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Rate Adaptation and Reach Increase by Probabilistically Shaped 64-QAM: An Experimental Demonstration
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 Gb/s 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 transmission reach.
... High Spectral Efficiency (SE) is one of the necessary and crucial requirements in future communication systems, where many techniques, such as channel coding, high-order modulation schemes, and others, play an essential role [1][2][3]. The traditional transmission of data in most communication systems cannot utilize channel capacity optimally [4] due to data having a uniform distribution that leads to a loss reaching 1.53 dB in achievable data rate (Shaping gap) [5]. Therefore, this transmission type is unsuitable for Additive-White-Gaussian Noise (AWGN) channels, and the performance will deteriorate significantly in the fading and multipath wireless channels [6]. ...
... In all these studies, the considered input symbols were the uniform distribution symbols. One of the crucial techniques that have gained increasing and pivotal interest in improving the quality of communication systems and overcoming (the shaping gap) is Probabilistic Shaping (PS) by optimizing the input symbols distribution through signal shaping to improve energy efficiency [4,5]. ...
... However, ESS still has some limitations and computational complexity and required storage capacity becomes high, particularly with long data packets. In optical fiber communications and free space optical communications [4,16,[21][22][23][24][25], the PS is presented as an optimum technique that achieves excellent transmission rates and distances and maximizes the transmission capacity and system performance. This paper will provide an extended study of the symbol error performance of probabilistic shaping based on a modified distribution matcher called a Multi-Repeat Distribution Matcher (MRDM) [26] under AWGN and various fading channel types. ...
... The way to map uniform i.i.d. information bits to MB-distributed symbols, and to combine shaping with forward error correction (FEC) has been deeply investigated in the last years [7], [8], [10]- [13], and still is an active research topic nowadays. ...
... In the past years, research has focused on the design of practical approaches for the implementation of probabilistic shaping, leading in particular to the development of the widely deployed probabilistic amplitude shaping (PAS) technique [7], [8]. The key idea of PAS is that of achieving probabilistic shaping by concatenating a fixed-length-to-fixed-length distribution matcher (DM) to shape the probability distribution of the amplitudes, and a systematic binary encoder for forward error correction (FEC), whose parity bits (possibly together with other information bits) are mapped to the signs. ...
... V-C]. Though generally suboptimal in terms of AIR maximization, 8 the metric provides an accurate estimate of the NLI in a single-channel scenario, including the average impact of inter-block NLI due to adjacent sequences, and is a good selection metric in the nonlinear regime when an AWGN decoding metric is employed at the receiver [19, Sec. III-D]. ...
Probabilistic shaping is, nowadays, a pragmatic and popular approach to improve the performance of coherent optical fiber communication systems. In the linear regime, the potential of probabilistic shaping in terms of shaping gain and rate granularity is well known, and its practical implementation has been mostly mastered. In the nonlinear regime, the advantages offered by probabilistic shaping remain not only valid, but might also increase thanks to the appealing opportunity to use the same technique to mitigate nonlinear effects and obtain an additional nonlinear shaping gain. Unfortunately, despite the recent research efforts, the optimization of conventional shaping techniques, such as probabilistic amplitude shaping (PAS), yields a relevant nonlinear shaping gain only in particular scenarios of limited practical interest, e.g., in the absence of carrier phase recovery. Recently, a more theoretical approach, referred to as sequence selection, has been proposed to understand the performance and limitation of nonlinear constellation shaping. Sequence selection shapes the distribution of the transmitted symbols by selecting or discarding the sequences generated by a certain source according to a metric that measures their
quality
. In this manuscript, after a brief review of
conventional
probabilistic shaping, we use sequence selection to investigate through simulations the potential, opportunities, and challenges offered by probabilistic shaping for nonlinear channels. First, we show that ideal sequence selection is able to provide up to 0.13 bit/s/Hz additional gain with respect to PAS with an optimized blocklength. However, this additional gain is obtained only if the selection metric accounts for the signs of the symbols, ruling out the possibility of using one of the simple recently proposed sign-independent metrics. We also show that, while the signs must be known to compute the selection metric, there is no need to shape them, since nearly the same gain can be obtained by properly selecting the amplitudes (with a sign-dependent metric) and leaving the signs uniform i.i.d. Furthermore, we show that the selection depends in a non-critical way on the symbol rate and link length: the sequences selected for a certain scenario still provide a relevant gain if the link length or baud rate are modified (within a reasonable range). Then, we analyze and compare several practical implementations of sequence selection by taking into account interaction with forward error correction (FEC), information loss due to selection, and complexity. Overall, we conclude that the single block and the multi block FEC-independent bit scrambling are the best options for the practical implementation of sequence selection, with a gain up to 0.08 bit/s/Hz. The main challenge and limitation to their practical implementation remains the evaluation of the metric, whose complexity is currently too high. Finally, we show that the nonlinear shaping gain provided by sequence selection persists when carrier phase recovery is included, in contrast to the nonlinear shaping gain offered by optimizing the blocklength of conventional PAS techniques.
... For an amplified coherent transmission system subjected to an optical APC, probabilistic constellation shaping (PCS) is a powerful tool to approach the Shannon capacity of the optical fiber channel [61,62]. However, it brings extensive debates on whether the PCS benefits are relevant to an IM-DD system with PPC. ...
