82 research outputs found
Statistics of the Eigenvalues of a Noisy Multi-Soliton Pulse
For Nonlinear-Frequency Division-Multiplexed (NFDM) systems, the statistics
of the received nonlinear spectrum in the presence of additive white Gaussian
noise (AWGN) is an open problem. We present a novel method, based on the
Fourier collocation algorithm, to compute these statistics.Comment: Accepted for presentation at European Conference on Optical
Communications (ECOC) 201
Approaching the Rate-Distortion Limit with Spatial Coupling, Belief propagation and Decimation
We investigate an encoding scheme for lossy compression of a binary symmetric
source based on simple spatially coupled Low-Density Generator-Matrix codes.
The degree of the check nodes is regular and the one of code-bits is Poisson
distributed with an average depending on the compression rate. The performance
of a low complexity Belief Propagation Guided Decimation algorithm is
excellent. The algorithmic rate-distortion curve approaches the optimal curve
of the ensemble as the width of the coupling window grows. Moreover, as the
check degree grows both curves approach the ultimate Shannon rate-distortion
limit. The Belief Propagation Guided Decimation encoder is based on the
posterior measure of a binary symmetric test-channel. This measure can be
interpreted as a random Gibbs measure at a "temperature" directly related to
the "noise level of the test-channel". We investigate the links between the
algorithmic performance of the Belief Propagation Guided Decimation encoder and
the phase diagram of this Gibbs measure. The phase diagram is investigated
thanks to the cavity method of spin glass theory which predicts a number of
phase transition thresholds. In particular the dynamical and condensation
"phase transition temperatures" (equivalently test-channel noise thresholds)
are computed. We observe that: (i) the dynamical temperature of the spatially
coupled construction saturates towards the condensation temperature; (ii) for
large degrees the condensation temperature approaches the temperature (i.e.
noise level) related to the information theoretic Shannon test-channel noise
parameter of rate-distortion theory. This provides heuristic insight into the
excellent performance of the Belief Propagation Guided Decimation algorithm.
The paper contains an introduction to the cavity method
On the Convergence Speed of Spatially Coupled LDPC Ensembles
Spatially coupled low-density parity-check codes show an outstanding
performance under the low-complexity belief propagation (BP) decoding
algorithm. They exhibit a peculiar convergence phenomenon above the BP
threshold of the underlying non-coupled ensemble, with a wave-like convergence
propagating through the spatial dimension of the graph, allowing to approach
the MAP threshold. We focus on this particularly interesting regime in between
the BP and MAP thresholds.
On the binary erasure channel, it has been proved that the information
propagates with a constant speed toward the successful decoding solution. We
derive an upper bound on the propagation speed, only depending on the basic
parameters of the spatially coupled code ensemble such as degree distribution
and the coupling factor . We illustrate the convergence speed of different
code ensembles by simulation results, and show how optimizing degree profiles
helps to speed up the convergence.Comment: 11 pages, 6 figure
Does the Cross-Talk Between Nonlinear Modes Limit the Performance of NFDM Systems?
We show a non-negligible cross-talk between nonlinear modes in Nonlinear
Frequency-Division Multiplexed system when data is modulated over the nonlinear
Fourier spectrum, both the continuous spectrum and the discrete spectrum, and
transmitted over a lumped amplified fiber link. We evaluate the performance
loss if the cross-talks are neglected.Comment: Invited paper, European Conference on Optical Communication (ECOC
2017), Sept. 2017, p. Th.1.D.
125 Gbps Pre-Compensated Nonlinear Frequency-Division Multiplexed Transmission
Record-high data rate of 125 Gb/s and SE over 2 bits/s/Hz in burst-mode
single-polarization NFDM transmissions were achieved over 976 km of SSMF with
EDFA-only amplification by transmitting and processing 222 32 QAM-modulated
nonlinear subcarriers simultaneouslyComment: This paper will be presented at ECOC 2017, Gothenburg, Swede
- …