Probabilistic Shaping Research Articles

400G Probabilistic Shaped PDM-64QAM Synchronization in the Frequency Domain

A low complexity digital signal processing architecture for dual-polarization coherent detection is presented. It synchronizes impairments in the frequency domain and uses synergies between the filtering processing stages to minimize overall complexity. We show how chromatic dispersion, skew, carrier frequency offset, timing error, and the state of polarization can be mitigated with a single filtering stage in the frequency domain. The error estimation in the frequency domain is based on the modified Godard algorithm, which calculates the clock tone with less than two samples per symbol and small timing jitter. The synchronization in the frequency domain is independent of the modulation format and therefore a good candidate for higher order modulation formats and so the synchronization of probabilistic shaped (PS) signals based on a high cardinality rectangular QAM format. We show the synchronization of PS polarization-division multiplexed (PDM)-64QAM signals with a symbol rate of 42.7 GBd in the frequency domain. The simulative results for the influence of the FFT size and the number of FFT blocks used for the error estimation are shown. Finally, we show experimental results for four different probabilistic shapings in back-to-back and transmission over 300 km, which are synchronized with the introduced digital signal processing (DSP).

Self-adaptive probabilistically shaped star-carrier-less amplitude/phase passive optical network based on simulated annealing algorithm

A self-adaptive probabilistically shaped (PS) star-carrier-less amplitude/phase (CAP)-24 modulated passive optical network (PON) is proposed to adaptively adjust the probability distribution of the signal points. The proposed scheme is capable of accommodating different channels and transmission distances to obtain the optimal probability distribution. The employment of the simulated annealing algorithm in the constellation can significantly reduce the average signal power, as well as facilitating the flexible deployment and enhancement of the PON system. The experimental results show that the self-adaptive optimal signal transmission can be acquired when the probability ratio of signal points located in the three well-designed rings of the CAP-24 constellation is set as 0.724:0.175:0.101. Compared with the general PS-star-CAP-32 signal, the self-adaptive PS-star-CAP-24 signal has a gain of 1.5 dB at the 7% hard decision forward error correction (HD-FEC) limit. What is more, the proposed PS self-adaptive PS-star-CAP-24 can outperform the general PS-star-CAP-24 constellation by 0.2 dB at the 7% HD-FEC limit.

A probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions.

A novel, probabilistically shaped star-CAP-16/32 modulation based on constellation design with honeycomb-like decision regions is proposed in this paper. The proper geometric structural design of the star constellation, along with the probabilistic shaping, is able to achieve better improvement with regards to constellation figure of merit (CFM) and bit error rate (BER) performance. A 25-km standard single-mode fiber (SSMF) data transmission employing the proposed PS star-CAP modulation scheme is successfully demonstrated. Experiment results show that the proposed PS star-CAP-16 in C4,4,4,4 excels the traditional PS star-CAP-16 in C8,8 by 1.5 dB in receiver sensitivity at the BER of 1×10-3 . At the same time, the novel PS star-CAP-32 with entropy of 4.4 bits/symbol defeats the uniform star-CAP-32 by 1.6 dB improvement under the same bit rate.

Hierarchical Distribution Matching for Probabilistically Shaped Coded Modulation

The implementation difficulties of combining distribution matching (DM) and dematching (invDM) for probabilistic shaping (PS) with soft-decision forward error correction (FEC) coding can be relaxed by reverse concatenation, for which the FEC coding and decoding lies inside the shaping algorithms. PS can seemingly achieve performance close to the Shannon limit, although there are practical implementation challenges that need to be carefully addressed. We propose a hierarchical DM (HiDM) scheme, having fully parallelized input/output interfaces and a pipelined architecture that can efficiently perform the DM/invDM without the complex operations of previously proposed methods such as constant composition DM (CCDM). Furthermore, HiDM can operate at a significantly larger post-FEC bit error rate (BER) for the same post-invDM BER performance, which facilitates simulations. These benefits come at the cost of a slightly larger rate loss and required signal-to-noise ratio at a given post-FEC BER.

Probabilistic Shaping and Forward Error Correction for Fiber-Optic Communication Systems

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.

Constellation-designed 32QAM with geometric and probabilistic shaping for optical fiber system

A constellation-designed 32QAM method is proposed using geometric shaping (GS) and probabilistic shaping (PS). In addition, a 50-Gbaud polarization division multiplexed multispan optical fiber link for the proposed scheme is set up. The simulation results show that when the net data rate reaches 211 Gbit/s, the proposed 32QAM with GS and PS is capable of achieving about 0.1- and 0.3-dB OSNR gain over PS-32QAM and regular 32QAM (R-32QAM), respectively. When 213 Gbit/s net data rate transmission is achieved, the use of the proposed 32QAM can increase the transmission length by ∼60 km over PS-32QAM and ∼210 km over R-32QAM. Moreover, when OSNR is set to 19 dB and signal bandwidth is 40 Gbaud, the net data rate of the proposed 32QAM is 2 and 7.5 Gbit/s larger than PS-32QAM and R-32QAM, respectively.

