277 research outputs found
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
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
Probabilistic Eigenvalue Shaping for Nonlinear Fourier Transform Transmission
We consider a nonlinear Fourier transform (NFT)-based transmission scheme,
where data is embedded into the imaginary part of the nonlinear discrete
spectrum. Inspired by probabilistic amplitude shaping, we propose a
probabilistic eigenvalue shaping (PES) scheme as a means to increase the data
rate of the system. We exploit the fact that for an NFT-based transmission
scheme the pulses in the time domain are of unequal duration by transmitting
them with a dynamic symbol interval and find a capacity-achieving distribution.
The PES scheme shapes the information symbols according to the
capacity-achieving distribution and transmits them together with the parity
symbols at the output of a low-density parity-check encoder, suitably
modulated, via time-sharing. We furthermore derive an achievable rate for the
proposed PES scheme. We verify our results with simulations of the
discrete-time model as well as with split-step Fourier simulations.Comment: Published in IEEE/OSA Journal of Lightwave Technology, 201
Wave-like Decoding of Tail-biting Spatially Coupled LDPC Codes Through Iterative Demapping
For finite coupling lengths, terminated spatially coupled low-density
parity-check (SC-LDPC) codes show a non-negligible rate-loss. In this paper, we
investigate if this rate loss can be mitigated by tail-biting SC-LDPC codes in
conjunction with iterative demapping of higher order modulation formats.
Therefore, we examine the BP threshold of different coupled and uncoupled
ensembles. A comparison between the decoding thresholds approximated by EXIT
charts and the density evolution results of the coupled and uncoupled ensemble
is given. We investigate the effect and potential of different labelings for
such a set-up using per-bit EXIT curves, and exemplify the method for a 16-QAM
system, e.g., using set partitioning labelings. A hybrid mapping is proposed,
where different sub-blocks use different labelings in order to further optimize
the decoding thresholds of tail-biting codes, while the computational
complexity overhead through iterative demapping remains small.Comment: presentat at the International Symposium on Turbo Codes & Iterative
Information Processing (ISTC), Brest, Sept. 201
Decoder-in-the-Loop: Genetic Optimization-based LDPC Code Design
LDPC code design tools typically rely on asymptotic code behavior and are
affected by an unavoidable performance degradation due to model imperfections
in the short length regime. We propose an LDPC code design scheme based on an
evolutionary algorithm, the Genetic Algorithm (GenAlg), implementing a
"decoder-in-the-loop" concept. It inherently takes into consideration the
channel, code length and the number of iterations while optimizing the
error-rate of the actual decoder hardware architecture. We construct short
length LDPC codes (i.e., the parity-check matrix) with error-rate performance
comparable to, or even outperforming that of well-designed standardized short
length LDPC codes over both AWGN and Rayleigh fading channels. Our proposed
algorithm can be used to design LDPC codes with special graph structures (e.g.,
accumulator-based codes) to facilitate the encoding step, or to satisfy any
other practical requirement. Moreover, GenAlg can be used to design LDPC codes
with the aim of reducing decoding latency and complexity, leading to coding
gains of up to dB and dB at BLER of for both AWGN and
Rayleigh fading channels, respectively, when compared to state-of-the-art short
LDPC codes. Also, we analyze what can be learned from the resulting codes and,
as such, the GenAlg particularly highlights design paradigms of short length
LDPC codes (e.g., codes with degree-1 variable nodes obtain very good results).Comment: in IEEE Access, 201
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