301 research outputs found
Design of APSK Constellations for Coherent Optical Channels with Nonlinear Phase Noise
We study the design of amplitude phase-shift keying (APSK) constellations for
a coherent fiber-optical communication system where nonlinear phase noise
(NLPN) is the main system impairment. APSK constellations can be regarded as a
union of phase-shift keying (PSK) signal sets with different amplitude levels.
A practical two-stage (TS) detection scheme is analyzed, which performs close
to optimal detection for high enough input power. We optimize APSK
constellations with 4, 8, and 16 points in terms of symbol error probability
(SEP) under TS detection for several combinations of input power and fiber
length. Our results show that APSK is a promising modulation format in order to
cope with NLPN. As an example, for 16 points, performance gains of 3.2 dB can
be achieved at a SEP of 10^-2 compared to 16-QAM by choosing an optimized APSK
constellation. We also demonstrate that in the presence of severe nonlinear
distortions, it may become beneficial to sacrifice a constellation point or an
entire constellation ring to reduce the average SEP. Finally, we discuss the
problem of selecting a good binary labeling for the found constellations. For
the class of rectangular APSK a labeling design method is proposed, resulting
in near-optimal bit error probability.Comment: Submitted to IEEE Transactions on Communication
Improving soft FEC performance for higher-order modulations via optimized bit channel mappings
Soft forward error correction with higher-order modulations is often
implemented in practice via the pragmatic bit-interleaved coded modulation
paradigm, where a single binary code is mapped to a nonbinary modulation. In
this paper, we study the optimization of the mapping of the coded bits to the
modulation bits for a polarization-multiplexed fiber-optical system without
optical inline dispersion compensation. Our focus is on protograph-based
low-density parity-check (LDPC) codes which allow for an efficient hardware
implementation, suitable for high-speed optical communications. The
optimization is applied to the AR4JA protograph family, and further extended to
protograph-based spatially coupled LDPC codes assuming a windowed decoder. Full
field simulations via the split-step Fourier method are used to verify the
analysis. The results show performance gains of up to 0.25 dB, which translate
into a possible extension of the transmission reach by roughly up to 8%,
without significantly increasing the system complexity.Comment: This paper was published in Optics Express and is made available as
an electronic reprint with the permission of OSA. The paper can be found at
the following URL on the OSA website:
http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-22-12-1454
On Optimal TCM Encoders
An asymptotically optimal trellis-coded modulation (TCM) encoder requires the
joint design of the encoder and the binary labeling of the constellation. Since
analytical approaches are unknown, the only available solution is to perform an
exhaustive search over the encoder and the labeling. For large constellation
sizes and/or many encoder states, however, an exhaustive search is unfeasible.
Traditional TCM designs overcome this problem by using a labeling that follows
the set-partitioning principle and by performing an exhaustive search over the
encoders. In this paper we study binary labelings for TCM and show how they can
be grouped into classes, which considerably reduces the search space in a joint
design. For 8-ary constellations, the number of different binary labelings that
must be tested is reduced from 8!=40320 to 240. For the particular case of an
8-ary pulse amplitude modulation constellation, this number is further reduced
to 120 and for 8-ary phase shift keying to only 30. An algorithm to generate
one labeling in each class is also introduced. Asymptotically optimal TCM
encoders are tabulated which are up to 0.3 dB better than the previously best
known encoders
Optimized Bit Mappings for Spatially Coupled LDPC Codes over Parallel Binary Erasure Channels
In many practical communication systems, one binary encoder/decoder pair is
used to communicate over a set of parallel channels. Examples of this setup
include multi-carrier transmission, rate-compatible puncturing of turbo-like
codes, and bit-interleaved coded modulation (BICM). A bit mapper is commonly
employed to determine how the coded bits are allocated to the channels. In this
paper, we study spatially coupled low-density parity check codes over parallel
channels and optimize the bit mapper using BICM as the driving example. For
simplicity, the parallel bit channels that arise in BICM are replaced by
independent binary erasure channels (BECs). For two parallel BECs modeled
according to a 4-PAM constellation labeled by the binary reflected Gray code,
the optimization results show that the decoding threshold can be improved over
a uniform random bit mapper, or, alternatively, the spatial chain length of the
code can be reduced for a given gap to capacity. It is also shown that for
rate-loss free, circular (tail-biting) ensembles, a decoding wave effect can be
initiated using only an optimized bit mapper
On the Information Loss of the Max-Log Approximation in BICM Systems
We present a comprehensive study of the information rate loss of the max-log
approximation for -ary pulse-amplitude modulation (PAM) in a bit-interleaved
coded modulation (BICM) system. It is widely assumed that the calculation of
L-values using the max-log approximation leads to an information loss. We prove
that this assumption is correct for all -PAM constellations and labelings
with the exception of a symmetric 4-PAM constellation labeled with a Gray code.
