Rate Adaptation and Reach Increase by Probabilistically Shaped 64-QAM: An Experimental Demonstration
TL;DR: A transmission system with adjustable data rate for single-carrier coherent optical transmission is proposed, which enables high-speed transmission close to the Shannon limit, and it is experimentally demonstrated that the optical transmission of probabilistically shaped 64-QAM signals outperforms the transmission reach of regular 16- QAM and regular 64-ZAM signals.
Abstract: A transmission system with adjustable data rate for single-carrier coherent optical transmission is proposed, which enables high-speed transmission close to the Shannon limit. The proposed system is based on probabilistically shaped 64-QAM modulation formats. Adjustable shaping is combined with a fixed-QAM modulation and a fixed forward-error correction code to realize a system with adjustable net data rate that can operate over a large reach range. At the transmitter, an adjustable distribution matcher performs the shaping. At the receiver, an inverse distribution matcher is used. Probabilistic shaping is implemented into a coherent optical transmission system for 64-QAM at 32 Gbaud to realize adjustable operation modes for net data rates ranging from 200 to 300 Gb/s. It is experimentally demonstrated that the optical transmission of probabilistically shaped 64-QAM signals outperforms the transmission reach of regular 16-QAM and regular 64-QAM signals by more than 40% in the transmission reach.
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TL;DR: Focusing on the optical transport and switching layer, aspects of large-scale spatial multiplexing, massive opto-electronic arrays and holistic optics-electronics-DSP integration, as well as optical node architectures for switching and multiplexed of spatial and spectral superchannels are covered.
Abstract: Celebrating the 20th anniversary of Optics Express, this paper reviews the evolution of optical fiber communication systems, and through a look at the previous 20 years attempts to extrapolate fiber-optic technology needs and potential solution paths over the coming 20 years. Well aware that 20-year extrapolations are inherently associated with great uncertainties, we still hope that taking a significantly longer-term view than most texts in this field will provide the reader with a broader perspective and will encourage the much needed out-of-the-box thinking to solve the very significant technology scaling problems ahead of us. Focusing on the optical transport and switching layer, we cover aspects of large-scale spatial multiplexing, massive opto-electronic arrays and holistic optics-electronics-DSP integration, as well as optical node architectures for switching and multiplexing of spatial and spectral superchannels.
498 citations
TL;DR: The star-shaped 16-ary quadrature amplitude modulation scheme shows superiority over the PS-Square-16QAM in terms of the BER improvement.
Abstract: We investigate and compare the performance of star-shaped 16-ary quadrature amplitude modulation (Star-16QAM) and square-shaped 16QAM (Square-16QAM) in the probabilistic shaping (PS) and uniform schemes with coherent detection. With the help of PS technology, the bit error ratio (BER) improvement achieved in the PS-Star-16QAM scheme is greater than that of the PS-Square-16QAM when compared with the uniform schemes in our numerical simulation and experiment. Therefore, the PS-Star-16QAM shows superiority over the PS-Square-16QAM in terms of the BER improvement.
308 citations
Cites methods from "Rate Adaptation and Reach Increase ..."
...The application of PS in optical communication is able to operate the systems more approach to the Shannon limit thus outperforming conventional modulation formats [2]–[4], [11]....
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TL;DR: In this paper, the effect of using a small number of input probability mass functions (PMFs) for a range of signal-to-noise ratios (SNRs), instead of optimizing the constellation shaping for each SNR, was investigated.