... First, to avoid a huge constellation power loss, the MB-PCS signal should never be strongly shaped. It was revealed [61] that a lightly shaped PCS signal retains a shaping gain in the APC system. Light shaping means the source entropy should be close to (and less than) an integer, namely, the entropy of a uniform PAM-signal where = 2 ( = 2,3,4 …). ...
... A strategy to alleviate the issue is to allow ≠ 2 for the PAM-templates. should remain an even number (i.e., = 2 ) to be compatible with the probabilistic amplitude shaping (PAS) architecture [61]. A non-2 PAMtemplate is simply generated by truncating the 2 constellation [65]. ...
200-Gb/s per lane intensity-modulation (IM) direct-detection (DD) optics are being commercialized to support 800G and 1.6T applications inside datacenters. Though IM-DD remains its cost and power consumption advantages over Coherent at 1.6T for short-reach interconnect below 10 km, its roadmap is not clear towards the next capacity doubling, considering it becomes more challenging to scale the components bandwidth linearly with the capacity demand. This makes both advanced modulation formats and digital signal processing (DSP) indispensable for an IM-DD system aiming at higher speed. From a system perspective, this paper reviews candidate modulation formats and DSP for IM-DD optics at post 200G (per lane) era. By taking into account generic constraints for future IM-DD systems like bandwidth limit, peak power constraint, transceiver nonlinearity, fiber dispersion and so on, it discusses a wide range of techniques including probabilistic constellation shaping (PCS), high symbol rate pulse amplitude modulation (PAM), faster than Nyquist (FTN) signaling, nonlinear equalizations and multicarrier modulations. Different from prior IM-DD review literature, we mainly focus on if it is meaningful to exploit a DSP technique with respect to constraints in practical systems, rather than just the technique itself. The study is backed with rich simulation and experiment results.
... The way to map uniform i.i.d. information bits to MB-distributed symbols, and to combine shaping with forward error correction (FEC) has been deeply investigated in the last years [7], [8], [10]- [13], and still is an active research topic nowadays. ...
... In the past years, research has focused on the design of practical approaches for the implementation of probabilistic shaping, leading in particular to the development of the widely deployed probabilistic amplitude shaping (PAS) technique [7], [8]. The key idea of PAS is that of achieving probabilistic shaping by concatenating a fixed-to-fixed distribution matcher (DM) to shape the probability distribution of the amplitudes, and a systematic binary encoder for forward error correction (FEC), whose parity bits (possibly together with other information bits) are mapped to the signs. ...
... In practice, Fig. 4(a) shows that an effective sequence selection strategy requires the use of a signdependent selection metric, while no relevant improvements can be expected with sign-independent metrics (e.g., the EDI, LSAS, NPN, and Kurtosis), unless the unbiased source (before selection) is not properly optimized to remove intensity fluctuations. 8 This is probably not a sufficient reason to use sequence selection with a sign-independent metric, given that the same performance can be achieved (with significantly lower complexity) by optimizing the PAS blocklength and/or including CPR. On the other hand, Fig. 4(b) shows that sequence selection with unshaped but known signs (dottedline curves) achieves almost the same performance as sequence selection with shaped signs. ...
Probabilistic shaping is a pragmatic approach to improve the performance of coherent optical fiber communication systems. In the nonlinear regime, the advantages offered by probabilistic shaping might increase thanks to the opportunity to obtain an additional nonlinear shaping gain. Unfortunately, the optimization of conventional shaping techniques, such as probabilistic amplitude shaping (PAS), yields a relevant nonlinear shaping gain only in scenarios of limited practical interest. In this manuscript we use sequence selection to investigate the potential, opportunities, and challenges offered by nonlinear probabilistic shaping. First, we show that ideal sequence selection is able to provide up to 0.13 bit/s/Hz gain with respect to PAS with an optimized blocklength. However, this additional gain is obtained only if the selection metric accounts for the signs of the symbols: they must be known to compute the selection metric, but there is no need to shape them. Furthermore, we show that the selection depends in a non-critical way on the symbol rate and link length: the sequences selected for a certain scenario still provide a relevant gain if these are modified. Then, we analyze and compare several practical implementations of sequence selection by taking into account interaction with forward error correction (FEC) and complexity. Overall, the single block and the multi block FEC-independent bit scrambling are the best options, with a gain up to 0.08 bit/s/Hz. The main challenge and limitation to their practical implementation remains the evaluation of the metric, whose complexity is currently too high. Finally, we show that the nonlinear shaping gain provided by sequence selection persists when carrier phase recovery is included.
... Yet, in the conventional data transmission, in which each symbol (or constellation point) is transmitted with equal probability, the distribution of input symbols is not a perfect fit for the linear additive white Gaussian noise (AWGN) channel. Consequently, it does not allow for optimal utilisation of the channel capacity [1]. Moreover, in a wireless channel, the influence of fading and multipath propagation deteriorate the system performance [2]. ...
... One shaping method that has garnered considerable attention is probabilistic shaping (PS). It involves adjusting the probabilities of occurrence of constellation points to create a Gaussian-like distribution [1], [8]. Thus, resulting in non-uniform distribution of data symbols. ...
... PS has shown to be an optimum technique in optical fibre communications to achieve record-setting transmission rates and distances [1], [12]- [14], as well as in optical wireless communications [15]- [17]. Similarly, PS has been employed in wireless communications to maximise transmission capacity and improve system performance. ...