We also show that for max-log L-values, the BICM generalized mutual information
(GMI), which is an achievable rate for a standard BICM decoder, is too
pessimistic. In particular, it is proved that the so-called "harmonized" GMI,
which can be seen as the sum of bit-level GMIs, is achievable without any
modifications to the decoder. We then study how bit-level channel
symmetrization and mixing affect the mutual information (MI) and the GMI for
max-log L-values. Our results show that these operations, which are often used
when analyzing BICM systems, preserve the GMI. However, this is not necessarily
the case when the MI is considered. Necessary and sufficient conditions under
which these operations preserve the MI are provided
A Low-Complexity Detector for Memoryless Polarization-Multiplexed Fiber-Optical Channels
A low-complexity detector is introduced for polarization-multiplexed M-ary
phase shift keying modulation in a fiber-optical channel impaired by nonlinear
phase noise, generalizing a previous result by Lau and Kahn for
single-polarization signals. The proposed detector uses phase compensation
based on both received signal amplitudes in conjunction with simple
straight-line rather than four-dimensional maximum-likelihood decision
boundaries.Comment: accepted for publication in IEEE Comm. Let
Spatially-Coupled Codes for Optical Communications: State-of-the-Art and Open Problems
We give a brief survey of a particularly interesting class of codes, called spatially-coupled codes, which are strong candidates for future optical communication systems. We discuss some recent research on this class of codes in the area of optical communications, and summarize some open research problems
Constellation Optimization for Coherent Optical Channels Distorted by Nonlinear Phase Noise
We consider the design of amplitude phase-shift keying (APSK) constellations, targeting their application to coherent fiber-optical communications. Phase compensation is used at the receiver to combat nonlinear phase noise caused by the Kerr-effect. We derive the probability density function of the post- compensated observation for multilevel constellations. Optimal APSK constellations in terms of symbol error probability (SEP) are found assuming a two-stage detector. Performance gains of 3.2 dB can be achieved compared to 16-QAM at a SEP of 10^â2. We optimize the number of rings, the number of points per ring, as well as the radius distribution of the constellation. For low to moderate nonlinearities, radius optimization only yields minor improvements over an equidistant spacing of rings. In the highly nonlinear regime, however, a smaller SEP can be achieved by âsacrificingâ the outer ring of the constellation, in favor of achieving good SEP in the remaining rings
Terminated and Tailbiting Spatially-Coupled Codes with Optimized Bit Mappings for Spectrally Efficient Fiber-Optical Systems
We study the design of spectrally efficient fiber-optical communication
systems based on different spatially coupled (SC) forward error correction
(FEC) schemes. In particular, we optimize the allocation of the coded bits from
the FEC encoder to the modulation bits of the signal constellation. Two SC code
classes are considered. The codes in the first class are protograph-based
low-density parity-check (LDPC) codes which are decoded using iterative
soft-decision decoding. The codes in the second class are generalized LDPC
codes which are decoded using iterative hard-decision decoding. For both code
classes, the bit allocation is optimized for the terminated and tailbiting SC
cases based on a density evolution analysis. An optimized bit allocation can
significantly improve the performance of tailbiting SC codes codes over the
baseline sequential allocation, up to the point where they have a comparable
gap to capacity as their terminated counterparts, at a lower FEC overhead. For
the considered terminated SC codes, the optimization only results in marginal
performance improvements, suggesting that in this case a sequential allocation
is close to optimal.Comment: This paper has been accepted for publication in the IEEE/OSA Journal
of Lightwave Technolog
Ultra-Wideband Nonlinearity Compensation Performance in the Presence of PMD
We investigate the performance of multi-channel digital backpropagation for 1 THz bandwidth optical fibre transmission in the presence of polarisation-mode dispersion. We show that the average SNR performance rapidly saturates as a function of the compensation bandwidth
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