAS) techniques
in the nonlinear regime is investigated, highlighting its dependence on the PAS
block length and the interaction with carrier phase recovery (CPR). Different
PAS implementations are considered, based on different distribution matching
(DM) techniques-namely, sphere shaping, shell mapping with different number of
shells, and constant composition DM-and amplitude-to-symbol maps. When CPR is
not included, PAS with optimal block length provides a nonlinear shaping gain
with respect to a linearly optimized PAS (with infinite block length); among
the considered DM techniques, the largest gain is obtained with sphere shaping.
On the other hand, the nonlinear shaping gain becomes smaller, or completely
vanishes, when CPR is included, meaning that in this case all the considered
implementations achieve a similar performance for a sufficiently long block
length. Similar results are obtained in different link configurations (1x180km,
15x80km, and 27x80km single-mode-fiber links), and also including laser phase
noise, except when in-line dispersion compensation is used. Furthermore, we
define a new metric, the nonlinear phase noise (NPN) metric, which is based on
the frequency resolved logarithmic perturbation models and explains the
interaction of CPR and PAS. We show that the NPN metric is highly correlated
with the performance of the system. Our results suggest that, in general, the
optimization of PAS in the nonlinear regime should always account for the
presence of a CPR algorithm. In this case, the reduction of the rate loss
(obtained by using sphere shaping and increasing the DM block length) turns out
to be more important than the mitigation of the nonlinear phase noise (obtained
by using constant-energy DMs and reducing the block length), the latter being
already granted by the CPR algorithm.Comment: Accepter for publication to the Journal of Lightwave Technologies on
January 202
Exponentially-Weighted Energy Dispersion Index for the Nonlinear Interference Analysis of Finite-Blocklength Shaping
A metric called exponentially-weighted energy dispersion index (EEDI) is
proposed to explain the blocklength-dependent effective signal-to-noise ratio
(SNR) in probabilistically shaped fiber-optic systems. EEDI is better than
energy dispersion index (EDI) at capturing the dependency of the effective SNR
on the blocklength for long-distance transmission