189 research outputs found
Low-Complexity Soft-Decision Detection for Combating DFE Burst Errors in IM/DD Links
The deployment of non-binary pulse amplitude modulation (PAM) and soft
decision (SD)-forward error correction (FEC) in future intensity-modulation
(IM)/direct-detection (DD) links is inevitable. However, high-speed IM/DD links
suffer from inter-symbol interference (ISI) due to bandwidth-limited hardware.
Traditional approaches to mitigate the effects of ISI are filters and
trellis-based algorithms targeting symbol-wise maximum a posteriori (MAP)
detection. The former approach includes decision-feedback equalizer (DFE), and
the latter includes Max-Log-MAP (MLM) and soft-output Viterbi algorithm (SOVA).
Although DFE is easy to implement, it introduces error propagation. Such burst
errors distort the log-likelihood ratios (LLRs) required by SD-FEC, causing
performance degradation. On the other hand, MLM and SOVA provide near-optimum
performance, but their complexity is very high for high-order PAM. In this
paper, we consider a one-tap partial response channel model, which is relevant
for high-speed IM/DD links. We propose to combine DFE with either MLM or SOVA
in a low-complexity architecture. The key idea is to allow MLM or SOVA to
detect only 3 typical DFE symbol errors, and use the detected error information
to generate LLRs in a modified demapper. The proposed structure enables a
tradeoff between complexity and performance: (i) the complexity of MLM or SOVA
is reduced and (ii) the decoding penalty due to error propagation is mitigated.
Compared to SOVA detection, the proposed scheme can achieve a significant
complexity reduction of up to 94% for PAM-8 transmission. Simulation and
experimental results show that the resulting SNR loss is roughly 0.3 to 0.4 dB
for PAM-4, and becomes marginal 0.18 dB for PAM-8.Comment: This manuscript has been submitted to JL
Signal Design and Machine Learning Assisted Nonlinearity Compensation for Coherent Optical Fibre Communication Links
This thesis investigates low-complexity digital signal processing (DSP) for signal design and nonlinearity compensation strategies to improve the performance of single-mode optical fibre links over different distance scales.
The performance of a novel ML-assisted inverse regular perturbation technique that mitigates fibre nonlinearities was investigated numerically with a dual-polarization 64 quadrature amplitude modulation (QAM) link over 800 km distance. The model outperformed the heuristically-optimised digital backpropagation approach with <5 steps per span and mitigated the gain expansion issue, which limits the accuracy of an untrained model when the balance between the nonlinear and linear components becomes considerable.
For short reach links, the phase noise due to low-cost, high-linewidth lasers is a more significant channel impairment. A novel constellation optimisation algorithm was, therefore, proposed to design modulation formats that are robust against both additive white Gaussian noise (AWGN) and the residual laser phase noise (i.e., after carrier phase estimation). Subsequently, these constellations were numerically validated in the context of a 400ZR standard system, and achieved up to 1.2 dB gains in comparison with the modulation formats which were optimised only for the AWGN channel.
The thesis concludes by examining a joint strategy to modulate and demodulate signals in a partially-coherent AWGN (PCAWGN) channel. With a low-complexity PCAWGN demapper, 8- to 64-ary modulation formats were designed and validated through numerical simulations. The bit-wise achievable information rates (AIR) and post forward error correction (FEC) bit error rates (BER) of the designed constellations were numerically validated with: the theoretically optimum, Euclidean (conventional), and low-complexity PCAWGN demappers. The resulting constellations demonstrated post-FEC BER shaping gains of up to 2.59 dB and 2.19 dB versus uniform