Approaching Terabits Per Carrier Metro-Regional Transmission Using Beyond-100GBd Coherent Optics With Probabilistically Shaped DP-64QAM Modulation

This research work proposed and experimentally demonstrated beyond-100GBd probabilistically shaped coherent optics that support the transmission of a ~1.2 Tbps coded line rate and a ~0.9 Tbps net bit rate per optical carrier over metro-regional distances. Pursuing next-generation transmission systems having both high capacity approaching terabits per wavelength and high spectral efficiency require engineering efforts from different aspects, which may include the enhancement of analog-to-digital or digital-to-analog interfaces, the improvement of channel characteristics, and also the realization of better receiver sensitivities, preferably through DSP techniques such as probabilistic shaping (PS). By doing so, this work achieved a single-channel and a 112.5-GHz WDM transmission of 900G wavelengths over 800 and 400 km, respectively, which employed a PS DP-64QAM modulation format at 105 GBd, yielding a net spectral efficiency of 8.05 bits/s/Hz. Such a high symbol rate was demonstrated using a commercially available DAC unit without band-interleaving. The enhanced optical channel consists of ITU-T G.654 compliant Terawave SLA+ fiber spans with the backward-pumped Raman amplifiers. In addition, with the same PS DP-64QAM modulation format and the same enhanced channel, this research work also demonstrated that 400G wavelengths can be delivered over 2800 km supporting long-haul applications.

Probabilistic Shaping Design Based on Reduced-Exponentiation Subset Indexing and Honeycomb-Structured Constellation Optimization for 5G Fronthaul Network

A probabilistic shaping method based on reduced-exponentiation subset indexing and honeycomb-structured constellation optimization is proposed to compress the number of signal points in the constellation, so that the total number doesn't fit the traditional pattern of multiples of power exponents of 2. The proposed scheme can significantly reduce the average signal power, enhance the space utilization in view of (identifying signals in) the judgement area of the constellation, as well as improve the mutual information, owing to the combination of probabilistic shaping and constellation optimization. Moreover, an experiment of a 25 km intensity-modulation and direct-detection system (IM/DD) transmission system is successfully demonstrated to present the superiority of our proposed scheme. It is shown that the proposed probabilistic shaping 64-to-31 carrier-less amplitude and phase modulation (CAP) based on honeycomb constellation can achieve the gains of 1.5 dB and 3 dB over receiver sensitivity when compared with uniform 32-CAP and uniform 64-CAP at the bit error rate (BER) of 1*10 -3 , respectively. The experiment suggests the proposed scheme a promising technique for future 5G fronthaul network.

On the Probabilistic Shaping and Geometric Shaping in Optical Communication Systems

We introduce and compare typical shaping schemes suitable for optical communications. The geometrically shaped-quadrature amplitude modulation (GS-QAM) formats are characterized by the non-equidistant spacing of constellation points, transmitted uniformly, and applied to improve system capacity. On the other hand, the well-known constant composition distribution matcher (CCDM) is applied for the generation of probabilistically shaped QAM (PS-QAM) formats. Mutual information (MI) is used as a metric to analyze the performances of regular/GS/PS-MQAM formats. In a linear amplified spontaneous emission noise limited region, it can be proved by the numerical simulation that MI performances of the GS-8/16QAM are always better than regular 8/16QAM and PS-8/16QAM; the largest shaping gains can be separately reached by PS-32QAM and GS-32QAM. We continue with the experimental demonstration on the 16QAM-based transmission system, and find that GS-16QAM generally has the best MI performance. We also find that the modulation-dependent nonlinear noises of the GS-8/16/32QAM are comparable to that of the regular 8/16/32QAM and generally lower than PS-8/16/32QAM. By using the enhanced Gaussian noise model, we observe that the GS-8/16QAM formats have better performances than regular 8/16QAM and PS-8/16QAM over multi-span transmission. Meanwhile, PS-32QAM formats provide superior performance over a relatively long transmission distance.