Abstract: Different aspects of probabilistic shaping for a multispan optical communication system are studied. First, a numerical analysis of the additive white Gaussian noise (AWGN) channel investigates the effect of using a small number of input probability mass functions (PMFs) for a range of signal-to-noise ratios (SNRs), instead of optimizing the constellation shaping for each SNR. It is shown that if a small penalty of at most 0.1 dB SNR to the full shaping gain is acceptable, just two shaped PMFs are required per quadrature amplitude modulation (QAM) over a large SNR range. For a multispan wavelength division multiplexing optical fiber system with 64QAM input, it is shown that just one PMF is required to achieve large gains over uniform input for distances from 1400 to 3000 km. Using recently developed theoretical models that extend the Gaussian noise (GN) model and full-field split-step simulations, we illustrate the ramifications of probabilistic shaping on the effective SNR after fiber propagation. Our results show that, for a fixed average optical launch power, a shaping gain is obtained for the noise contributions from fiber amplifiers and modulation-independent nonlinear interference (NLI), whereas shaping simultaneously causes a penalty as it leads to an increased NLI. However, this nonlinear shaping loss is found to have a relatively minor impact, and optimizing the shaped PMF with a modulation-dependent GN model confirms that the PMF found for AWGN is also a good choice for a multi-span fiber system.
278 citations
TL;DR: This manuscript discusses the motivations for jointly utilizing transmission techniques such as probabilistic shaping and digital sub-carrier multiplexing in digital coherent optical transmissions systems and describes the key-building blocks of modern high-speed DSP-based transponders working at up to 800G per wave.
Abstract: The design of application-specific integrated circuits (ASIC) is at the core of modern ultra-high-speed transponders employing advanced digital signal processing (DSP) algorithms. This manuscript discusses the motivations for jointly utilizing transmission techniques such as probabilistic shaping and digital sub-carrier multiplexing in digital coherent optical transmissions systems. First, we describe the key-building blocks of modern high-speed DSP-based transponders working at up to 800G per wave. Second, we show the benefits of these transmission methods in terms of system level performance. Finally, we report, to the best of our knowledge, the first long-haul experimental transmission – e.g., over 1000 km – with a real-time 7 nm DSP ASIC and digital coherent optics (DCO) capable of data rates up to 1.6 Tb/s using two waves (2 × 800G).
181 citations
Cites background or methods from "Rate Adaptation and Reach Increase ..."
...For square shaped constellations with points located on a Cartesian grid such as 64QAM, this becomes even easier by applying the corresponding 1-D distribution on I- and Q-dimensions separately [37]....
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...Probabilistic shaping (PS) [37] and geometric shaping (GS) [38] are possible approaches to constellation shaping....
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TL;DR: A layered PS-FEC architecture consisting of a PS encoder and an FEC encoder is introduced, of which probabilistic amplitude shaping is a practical instance and achievable PS encoding rates and FEC decoding rates are derived using information-theoretic arguments.
Abstract: This tutorial paper provides a foundation for integrating probabilistic shaping (PS) and forward error correction (FEC). A layered PS-FEC architecture consisting of a PS encoder and an FEC encoder is introduced, of which probabilistic amplitude shaping is a practical instance. Achievable PS encoding rates and achievable FEC decoding rates are derived using information-theoretic arguments. The developed tools are applied to the design and performance assessment of optical transponders based on measurements from optical transmission experiments.
170 citations
Cites methods from "Rate Adaptation and Reach Increase ..."
...In the left plot, we illustrate the achievable FEC rates for the transmission experiment of [9]....
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...For this, the measurement x and y were taken from the transmission experiment in [9] which investigates four shaped modes OP 1 (H(X) = 5....
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References
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TL;DR: The information rate of finite-state source/channel models can be accurately estimated by sampling both a long channel input sequence and the corresponding channel output sequence, followed by a forward sum-product recursion on the joint source/ channel trellis.
Abstract: The information rate of finite-state source/channel models can be accurately estimated by sampling both a long channel input sequence and the corresponding channel output sequence, followed by a forward sum-product recursion on the joint source/channel trellis. This method is extended to compute upper and lower bounds on the information rate of very general channels with memory by means of finite-state approximations. Further upper and lower bounds can be computed by reduced-state methods
598 citations
"Rate Adaptation and Reach Increase ..." refers background in this paper
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TL;DR: Fixed-to-fixed length, invertible, and low complexity encoders and decoders based on constant composition and arithmetic coding are presented and the encoder achieves the maximum rate of the desired distribution, asymptotically in the blocklength.