64 QAM and 64-ary constellations shaped for the purely AWGN channel model, respectively.
The described geometric shaping strategies can be used to either relax linewidth and/or carrier phase estimator requirements, or to increase signal-to-noise ratio (SNR) tolerance of a system in the presence of residual phase noise
Doubly-Irregular Repeat-Accumulate Codes over Integer Rings for Multi-user Communications
Structured codes based on lattices were shown to provide enlarged capacity
for multi-user communication networks. In this paper, we study
capacity-approaching irregular repeat accumulate (IRA) codes over integer rings
for -PAM signaling, . Such codes
feature the property that the integer sum of codewords belongs to the
extended codebook (or lattice) w.r.t. the base code. With it, \emph{%
structured binning} can be utilized and the gains promised in lattice based
network information theory can be materialized in practice. In designing IRA
ring codes, we first analyze the effect of zero-divisors of integer ring on the
iterative belief-propagation (BP) decoding, and show the invalidity of
symmetric Gaussian approximation. Then we propose a doubly IRA (D-IRA) ring
code structure, consisting of \emph{irregular multiplier distribution} and
\emph{irregular node-degree distribution}, that can restore the symmetry and
optimize the BP decoding threshold. For point-to-point AWGN channel with -PAM inputs, D-IRA ring codes perform as low as 0.29 dB to the capacity
limits, outperforming existing bit-interleaved coded-modulation (BICM) and IRA
modulation codes over GF(). We then proceed to design D-IRA ring codes for
two important multi-user communication setups, namely compute-forward (CF) and
dirty paper coding (DPC), with -PAM signaling. With it, a physical-layer
network coding scheme yields a gap to the CF limit by 0.24 dB, and a simple
linear DPC scheme exhibits a gap to the capacity by 0.91 dB.Comment: 30 pages, 13 figures, submitted to IEEE Trans. Signal Processin
A Tutorial on Decoding Techniques of Sparse Code Multiple Access
Sparse Code Multiple Access (SCMA) is a disruptive code-domain non-orthogonal multiple access (NOMA) scheme to enable future massive machine-type communication networks. As an evolved variant of code division multiple access (CDMA), multiple users in SCMA are separated by assigning distinctive sparse codebooks (CBs). Efficient multiuser detection is carried out at the receiver by employing the message passing algorithm (MPA) that exploits the sparsity of CBs to achieve error performance approaching to that of the maximum likelihood receiver. In spite of numerous research efforts in recent years, a comprehensive one-stop tutorial of SCMA covering the background, the basic principles, and new advances, is still missing, to the best of our knowledge. To fill this gap and to stimulate more forthcoming research, we provide a holistic introduction to the principles of SCMA encoding, CB design, and MPA based decoding in a self-contained manner. As an ambitious paper aiming to push the limits of SCMA, we present a survey of advanced decoding techniques with brief algorithmic descriptions as well as several promising directions
GF(q) LDPC encoder and decoder FPGA implementation using group shuffled belief propagation algorithm
This paper presents field programmable gate array (FPGA) exercises of the GF(q) low-density parity-check (LDPC) encoder and interpreter utilizing the group shuffled belief propagation (GSBP) algorithm are presented in this study. For small blocks, non-dual LDPC codes have been shown to have a greater error correction rate than dual codes. The reduction behavior of non-binary LDPC codes over GF (16) (also known as GF(q)-LDPC codes) over the additive white Gaussian noise (AWGN) channel has been demonstrated to be close to the Shannon limit and employs a short block length (N=600 bits). At the same time, it also provides a non-binary LDPC (NB-LDPC) code set program. Furthermore, the simplified bubble check treasure event count is implemented through the use of first in first out (FIFO), which is based on an elegant design. The structure of the interpreter and the creation of the residential area he built were planned in very high speed integrated circuit (VHSIC) hardware description language (VHDL) and simulated in MODELSIM 6.5. The combined output of the Cyclone II FPGA is combined with the simulation output
Low-Complexity Near-Optimum Symbol Detection Based on Neural Enhancement of Factor Graphs
We consider the application of the factor graph framework for symbol
detection on linear inter-symbol interference channels. Based on the Ungerboeck
observation model, a detection algorithm with appealing complexity properties
can be derived. However, since the underlying factor graph contains cycles, the
sum-product algorithm (SPA) yields a suboptimal algorithm. In this paper, we
