29 research outputs found
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
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
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
Hierarchical Distribution Matching for Probabilistically Shaped Coded Modulation
The implementation difficulties of combining distribution matching (DM) and
dematching (invDM) for probabilistic shaping (PS) with soft-decision forward
error correction (FEC) coding can be relaxed by reverse concatenation, for
which the FEC coding and decoding lies inside the shaping algorithms. PS can
seemingly achieve performance close to the Shannon limit, although there are
practical implementation challenges that need to be carefully addressed. We
propose a hierarchical DM (HiDM) scheme, having fully parallelized input/output
interfaces and a pipelined architecture that can efficiently perform the
DM/invDM without the complex operations of previously proposed methods such as
constant composition DM (CCDM). Furthermore, HiDM can operate at a
significantly larger post-FEC bit error rate (BER) for the same post-invDM BER
performance, which facilitates simulations. These benefits come at the cost of
a slightly larger rate loss and required signal-to-noise ratio at a given
post-FEC BER.Comment: 11 pages, 7 figure
FPGA Implementation of Hierarchical Subcarrier Rate and Distribution Matching for up to 1.032 Tb/s or 262144-QAM
A novel hierarchical subcarrier rate and distribution matching has been implemented in an FPGA at 1.032 Tb/s. The implemented subsystem achieves seamless data flow among subcarriers at a resolution < 0.01 bit per channel use
Huffman-Coded Sphere Shaping for Extended Reach Single-Span Links
Huffman-coded sphere shaping (HCSS) is an algorithm for finite-length probabilistic constellation shaping, which provides nearly optimal energy efficiency at low implementation complexity. In this paper, we experimentally study the nonlinear performance of HCSS employing dual-polarization 64-ary quadrature amplitude modulation (DP-64QAM) in an extended-reach single-span link comprising 200 km of standard single-mode fiber (SSMF). We investigate the effects of shaping sequence length, dimensionality of symbol mapping, and shaping rate. We determine that the naïve approach of Maxwell-Boltzmann distribution matching-which is optimal in the additive white Gaussian noise channel-provides a maximum achievable information rate (AIR) gain of 0.18 bits/4D-symbol with respect to uniform signaling at optimum launch power in the infinite length regime. Conversely, HCSS can achieve a gain of 0.37 bits/4D-symbol over uniform signaling using amplitude sequence length of 32, which may be implemented without multiplications, using integer comparison and addition operations only. Coded system performance, with a net data rate of approximately 425 Gb/s for both shaped and uniform inputs, is also analyzed