In this work, we present symbol error performance analysis of probabilistic shaping (PS) for wireless communications in noise-limited and fading channels. Two fading models considered are the Rayleigh and log-normal fading channels. The results are corroborated with simulation and compared with the conventional uniformly distributed input symbols. In all channel conditions, PS results in significant reductions in the SNR required to achieve a specific error probability compared to the conventional uniformly shaped symbols. For example, in a noise-limited channel, PS based quadrature amplitude modulation (QAM) signal results in SNR gains of 1.16 dB, 1.41 dB, and 1.52 dB compared to the uniformly distributed QAM symbols at equal entropy rates of 4, 6, and 8 bit/symbol and a symbol error ratio (SER) of 1×10-3.
... And the performance of the mentioned schemes shown in [2] would be significantly degraded due to the limited bandwidth. Therefore, aiming to relax the requirements of bandwidth, high-cardinality modulation formats operating with a lower symbol rate could be a trade-off at the expense of the minimum Euclidean distance, resulting in a worse tolerance about impairments and a limited transmission distance, which could be alleviated by a probabilistic shaping technique [3]. ...
... Recently, the probabilistic shaping (PS) technique, including the derived truncated probabilistic shaping (TPS) technique, has been focused on and widely investigated owing to its inherent abilities on providing near Shannon-limit capacity, which could further boost the capacity and transmission distance [3][4][5]. For example, comparisons between a probabilistic shaped 64-ary quadrature amplitude modulation (PS-64QAM) and a uniformly distributed 16-ary QAM (UD-16QAM) or a uniformly distributed 32-ary QAM (UD-32QAM) operating with 100 Gb/s/channel are executed over different kinds of fibers employing various carrier phase recovery algorithms. ...
The impacts of limited bandwidth on the nonlinear transmission performance are investigated by employing a truncated probabilistic shaped 64-ary quadrature amplitude modulation (TPS-64QAM) and a uniformly distributed 16-ary quadrature amplitude modulation (UD-16QAM) over a bandwidth-limited 75-GHz spaced 25-Tb/s (60 × 416.7 Gb/s) 6300-km transmission system. In terms of nonlinear performance measured by optimal launch power, theoretical analyses show that a 0.4-dB improvement could be introduced by UD-16QAM with respect to TPS-64QAM over a 6300-km transmission without limited bandwidth. However, contrary results would be observed that TPS-64QAM would outperform UD-16QAM by about 0.8 dB in terms of optimal launch power when the impacts of limited bandwidth are considered. Besides, numerical simulations and experimental results could both validate that about 1.0-dB optimal launch power improvement could be obtained by TPS-64QAM under bandwidth-limited cases, which is roughly similar to the results of theoretical analyses. Additionally, WDM experimental results show that all 60 tested channels could agree with the BER requirements by employing TPS-64QAM, further validating the superiority of TPS-64QAM compared to UD-16QAM under bandwidth-limited cases.
... The combination of WDM and OTDM technologies [6] is expected to be promising. In addition, the PS-QAM format is also expected to increase the transmission distance in high-speed transmission systems, since it allows a higher noise tolerance than conventional QAM signals [13,14]. ...
We demonstrate the 1,600-km transmission at nearly 1-Tb/s/λ signals with a capacity of 21.5 Tb/s. Probabilistic shaping was newly applied to high-speed coherent optical Nyquist pulse transmission systems to maximize the transmission capacity. Employing a 160-GBd PS-32 QAM format, WDM signals at nearly 1-Tb/s/λ were successfully transmitted over 1,600 km with a capacity of 21.5 Tb/s.
... Figure 4 illustrates the performance of the 2D-CCDM over an AWGN channel with a SSPA (solid-state power amplifier). The log-likelihood ratios (LLRs) of codeword bits are obtained using MAP demodulation following [16]. We utilize a family of low-density parity-check (LDPC) codes [17] with a column weight of 3. The decoding algorithm employed is min-sum [18] with a scaling factor of 0.65 and a maximum iteration count of 10. ...
This Letter proposes a nonlinear-tolerant two-dimensional distribution matcher (2D-DM) scheme. It removes the corner points of probabilistically shaped quadrature amplitude modulation (QAM) to obtain better nonlinear tolerance. Because the remaining number of points is not a power of 2, we propose to divide constellation points into different layers and symbols. Then, the proposed 2D-DM performs matching using one-dimensional shapers, which generates the in-phase and quadrature components of QAM together. In fact, it realizes two-dimensional shapers from one-dimensional shapers. Simulation results show that two-dimensional shapers generated by the proposed 2D-DM have higher tolerance to power amplifier nonlinearity and fiber nonlinearity compared to one-dimensional shapers.
... Probabilistic shaping (PS) has emerged as a potent tool in digital signal processing (DSP) for various communication systems, particularly in achieving capacity-approaching performance and adapting rates in accordance with the Shannon limit Buchali et al., 2015). In typical PS systems, distribution matching (DM) is positioned outside forward error correction (FEC) coding for simplified implementation. ...