develop and evaluate efficient strategies to improve the performance of the
factor graph-based symbol detection by means of neural enhancement. In
particular, we consider neural belief propagation and generalizations of the
factor nodes as an effective way to mitigate the effect of cycles within the
factor graph. By applying a generic preprocessor to the channel output, we
propose a simple technique to vary the underlying factor graph in every SPA
iteration. Using this dynamic factor graph transition, we intend to preserve
the extrinsic nature of the SPA messages which is otherwise impaired due to
cycles. Simulation results show that the proposed methods can massively improve
the detection performance, even approaching the maximum a posteriori
performance for various transmission scenarios, while preserving a complexity
which is linear in both the block length and the channel memory.Comment: revised version. arXiv admin note: text overlap with arXiv:2203.0333
FPGA-Implemented Fractal Decoder with Forward Error Correction in Short-Reach Optical Interconnects
Forward error correction (FEC) codes combined with high-order modulator formats, i.e., coded modulation (CM), are essential in optical communication networks to achieve highly efficient and reliable communication. The task of providing additional error control in the design of CM systems with high-performance requirements remains urgent. As an additional control of CM systems, we propose to use indivisible error detection codes based on a positional number system. In this work, we evaluated the indivisible code using the average probability method (APM) for the binary symmetric channel (BSC), which has the simplicity, versatility and reliability of the estimate, which is close to reality. The APM allows for evaluation and compares indivisible codes according to parameters of correct transmission, and detectable and undetectable errors. Indivisible codes allow for the end-to-end (E2E) control of the transmission and processing of information in digital systems and design devices with a regular structure and high speed. This study researched a fractal decoder device for additional error control, implemented in field-programmable gate array (FPGA) software with FEC for short-reach optical interconnects with multilevel pulse amplitude (PAM-M) modulated with Gray code mapping. Indivisible codes with natural redundancy require far fewer hardware costs to develop and implement encoding and decoding devices with a sufficiently high error detection efficiency. We achieved a reduction in hardware costs for a fractal decoder by using the fractal property of the indivisible code from 10% to 30% for different n while receiving the reciprocal of the golden ratio
Trellis Decoding And Applications For Quantum Error Correction
Compact, graphical representations of error-correcting codes called trellises are a crucial tool in classical coding theory, establishing both theoretical properties and performance metrics for practical use. The idea was extended to quantum error-correcting codes by Ollivier and Tillich in 2005. Here, we use their foundation to establish a practical decoder able to compute the maximum-likely error for any stabilizer code over a finite field of prime dimension. We define a canonical form for the stabilizer group and use it to classify the internal structure of the graph. Similarities and differences between the classical and quantum theories are discussed throughout. Numerical results are presented which match or outperform current state-of-the-art decoding techniques. New construction techniques for large trellises are developed and practical implementations discussed. We then define a dual trellis and use algebraic graph theory to solve the maximum-likely coset problem for any stabilizer code over a finite field of prime dimension at minimum added cost.
Classical trellis theory makes occasional theoretical use of a graph product called the trellis product. We establish the relationship between the trellis product and the standard graph products and use it to provide a closed form expression for the resulting graph, allowing it to be used in practice. We explore its properties and classify all idempotents. The special structure of the trellis allows us to present a factorization procedure for the product, which is much simpler than that of the standard products.
Finally, we turn to an algorithmic study of the trellis and explore what coding-theoretic information can be extracted assuming no other information about the code is available. In the process, we present a state-of-the-art algorithm for computing the minimum distance for any stabilizer code over a finite field of prime dimension. We also define a new weight enumerator for stabilizer codes over F_2 incorporating the phases of each stabilizer and provide a trellis-based algorithm to compute it.Ph.D
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