1,916 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
Post-FEC BER Benchmarking for Bit-Interleaved Coded Modulation with Probabilistic Shaping
Accurate performance benchmarking after forward error correction (FEC)
decoding is essential for system design in optical fiber communications.
Generalized mutual information (GMI) has been shown to be successful at
benchmarking the bit-error rate (BER) after FEC decoding (post-FEC BER) for
systems with soft-decision (SD) FEC without probabilistic shaping (PS).
However, GMI is not relevant to benchmark post-FEC BER for systems with SD-FEC
and PS. For such systems, normalized GMI (NGMI), asymmetric information (ASI),
and achievable FEC rate have been proposed instead. They are good at
benchmarking post-FEC BER or to give an FEC limit in bit-interleaved coded
modulation (BICM) with PS, but their relation has not been clearly explained so
far. In this paper, we define generalized L-values under mismatched decoding,
which are connected to the GMI and ASI. We then show that NGMI, ASI, and
achievable FEC rate are theoretically equal under matched decoding but not
under mismatched decoding. We also examine BER before FEC decoding (pre-FEC
BER) and ASI over Gaussian and nonlinear fiber-optic channels with
approximately matched decoding. ASI always shows better correlation with
post-FEC BER than pre-FEC BER for BICM with PS. On the other hand, post-FEC BER
can differ at a given ASI when we change the bit mapping, which describes how
each bit in a codeword is assigned to a bit tributary.Comment: 14 pages, 8 figure
Signal Shaping for BICM at Low SNR
The mutual information of bit-interleaved coded modulation (BICM) systems,
sometimes called the BICM capacity, is investigated at low signal-to-noise
ratio (SNR), i.e., in the wideband regime. A new linear transform that depends
on bits' probabilities is introduced. This transform is used to prove the
asymptotical equivalence between certain BICM systems with uniform and
nonuniform input distributions. Using known results for BICM systems with a
uniform input distribution, we completely characterize the combinations of
input alphabet, input distribution, and binary labeling that achieve the
Shannon limit -1.59 dB. The main conclusion is that a BICM system achieves the
Shannon limit at low SNR if and only if it can be represented as a zero-mean
linear projection of a hypercube, which is the same condition as for uniform
input distributions. Hence, probabilistic shaping offers no extra degrees of
freedom to optimize the low-SNR mutual information of BICM systems, in addition
to what is provided by geometrical shaping. These analytical conclusions are
confirmed by numerical results, which also show that for a fixed input
alphabet, probabilistic shaping of BICM can improve the mutual information in
the low and medium SNR range over any coded modulation system with a uniform
input distribution
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
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