The technique of probabilistic amplitude modulation, based on distribution matching, has garnered considerable attention in recent years as a means to enhance spectral efficiency and diminish the constellation energy of coded modulation. This paper introduces the implementation of Probabilistic Amplitude Modulation (PAS) using a Modified Multi-Repeat Distribution Matcher (MMRDM) on a Field Programmable Gate Array (FPGA). The Modified Multiple Repetition Distribution Matcher (MMRDM) is integrated into a 2×2 Multiple Input Multiple Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) system, realized through the Xilinx System Generator (XSG). Simple Zero-Forced and Minimum Mean Squared Error (MMSE) equalizers are applied to the receiver for signal detection across the MIMO channel. The system incorporates enhanced security through chaos-based scrambling with 16 and 64 Quadrature Amplitude Modulation (QAM). VHDL code files for this system are generated for the Xilinx Kintex-7 (xc7k325t-3fbg676) for hardware implementation. Performance evaluation includes an assessment of required storage capacity, complexity, and bit error rate (BER). Using Vivado 2017.4, the system is successfully routed with resource utilization, for example, 0.67% Block RAM (BRAM), 68.6% Look-Up Tables (LUT), 83% DSP 48s, and 1.5% registers for 64-QAM uniform modulation. Similarly, for 64-QAM 10 level (shaper output 60 bit) shaped modulation, the resource utilization is 0.67% BRAM, 68.8% LUT, 83% DSP 48s, and 1.6% registers on the specified device. Simulation results demonstrate an improvement in the net shaping gain of approximately (2-4 dB) at 1×10^(-4) for different equalizer cases compared to uniform QAM, along with a notable reduction in required storage capacity and computational complexity.
... Nowadays, the demands for greater capacity, better system performance, longer transmission distance, lower system power consumption and more flexible modulation formats in optical fiber communication systems are increasing. Probabilistic shaping (PS) with a power-efficient probability distribution on the m-ary quadrature amplitude modulation (mQAM) constellation is a promising technology to meet the above requirements, and has become a hot topic for researchers [1,2], its superiorities in improving the capacity, the bit error rate (BER) performance and the transmission reach of the transmission system have been demonstrated by simulations or experiments in several research works [3][4][5][6][7][8]. Probabilistic amplitude shaping (PAS) [3] is regarded as an important milestone in the practicality of PS, which concatenates a shaping outer code, called a distribution matcher (DM) [4], and a forward error correction (FEC) inner code. ...
A novel probabilistic shaping (PS) scheme with parallelizing information bits to increase the throughput with fixed length distribution matching is proposed. Unlike the conventional bit-level probabilistic shaping scheme which performs binary probabilistic matching on all the input parallel bit tributaries, our proposed scheme performs bit-level probabilistic matching just on half of the parallel bit tributaries such that it not only increases throughput but also halves the number of distribution matchers. Simulations are conducted to demonstrate our proposed parallel bit-level energy level hierarchical distribution matcher (BL-NH-DM) scheme. Simulation results show that our proposed BL-NH-DM scheme with Gaussian-like symbol probability distribution achieves similar BER performance as the conventional symbol-level constant composition distribution match with Maxwell–Boltzmann distribution, and is superior to the uniform distribution scheme. At the BER of 3.8 × 10⁻³, the BL-NH-DM PS-64QAM-OOFDM signal outperforms the uniform 64QAM-OOFDM signal by 2.4 dB in receiver sensitivity under the same data rate of 40 Gbps.
... The PS has been demonstrated that it can improve the additive white Gaussian noise (AWGN) noise tolerance and realize adaptive rate transmissions in optical fiber communications [21]. Based on BAE, we propose an end-toend learning scheme for PS. ...
End-to-end learning based on autoencoder can realize robust constellation shaping for optical fiber communications. The existing schemes use the symbol-wise autoencoder (SAE) or bit-wise autoencoder (BAE) to realize the constellation shaping. The SAE mainly focus on the performance of mutual information (MI), this neglects the decoding loss so that the generalized mutual information (GMI) or the post forward error correction (FEC) bit error rate (BER) has almost no performance gain in bit-wise metric systems. In this paper, we propose a probabilistic shaping (PS) based on BAE with a modified loss function, where the mean square error and source entropy are used to construct the loss function. We compare the GMI and post-FEC performance of the PS and also geometric shaping (GS) based on SAE or BAE by numerical simulations and experiments. In simulations, we transmit 64-QAM signal with GS or PS over 100-km SSFM. The simulation results show that the GS or PS based on BAE can achieve 0.13-bits/sym or beyond 0.2-bits/sym GMI gain. In experiment, the GS based on BAE obtains 0.11-bits/sym GMI gain and 0.7-dB launch optical power gain after belief propagation decoding. The PS with source entropy of 5.5-bits/sym and 5.2-bits/sym outperforms uniform 64QAM by 0.25-bits/sym and 0.3-bits/sym, respectively
... PAS can be easily combined with the efficient FEC codes and the corresponding decoding algorithms commonly employed in digital communications (e.g., binary LDPC codes with iterative belief propagation), obtaining an excellent tradeoff between performance and complexity [43], [51], [52]. Ease of implementation, nearly optimal performance, fine rate tunability, and compatibility with existing devices and techniques make PAS one of the most popular solutions for the latest generation of coherent optical systems. ...
