566 research outputs found
On the BICM Capacity
Optimal binary labelings, input distributions, and input alphabets are
analyzed for the so-called bit-interleaved coded modulation (BICM) capacity,
paying special attention to the low signal-to-noise ratio (SNR) regime. For
8-ary pulse amplitude modulation (PAM) and for 0.75 bit/symbol, the folded
binary code results in a higher capacity than the binary reflected gray code
(BRGC) and the natural binary code (NBC). The 1 dB gap between the additive
white Gaussian noise (AWGN) capacity and the BICM capacity with the BRGC can be
almost completely removed if the input symbol distribution is properly
selected. First-order asymptotics of the BICM capacity for arbitrary input
alphabets and distributions, dimensions, mean, variance, and binary labeling
are developed. These asymptotics are used to define first-order optimal (FOO)
constellations for BICM, i.e. constellations that make BICM achieve the Shannon
limit -1.59 \tr{dB}. It is shown that the \Eb/N_0 required for reliable
transmission at asymptotically low rates in BICM can be as high as infinity,
that for uniform input distributions and 8-PAM there are only 72 classes of
binary labelings with a different first-order asymptotic behavior, and that
this number is reduced to only 26 for 8-ary phase shift keying (PSK). A general
answer to the question of FOO constellations for BICM is also given: using the
Hadamard transform, it is found that for uniform input distributions, a
constellation for BICM is FOO if and only if it is a linear projection of a
hypercube. A constellation based on PAM or quadrature amplitude modulation
input alphabets is FOO if and only if they are labeled by the NBC; if the
constellation is based on PSK input alphabets instead, it can never be FOO if
the input alphabet has more than four points, regardless of the labeling.Comment: Submitted to the IEEE Transactions on Information Theor
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
Achievable Rates for Four-Dimensional Coded Modulation with a Bit-Wise Receiver
We study achievable rates for four-dimensional (4D) constellations for
spectrally efficient optical systems based on a (suboptimal) bit-wise receiver.
We show that PM-QPSK outperforms the best 4D constellation designed for uncoded
transmission by approximately 1 dB. Numerical results using LDPC codes validate
the analysis
On BICM receivers for TCM transmission
Recent results have shown that the performance of bit-interleaved coded
modulation (BICM) using convolutional codes in nonfading channels can be
significantly improved when the interleaver takes a trivial form (BICM-T),
i.e., when it does not interleave the bits at all. In this paper, we give a
formal explanation for these results and show that BICM-T is in fact the
combination of a TCM transmitter and a BICM receiver. To predict the
performance of BICM-T, a new type of distance spectrum for convolutional codes
is introduced, analytical bounds based on this spectrum are developed, and
asymptotic approximations are also presented. It is shown that the minimum
distance of the code is not the relevant optimization criterion for BICM-T.
Optimal convolutional codes for different constrain lengths are tabulated and
asymptotic gains of about 2 dB are obtained. These gains are found to be the
same as those obtained by Ungerboeck's one-dimensional trellis coded modulation
(1D-TCM), and therefore, in nonfading channels, BICM-T is shown to be
asymptotically as good as 1D-TCM.Comment: Submitted to the IEEE Transactions on Communication
Towards Fully Optimized BICM Transceivers
Bit-interleaved coded modulation (BICM) transceivers often use equally spaced
constellations and a random interleaver. In this paper, we propose a new BICM
design, which considers hierarchical (nonequally spaced) constellations, a
bit-level multiplexer, and multiple interleavers. It is shown that this new
scheme increases the degrees of freedom that can be exploited in order to
improve its performance. Analytical bounds on the bit error rate (BER) of the
system in terms of the constellation parameters and the multiplexing rules are
developed for the additive white Gaussian Noise (AWGN) and Nakagami- fading
channels. These bounds are then used to design the BICM transceiver. Numerical
results show that, compared to conventional BICM designs, and for a target BER
of , gains up to 3 dB in the AWGN channel are obtained. For fading
channels, the gains depend on the fading parameter, and reach 2 dB for a target
BER of and .Comment: Submitted to the IEEE Transactions on Communication
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
Increasing Achievable Information Rates via Geometric Shaping
Achievable information rates are used as a metric to design novel modulation
formats via geometric shaping. The proposed geometrically shaped 256-ary
constellation achieves SNR gains of up to 1.18 dB.Comment: Additional references have been adde
General BER Expression for One-Dimensional Constellations
A novel general ready-to-use bit-error rate (BER) expression for
one-dimensional constellations is developed. The BER analysis is performed for
bit patterns that form a labeling. The number of patterns for equally spaced
M-PAM constellations with different BER is analyzed.Comment: To appear in the Proceedings of the IEEE Global Communications
Conference (GLOBECOM) 2012. Remark 3 modifie
On Achievable Rates for Long-Haul Fiber-Optic Communications
Lower bounds on mutual information (MI) of long-haul optical fiber systems
for hard-decision and soft-decision decoding are studied. Ready-to-use
expressions to calculate the MI are presented. Extensive numerical simulations
are used to quantify how changes in the optical transmitter, receiver, and
channel affect the achievable transmission rates of the system. Special
emphasis is put to the use of different quadrature amplitude modulation
formats, channel spacings, digital back-propagation schemes and probabilistic
shaping. The advantages of using MI over the prevailing -factor as a figure
of merit of coded optical systems are also highlighted.Comment: Hard decision mutual information analysis added, two typos correcte
Eight-dimensional Polarization-ring-switching Modulation Formats
We propose two 8-dimensional (8D) modulation formats (8D-2048PRS-T1 and
8D-2048PRS-T2) with a spectral efficiency of 5.5 bit/4D-sym, where the 8
dimensions are obtained from two time slots and two polarizations. Both formats
provide a higher tolerance to nonlinearity by selecting symbols with
nonidentical states of polarization (SOPs) in two time slots. The performance
of these novel 8D modulation formats is assessed in terms of the effective
signal-to-noise ratio (SNR) and normalized generalized mutual information.
8D-2048PRS-T1 is more suitable for high SNRs, while 8D-2048PRS-T2 is shown to
be more tolerant to nonlinearities. A sensitivity improvement of at least 0.25
dB is demonstrated by maximizing normalized generalized mutual information
(NGMI). For a long-haul nonlinear optical fiber transmission system, the
benefit of mitigating the nonlinearity is demonstrated and a reach increase of
6.7% (560 km) over time-domain hybrid four-dimensional two-amplitude
eight-phase shift keying (TDH-4D-2A8PSK) is observed
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