Abstract: Distribution matching transforms independent and Bernoulli(1/2) distributed input bits into a sequence of output symbols with a desired distribution. Fixed-to-fixed length, invertible, and low complexity encoders and decoders based on constant composition and arithmetic coding are presented. The encoder achieves the maximum rate, namely, the entropy of the desired distribution, asymptotically in the blocklength. Furthermore, the normalized divergence of the encoder output and the desired distribution goes to zero in the blocklength.
510 citations
"Rate Adaptation and Reach Increase ..." refers background or methods in this paper
...We use Constant Composition Distribution Matching (CCDM) as proposed in [12]....
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TL;DR: In this paper, perturbative models for the impact of nonlinear propagation in uncompensated links were proposed and analyzed for a set of formats including PM-BPSK, PM-QPSK and PM-8QAM.
Abstract: We address perturbative models for the impact of nonlinear propagation in uncompensated links. We concentrate on a recently-proposed model which splits up the signal into spectral components and then resorts to a four-wave-mixing-like approach to assess the generation of nonlinear interference due to the beating of the signal spectral components. We put its founding assumptions on firmer ground and we provide a detailed derivation for its main analytical results. We then carry out an extensive simulative validation by addressing an ample and significant set of formats encompassing PM-BPSK, PM-QPSK, PM-8QAM, and PM-16QAM, all operating at 32 GBaud. We compare the model prediction of maximum system reach and optimum launch power versus simulation results, for all four formats, three different kinds of fibers (PSCF, SMF, and NZDSF) and for several values of WDM channel spacing, ranging from 50 GHz down to the symbol-rate. We found that, throughout all tests, the model delivers accurate predictions, potentially making it an effective general-purpose system design tool for coherent uncompensated transmission systems.
417 citations
"Rate Adaptation and Reach Increase ..." refers background in this paper
...Literature [27], [28] suggests that it is reasonable to model the optical channel by a memoryless AWGN channel....
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TL;DR: The key technical result is a proof that, under belief-propagation decoding, spatially coupled ensembles achieve essentially the area threshold of the underlying uncoupled ensemble.
Abstract: We investigate spatially coupled code ensembles. For transmission over the binary erasure channel, it was recently shown that spatial coupling increases the belief propagation threshold of the ensemble to essentially the maximum a priori threshold of the underlying component ensemble. This explains why convolutional LDPC ensembles, originally introduced by Felstrom and Zigangirov, perform so well over this channel. We show that the equivalent result holds true for transmission over general binary-input memoryless output-symmetric channels. More precisely, given a desired error probability and a gap to capacity, we can construct a spatially coupled ensemble that fulfills these constraints universally on this class of channels under belief propagation decoding. In fact, most codes in this ensemble have this property. The quantifier universal refers to the single ensemble/code that is good for all channels but we assume that the channel is known at the receiver. The key technical result is a proof that, under belief-propagation decoding, spatially coupled ensembles achieve essentially the area threshold of the underlying uncoupled ensemble. We conclude by discussing some interesting open problems.
356 citations
01 Jul 2012
TL;DR: The key technical result is a proof that, under belief-propagation decoding, spatially coupled ensembles achieve essentially the area threshold of the underlying uncoupled ensemble.
Abstract: We investigate spatially coupled code ensembles. For transmission over the binary erasure channel, it was recently shown that spatial coupling increases the belief propagation threshold of the ensemble to essentially the maximum a-priori threshold of the underlying component ensemble. This explains why convolutional LDPC ensembles, originally introduced by Felstrom and Zigangirov, perform so well over this channel. We show that the equivalent result holds true for transmission over general binary-input memoryless output-symmetric channels. More precisely, given a desired error probability and a gap to capacity, we can construct a spatially coupled ensemble which fulfills these constraints universally on this class of channels under belief propagation decoding. In fact, most codes in that ensemble have that property. The quantifier universal refers to the single ensemble/code which is good for all channels if we assume that the channel is known at the receiver. The key technical result is a proof that under belief propagation decoding spatially coupled ensembles achieve essentially the area threshold of the underlying uncoupled ensemble. We conclude by discussing some interesting open problems.
321 citations