To achieve the maximum information transfer and face a possible eavesdropper, the samples transmitted in continuous-variable quantum key distribution (CV-QKD) protocols are to be drawn from a continuous Gaussian distribution. As a matter of fact, in practical implementations the transmitter has a finite (power) dynamics and the Gaussian sampling can be only approximated. This requires the quantum protocols to operate at small powers. In this paper, we show that a suitable probabilistic amplitude shaping of a finite set of symbols allows to approximate at will the optimal channel capacity also for increasing average powers. We investigate the feasibility of this approach in the framework of CV-QKD, propose a protocol employing discrete quadrature amplitude modulation assisted with probabilistic amplitude shaping, and we perform the key generation rate analysis assuming a wiretap channel and lossless homodyne detection.
... By reallocating independently within each ring, the new PMF is of almost the same entropy and transmitted power as the original distribution. In a practical coherent transmission system, the entropy of the transmitted signal is usually determined by the user's needs and the required transmission length [13]. Therefore, it is undesirable if the entropy of the signal is unpredictable during the PMF optimization. ...
We propose a probability mass function (PMF) optimization scheme for quadrature amplitude modulation (QAM) signals by considering the parametric characteristic of the training sequence. The training sequence for optimization is mapped in standard Maxwell-Boltzmann (M-B) distribution, and the considered characterizing parameters incorporate either the noise variance or the error matrix of the received symbols. The proposed PMF optimization is based on independent reallocation within each constellation ring, generating new distribution with almost the same entropy and transmitted power as the original distribution. This reallocation mechanism is model-free and iterative-free with very low computational complexity. By characterizing the channel in terms of constellation performance asymmetry, PMF reallocation can be effectively implemented to supplement the existing equalization algorithm. The effectiveness of this approach is experimentally verified in a 40-km transmission system with 24 Gbaud 64-QAM signals under three different scenarios. Through PMF reallocation, we achieve generalized mutual information (GMI) improvement of ∼0.06 and throughput improvement of ∼1.5 Gbit/s before forward error correction in comparison with the standard M-B distribution. The proposed mechanism provides a solution to obtain the optimal PMF in practical communication channels, which suffer from various types of noises and distortions.
... Of course, many scholars have paid attention to the transmission of low-entropy PS-QAM. For low-entropy PS-QAM transmission, researchers often modify the receiving DSP algorithm [28][29][30], which will undoubtedly increase the complexity of the receiving algorithm. Therefore, this paper deals with the shaping scheme and reduces the influence of PS and GS through reasonable constellation layout and shaping methods. ...
Constellation shaping (CS) has always been a popular research hotspot in optical communication. Recently, most researchers have focussed on using constellation-shaping technology to improve the system's performance, ignoring the additional penalty it brings to the coherent system. This paper proposes a method of constellation truncation using sub-constellation overlap to perform CS on quadrature amplitude modulation (QAM). The experimental results show that compared with the traditional probabilistic shaping 16QAM, the proposed scheme can effectively avoid the extra penalty brought by CS and achieve a gain from 0.5 to 1.5 dB in optical signal-to-noise ratio. To practically verify the proposed scheme's performance, 7-core 16 km fiber span is deployed in the field to experimentally perform space division multiplexed coherent transmission. The wavelength division multiplexing (WDM) of 93 carriers was used to achieve coherent transmission at a net rate of 116.66-Tb/s.
... The study of PS has been well established in the field of long-haul transmission systems, which are average-power constraint (APC) systems that use multiple optical amplifiers to boost the transmitted light power. An increase in the information rate for the same optical launch power is achieved using classical probabilistic shaping (CPS) [18]. In addition, a previous study [19] has reported that reversed probabilistic shaping (RPS) is more suitable for peak-power constraint (PPC) IM/DD systems. ...
The coherent passive optical network (CPON) has received a great deal of attention in recent years due to its superior receiver sensitivity and extended power budget for 100G and beyond. In order to fully utilize the channel capacity and achieve adaptive rate adjustment in a flexible coherent passive optical network (FLCS-CPON), constellation-shaping techniques, such as probabilistic shaping (PS), have been introduced. Unlike long-distance transmission networks, which are subject to average power constraint when optical amplifiers are utilized, commercial passive optical network systems are generally subject to peak power constraint, as no optical amplifiers are used. This difference makes the classical probabilistic-shaping (CPS) technology less efficient in CPON systems without optical amplifiers. In this study, the use cases of PS in a flexible coherent access network, including nonlinear-penalty-dominant and noise-dominated regions, are thoroughly explored. By fixing the modulation order and utilizing CPS and reversed probabilistic shaping with a fixed modulation format, a hybrid PS-based FLCS-CPON without optical amplifiers is demonstrated, achieving a peak rate of 200G and a high dynamic range boost of up to 72% from 16 to 27.5 dB in upstream burst-mode-based PS-16 quadrature amplitude modulation. Over the entire dynamic range, the net data rate varies from 168 to 85 Gbps with a power budget of 37 dB, and a dynamic range and net-rate product improvement of 55% is achieved.
... In all foreseen roadmaps the capacity requires high order modulation formats, that is Quadrature Amplitude Modulation (QAM) with cardinality M>16 at high symbol rates (>64 Gbaud) and the adoption of ultra-high bandwidth channels in wavelength division multiplexing (WDM) scenarios, characterized by ultra-dense arrangement. As required capacities tend to approach the Shannon limit [8], [9], one of the major constraints will be the stimulation of nonlinearities due to Kerr effect and their interaction with amplified spontaneous emission noise which emerges in the form of cross-phase modulation and four-wave mixing between the closely positioned wavelengths and sub-carriers [2]. Many techniques for the compensation of nonlinearities have been proposed in the past, such as optical phase conjugation [10], digital back propagation [11], nonlinear Fourier transform [12] and inverse-Volterra series-transfer function [13]. ...
