40 research outputs found
Probabilistic Constellation Shaping Algorithms: Performance vs. Complexity Trade-offs:Performance vs. Complexity Trade-offs
We review the recent advances in the design of probabilistic shaping algorithms. We investigate the implementation complexity of these algorithms in terms of required storage and computational power. We show that (1) the optimum performance can be achieved via different algorithms creating a trade-off between storage and computational complexities, and (2) a significant reduction in complexity can be achieved via the recently-proposed shift-based band-trellis enumerative sphere shaping if a slight degradation in performance is tolerated
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
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
Partial Enumerative Sphere Shaping
The dependency between the Gaussianity of the input distribution for the
additive white Gaussian noise (AWGN) channel and the gap-to-capacity is
discussed. We show that a set of particular approximations to the
Maxwell-Boltzmann (MB) distribution virtually closes most of the shaping gap.
We relate these symbol-level distributions to bit-level distributions, and
demonstrate that they correspond to keeping some of the amplitude bit-levels
uniform and independent of the others. Then we propose partial enumerative
sphere shaping (P-ESS) to realize such distributions in the probabilistic
amplitude shaping (PAS) framework. Simulations over the AWGN channel exhibit
that shaping 2 amplitude bits of 16-ASK have almost the same performance as
shaping 3 bits, which is 1.3 dB more power-efficient than uniform signaling at
a rate of 3 bit/symbol. In this way, required storage and computational
complexity of shaping are reduced by factors of 6 and 3, respectively.Comment: 6 pages, 6 figure