Flexible Filter Bank Multi-Carriers PON Based on Two-Dimensional Multiple Probabilistic Shaping Distribution

We propose a filter bank multi-carriers (FBMC) passive optical network (PON) system based on 2-D multiple probabilistic shaping (MPS) distribution to achieve flexible and adjustable access bit-rates. The proposed PON can assign different probabilistic shaping schemes to different time-slots and subcarriers, thus improving the system flexibility and adjustability in both the time and frequency domains. Carrier-less amplitude and phase modulation are adopted to achieve the implementation of the intensity-modulation and direct-modulation applied in our proposed PON system. Moreover, for the first time, an experiment demonstrating MPS FBMC signal transmission over a 25-km standard single mode fiber in PON system is successfully carried out to verify the favorable performance. The bit error rate performance of different MPS time-slots at bit-rates of 23.665, 20.663, 17.666, and 15.481 Gbit/s are investigated. The received optical powers at the threshold for hard-decision forward error correction are −16.13, −16.94, −17.85, and −18.81 dBm, respectively. These experiment results indicate that our proposed MPS FBMC PON system can be flexible and adjustable in acquiring different and dynamic access bit-rates, which suggests a prospective solution for the next generation passive optical network.

Flexible Probabilistic Shaping RoF Signal Transmission With Adjustable ACO

We first propose and experimentally demonstrate an optical multi-carrier generation system based on probabilistic shaping, which can dynamically modify the frequency and probability in the time and frequency domains. In this paper, the variability of the adjustable crystal oscillator is used to realize the dynamic adjustment of local vibration frequency and the change of the frequency of optical millimeter wave (MMW). On the other hand, the multi-probability mapping is carried out through probability shaping. In this way, the MMW with multiple frequencies and probabilities is obtained. The frequency-hopping multi-carriers are generated into three groups by using 20, 25, and 30 GHz as the local frequency and the BER of 20, 40, and 60 GHz under a different information entropy (3.15, 3.3, 3.45, 3.6, 3.75, and 3.9 bits/symbol) are measured. Through quadrature amplitude modulation, the transmission rate of 40 Gb/s can be realized. The experimental results indicate that the scheme has the advantages of higher flexibility and low cost, which can be applied to the approaching era of the fifth generation (5G) and the development of super 5G in the future.

Probabilistic Shaping Using 5G New Radio Polar Codes

An extension to the 5G New Radio polar coding chain is proposed by introducing a shaping encoder prior to the polar encoder that improves the performance with higher order modulation via probabilistic shaping. The method is based on attaching shaping bits to the data bits that force the resulting channel input symbols (after rate matching, scrambling, and symbol mapping) to have a desired non-uniform distribution, such that a shaping gain is obtained. The shaping encoder is realized by using a polar decoder so that no additional hardware is required. The extension does not change the structure of the existing blocks in the transmission chain but only modifies the input parameters. The required changes at the receiver are also very small and can be realized by simple operations without increasing the required computational power. The simulation results validate the performance improvements on the additive white Gaussian noise channels, which can be more than 1 dB for typical scenarios.

Spectrally efficient single carrier 400G optical signal transmission

In this paper, the recent progress on spectrally efficient single carrier (SC) 400G optical signal transmission was summarized. By using quadrature phase shift keying (QPSK), 16 quadrature amplitude modulation (16QAM) and 64QAM, we can realize transmission distance over 10000, 6000 and 3000 km, respectively, with large area fiber and all-Raman amplification. To improve the system performance and generate high-order QAM, advanced digital signal processing algorithms such as probabilistic shaping and look-up table pre-distortion are employed to improve the transmission performance.

Probabilistically shaped 64QAM OFDM signal transmission in a heterodyne coherent detection system

Abstract We experimentally demonstrated the transmission of uniform and probabilistically-shaped (PS) 64-ary quadrature amplitude modulated (64QAM) orthogonal frequency division multiplexing (OFDM) signal in a heterodyne coherent detection system. In the demonstrated system, the signal can be transmitted over 22 km single-mode optical fiber and 1, 3, 5, 13 m wireless link. To the best of our knowledge, this is the first time that PS-64QAM OFDM signal is transmitted in an optical wireless integration system. Heterodyne coherent detection is employed at the receiving end in this system.

A robust probabilistic shaping PON based on symbol-level labeling and rhombus-shaped modulation.

A probabilistic shaping passive optical network (PON) based on symbol-level labeling and rhombus-shaped modulation is proposed in this paper, which indicates optical access network can be deployed in a flexible and robust way with reasonable costs. Energy efficiency is also achieved significantly. An experiment that demonstrates probabilistic shaping PON data transmission over 25 km standard single-mode fiber (SSMF) with CAP (carrier-less amplitude and phase) modulation is successfully conducted. Results show that the received optical power has improved by 2 dB at the threshold of 1×10-3 BER compared with the conventional 16-CAP, which suggests the superiority of our proposed scheme in next generation PON.