The transition to the edge-cloud era makes ultra-high data rate signals indispensable for covering the immense and increasing traffic demands created. This ecosystem also seeks for power efficient optical modules that will deliver this enormous data load. Optical communication systems and their continuous evolution have responded to the upward trend of capacity needs in all different network ecosystems, scaling from short-reach links serving data center, fiber-to-the-home and 5G/B5G services to metro and long-haul transoceanic cables. Kerr induced non-linearities at long haul and dispersion induced power fading at short reach remain intractable problems that vastly affect high symbol rate systems. So, they must be addressed in a power efficient way in order to cope with the ever-increasing traffic requirements.
In this paper, we review our recent work in machine learning and neuromorphic processing in the optical domain for the mitigation of transmission impairments at very high symbol rates. Post-detection techniques based on bidirectional recurrent neural networks for non-linearity compensation and neuromorphic recurrent optical spectrum slicers for power fading mitigation and self-coherent detection emerge as promising solutions for mid-term deployment in long-haul and short-reach communication systems respectively. The current work provides new results in both fields focusing on multi-channel detection in the coherent long-haul domain and on a cost/consumption/performance assessment of neuromorphic photonic processing based on recurrent spectrum slicing in comparison to the state-of-the-art. A thorough analysis of other state-of-the-art techniques in both domains is also provided revealing the merits and shortcomings of recurrent neural networks and neuromorphic photonic processing in high-speed optical communication systems.</p
We propose a generic method to optimize the probabilistic distributions for a peak-power constraint system with arbitrary peak enhancement effects. The technique is useful for developing flexible-rate optical transceivers in links without optical amplifiers.
We experimentally demonstrate 50-GBaud probabilistically shaped 64-QAM transmission with 5.6-bits/symbol entropy over 80-km SSMF using carrierless intensity-only detection via a distortion-aware phase retrieval receiver, resulting net capacity over 200 Gb/s.
We implemented and evaluated probabilistically-shaped multilevel coded modulation and soft-information based performance monitoring at throughputs from 200 Gb/s to 1.2 Tb/s for multi-haul fiber-optic communications. Error-free operations were observed in 5- to 128-ary modulation formats.
In this paper, an enhanced entropy loading discrete multi-tone (EEL-DMT) scheme is proposed for the flexible-rate passive optical network (PON). To achieve a wide range of rate adjustment with fine granularity and performance improvements, probabilistic constellation shaping (PCS)-quadrature amplitude modulation (QAM), quadrature phase shift keying (QPSK), and binary phase shift keying (BPSK) are combined in this scheme, and the modulation format of each subcarrier is determined by the allocated entropy. For verifying the feasibility of the proposed scheme, an O-band DMT system is experimentally demonstrated over 20-km standard single-mode fiber (SSMF) transmission using 10G-class directly modulated laser (DML). The experimental results show that the flexible-rate PON based on the EEL-DMT can achieve a wide-range rate adjustment from 12.5 Gb/s to 87.5 Gb/s under the optical power budget from 38 dB to 26 dB, and up to 2-dB receiver sensitivity gain is obtained compared with the adaptive bit and power loading (ABPL)-DMT.
Discussions on 6G point to one terabit-per-second as a reasonable goal for the peak bit rate of next-generation wireless systems. To meet this goal, the adoption of the sub-terahertz and terahertz bands (from 100 GHz to 10 THz), which can provide ample bandwidth for both communication and sensing systems, has been proposed by academia and industry. Fortunately, in the last decade, the terahertz technology gap has been progressively closed through major advancements in electronic, photonic, and plasmonic technologies. In parallel, the propagation of terahertz signals has been studied through both physics-based and data-driven approaches, debunking some of the established myths. Nevertheless, there are several communication roadblocks that need to be overcome to unleash the spectrum above 100 GHz. In this chapter, a bottom-up approach will be followed to high-light unexpected findings, innovative solutions, and open challenges for terahertz communications and sensing systems on the ground, in the air, and in space.
In digital mobile fronthaul, multi-level modulation formats such as 4-level pulse amplitude modulation have been considered as viable solutions for bandwidth-efficient digital radio-over-fiber (DRoF). Unlike standard digital communication of 0/1 bit streams with equal bit importance, the quantized bits of wireless waveforms have varied importance, requiring unequal bit protection in DRoF transmission. In this paper, we propose and experimentally demonstrate a multicarrier-modulation-enabled unequal bit protection (MC-UBP) scheme for DRoF systems. Bit and power allocation are employed among digital subcarriers to ensure the superior performance of more important bits. Under the assumption of an additive white Gaussian noise (AWGN) channel, a theoretical analysis of the MC-UBP scheme is performed, including the theoretical derivation of the signal-to-noise ratio (SNR) of recovered wireless signals and the optimization results of the subcarrier power factors. In the experiment based on a coherent optical system, a SNR enhancement of 16.6 dB is achieved compared with the conventional single carrier scheme, which can support the transmission of up to 16384-QAM wireless signals. Different pre-emphasis filters have been used in the experiment to emulate the diverse transfer responses of the systems. The results indicate that the MC-UBP scheme is suitable for these systems with more than 10 dB SNR gain.