1-Tb/s Millimeter-Wave Signal Wireless Delivery at D-Band

We experimentally demonstrate the photonics-aided wireless transmission of 4 × 4 multiple-input multiple-output probabilistic shaping 64-ary quadrature-amplitude-modulation (PS 64QAM) millimeter-wave signals at D-band (110–170 GHz) over 3.1-m distance with a total bit rate of 1.056 Tb/s and a bit-error ratio under 4 × 10−2. The employment of advanced digital-signal-processing techniques, including probabilistic shaping, the Nyquist shaping, and look-up-table predistortion, significantly improves the transmission capacity and distance as well as the system performance. To the best of our knowledge, this is the first time to realize >1-Tb/s millimeter-wave signal wireless delivery.

Exploring and Experimenting With Shaping Designs for Next-Generation Optical Communications

A class of circular 64-QAM that combines 'geometric' and 'probabilistic' shaping aspects is presented. It is compared to square 64-QAM in back-to-back, single-channel, and WDM transmission experiments. First, for the linear AWGN channel model, it permits to operate close to the Shannon limits for a wide range of signal-to-noise ratios. Second, WDM simulations over several hundreds of kilometers show that the obtained signal-to-noise ratios are equivalent to - or slightly exceed - those of probabilistic shaped 64-QAM. Third, for real-life validation purpose, an experimental comparison with unshaped 64-QAM is performed where 28% distance gains are recorded when using 19 channels at 54.2 GBd. This again is in line - or slightly exceeds - the gains generally obtained with probabilistic shaping. Depending upon implementation requirements (core forward-error correcting scheme for example), the investigated modulation schemes may be key alternatives for next-generation optical systems.

Interplay of Probabilistic Shaping and the Blind Phase Search Algorithm

Probabilistic shaping (PS) is a promising technique to approach the Shannon limit using typical constellation geometries. However, the impact of PS on the chain of signal processing algorithms of a coherent receiver still needs further investigation. In this work we study the interplay of PS and phase recovery using the blind phase search (BPS) algorithm, which is widely used in optical communications systems. We first investigate a supervised phase search (SPS) algorithm as a theoretical upper bound on the BPS performance, assuming perfect decisions. It is shown that PS influences the SPS algorithm, but its impact can be alleviated by moderate noise rejection window sizes. On the other hand, BPS is affected by PS even for long windows because of correlated erroneous decisions in the phase recovery scheme. The simulation results also show that the capacity-maximizing shaping is near to the BPS worst-case situation for square-QAM constellations, causing potential implementation penalties.

Physical Layer Strategies to Save Lightpath Regenerators

We investigate the viability of hybrid fiber amplifiers (HFA) and advanced digital signal processing (DSP)-based transceivers in translucent optical networks. We focus on the reduction of optical-electro-optical (OEO) regenerators required to support a 200 Gbps any-to-any traffic. In this paper, two network topologies, Pan-European and USNET, are quantitatively analyzed according to three different upgrade strategies. The first upgrade strategy includes selective placement of HFA in a network using different Raman amplification levels. The second upgrade strategy includes the use of two different DSP techniques of digital backpropagation and probability shaping (PS) at the transceivers. The third upgrade strategy involves a combination of both HFA and DSP techniques in a network. Our results indicate that by using these upgradation strategies, a prominent reduction in OEO regenerators can be obtained, which can lead to full transparency of a network. In the Pan-European topology, improving the equivalent noise figure (ENF) of the optical amplifiers by 5 dB, it is possible to reduce by 74% the amount of required regenerators. Then, by applying advanced DSP techniques like PS, this percentage grows up to 82%. In the USNET topology, by reducing the ENF by 2 dB, it is possible to reach full transparency. By using PS, it is enough to reduce the ENF by just 0.5 dB to reach the same results.

Experimental and numerical comparison of probabilistically shaped 4096 QAM and a uniformly shaped 1024 QAM in all-Raman amplified 160 km transmission.

We describe an experimental and numerical comparison of a probabilistically shaped (PS) 4096 QAM signal and a uniformly shaped 1024 QAM signal. Both modulation formats have the same transmission rate and a spectral efficiency of 15.3 bit/s/Hz. In the computational simulation, we compared the generalized mutual information (GMI) of both modulation formats with bit-wise soft decision decoding and bit-wise hard decision decoding. For bit-wise hard decision decoding with an overhead of 7%, a shaping gain of 1.8 dB was attained. Then we successfully transmitted a single-channel PS-4096 QAM signal for the first time in an all-Raman amplified 160-km link, in which the transmission performance was improved compared with a uniformly shaped 1024 QAM with the same transmission rate. Transmissions with a high QAM multiplicity were achieved by using an optical phase-locked loop (OPLL) and a frequency stabilized fiber laser locked to an acetylene absorption line. Thanks to a shaping gain based on a bit-wise hard decision decoder, the 1.9-dB power margin, which agreed with the simulation result to within 0.1 dB, was increased after transmission.