The escalating datacenter traffic emphasizes the need for high-performance, cost-effective, and energy-efficient optical transceivers. We demonstrate barium titanate (BTO) electro-optic Mach-Zehnder modulators (MZMs) integrated on the silicon photonic platform, surpassing all-silicon counterparts in key metrics: modulation efficiency (VπL = 4.8 Vmm), loss (∼2 dB), and static tuning power (∼100 μW), while maintaining CMOS compatibility. Employing BTO MZMs, we showcase, for the first time, short-reach intensity-modulation and direct-detection (IMDD) transmissions beyond 200 Gbps/λ. In the C-band, over 500 m of standard single-mode fiber (SSMF), we have achieved: (a) a 122 Gbaud PCS-PAM-8 (net 300 Gbps) below the 20% overhead soft-decision forward error correction (SD-FEC) BER threshold of 2.4 × 10
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, and (b) a 106 Gbaud PAM-4 (net 200 Gbps) below the 6.7% overhead hard-decision (HD) FEC threshold of 3.8 × 10
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, with a remarkably 9-fJ/bit electrical power dissipation. In the O-band, we transmit (a) a net 200 Gbps over 10-km SSMF below the 5.8% overhead KP4-FEC BER threshold across wavelengths from 1301 nm to 1321 nm, and (b) a net 250 Gbps over 2-km SSMF below the HD-FEC BER threshold ranging from 1291 nm to 1321 nm. Our research highlights BTO MZMs as potent, power-efficient solutions for next-gen transmitters beyond 200 Gbps/λ for intra- and inter-datacenter applications.
We propose a feed-forward fitting artificial neural network (ANN) to estimate scaling factors in the adaptive communication system supporting probabilistically shaped QAM signals with variable entropy. Utilizing simulation data sets generated under different additive white Gaussian noise channels, we enhanced the robustness of the ANN. The impact of hidden layer neuron numbers and probe length on the convergence speed and normalized general mutual information performance is investigated. Experimental verification has been performed in a rate-adaptive 48 to 96 Gbit/s coherent system under different optical signal-to-noise ratios. The result shows that our sequence-based monitoring scheme estimates effectively the scaling factors over a continuous range in the rate-adaptive coherent system.
We experimentally demonstrate a 214.7 Tbit/s generalized mutual information (GMI) estimated throughput by ultra-wideband wavelength division multiplexing (WDM) transmission in standard single-mode fiber (SSMF). With 50-GHz grid, 396 transmission channels are used to deliver 49 GBaud probabilistically constellation-shaped (PCS) 256 quadrature amplitude modulation (QAM) and PCS-64QAM signals. Silicon photonic integrated transceiver is employed to complete electro-optic and optic-electro conversion of the modulated signals. S, C, and L-band rare-earth-doped amplifiers enable the 19.8 THz bandwidth WDM transmission without the assistance of distributed Raman amplification. The measured data rate shows great potential for Silicon photonic devices deployed in ultra-wideband WDM transmission.
Recently, incredible progress has been achieved in creating radio frequency (RF) carriers for millimeter wave (30–300 GHz) optical communication systems with ultrahigh data rates. Using a constant-composition distribution matcher (CCDM) to achieve probabilistic amplitude shaping (PAS) is a practical way to improve the efficiency and adaptability of coded modulations that use minimal bandwidth. Therefore, in this research article, a 100 Gbps–100 GHz radio over fiber (RoF) system is presented by incorporating PAS-CCDM in 32-quadrature amplitude modulation (QAM) (32-QAM) system over a 160-km link distance. A comparative analysis is presented between the proposed system and conventional-32-QAM-based RoF system at different link lengths and input power levels in terms of symbol error rate and Q factor. Performance comparison of the presented system and reported RoF systems revealed that the proposed system has carried maximum RF signal, highest data rate, and prolonged distance without using any amplifier.
High spectral efficiency (SE) transmission is a critical topic for next-generation ultra-high-speed optical networks, particularly for intensity-modulation with direct-detection (IM-DD) systems where the degree of freedom for data delivery is severely constrained. In this article, two high SE transmission approaches, namely fast than Nyquist (FTN) and high order modulation formats (HoMF) signaling, are experimentally demonstrated for peak-power constrained IM-DD systems. For FTN signaling, not only the sequence decoder based on M-Viterbi algorithm (M-VA), but also colored noise suppressed processing including partial response precoding (PRP), partial response equalization (PRE), nonlinear differential precoding (NLDP), Tomlinson-Harashima precoding (THP), and simplified THP (SfTHP) are investigated cooperatively to enhance the robustness of the system against inter-symbol interference (ISI) caused by acceleration. For HoMF signaling, probabilistic shaping (PS) with Maxwell Boltzmann (MB) and inverse MB distributions are discussed for rate adaptation. In a slight bandwidth-limited IM-DD system, although the PRE or SfTHP coupled with M-VA decoder enabled 56GBaud FTN PAM4 signal with 0.7 compression factor is successfully transmitted over 2-km single-mode fiber (SMF) with BER under the 7% hard-decision forward error correction (HD-FEC) threshold of 3.8×10
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, a 39.2GBaud MB-PS PAM8 with the same spectral efficiency, 2/0.7, shows about 1.8dB receiver sensitivity improvement. However, in an IM-DD system with 32GHz cut-off bandwidth and severe in-band degradation, the maximum achievable transmission rate of FTN PAM4 and PS-PAM8 are 162Gb/s and 145Gb/s, corresponding to 2.53 and 2.266 bits/symbol SEs, respectively, at BER of 3.8×10
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. According to the experimental results, the proposed colored noise suppressed FTN signaling offers significant potential as a solution for bandwidth-starved high-speed IM-DD systems.
Probability Shaping (PS) is a method to improve a Modulation and Coding Scheme (MCS) in order to increase reliability of data transmission. It is already implemented in some modern radio broadcasting and optic systems, but not yet in wireless communication systems. Here we adapt PS for the 5G wireless protocol, namely, for relatively small transport block size, strict complexity requirements and actual low-density parity-check codes (LDPC). We support our proposal by a numerical experiment results in Sionna simulator, showing 0.6 dB gain of PS based MCS versus commonly used MCS.
A probabilistic constellation shaping (PCS)-aided single-carrier transceiver is proposed to improve spectral efficiency for underwater acoustic (UWA) communications. At the transmitter, the information bits are input into a distribution matcher followed by a systematic binary encoder, which yields a sequence of sign bits with a uniform distribution and a sequence of amplitude bits with a non-uniform distribution. Based on these two sequences, the PCS is then realized by mapping coded bits onto a quadrature amplitude modulation constellation. At the receiver, an improved frequency-domain turbo equalizer based on the vector approximate message passing (VAMP) is proposed for the PCS-UWA communication system to eliminate the multipath interference. It exploits the a priori symbol probability information benefiting from the PCS at the beginning of the turbo iteration and over the self-iteration of the VAMP soft equalizer, improving the symbol detection performance. Finally, the first experimental demonstration of a deep-sea PCS-UWA communication system and numerical simulation of shallower water are presented. The experimental results reveal the PCS-UWA communication system significantly outperforms traditional systems with no PCS. Also, the proposed receiver is superior to the classical adaptive turbo equalizer based on the improved proportionate normalized least mean square algorithm even with data reuse.
A novel triple-convex 8-ary pulse amplitude modulation (TC-PAM8) probabilistic constellation shaping (PCS) scheme with bipolar symmetric alphabet is proposed in the intensity modulation/direct detection (IM/DD) system. Maintaining the basic implementation structure of the probabilistic amplitude shaping (PAS), the target entropy of TC-PAM8 is adjusted by setting the one-degree-of-freedom shaping factor accordingly. The performance of the proposed scheme is verified by an O-band 20-GBaud experimental system over 20-km standard single-mode fiber (SSMF) transmission, where the entropy is set to 2.2, 2.5, and 2.8 bit/symbol. The experimental results show that the proposed TC-PAM8 exhibits a better transmission performance compared with Maxwell-Boltzmann PAM8 (MB-PAM8) and Reverse-Maxwell-Boltzmann PAM8 (Rev-MB-PAM8) shaping scheme. Specifically, TC-PAM8 achieves a maximum gain of up to 1 dB and 2.2 dB in receiver sensitivity compared with the MB-PAM8 and Rev-MB-PAM8, respectively when the entropy is 2.2 bit/symbol.
The use of multiple segments on a silicon photonic modulator can increase bandwidth at the cost of greater complexity in the driving signals. We propose and demonstrate a simple driving scheme for use with dual segment modulators that involves very little additional complexity when equal length segments are used. The increased bandwidth with segmentation scales linearly with the number of segments, but the net bit rate does not; net rate depends on many factors. With an IQ modulator with two 2 mm segments, we demonstrate an improvement of 14% in net bit rate as compared to a single 4 mm segment. We examine the trade-offs in moving to three-segment modulation. We explore implementation penalties and use probabilistic shaping and optical pre-emphasis to achieve a net rate of 1.07 Tb/s with dual polarization transmission over 80 km of fiber at 116 Gbaud using 64QAM modulation.
The main methods and achievements regarding probabilistic shaping are reviewed, highlighting the primary difficulties and opportunities.
We propose two novel techniques to implement sequence selection (SS) for fiber nonlinearity mitigation, demonstrating a nonlinear shaping gain of 0 . 24 bits/s/Hz, just 0 . 1bits/s/Hz below the SS capacity lower bound.
We discuss the hardware, architect and system control of a C+L long-haul transmission link with 11THz total bandwidth. We show that a hierarchy fast distributed fault recovery mechanism is critical for the successful system deployment.
This network study compares the benefit of Elastic Optical Transponders enabling 130GBaud WDM channels for transporting 800GE services, showing ability to minimize number of required EOTs per Gb/s in regional and long-haul networks.
End-to-end learning has become a popular method to optimize a constellation shape of a communication system. When the channel model is differentiable, end-to-end learning can be applied with conventional backpropagation algorithm for optimization of the shape. A variety of optimization algorithms have also been developed for end-to-end learning over a non-differentiable channel model. In this paper, we compare a gradient-free optimization method based on the cubature Kalman filter, model-free optimization and backpropagation for end-to-end learning on a fiber-optic channel modeled by the split-step Fourier method. The results indicate that the gradient-free optimization algorithms provide a decent replacement to backpropagation in terms of performance at the expense of computational complexity. Furthermore, the quantization problem of finite bit resolution of the digital-to-analog and analog-to-digital converters is addressed and its impact on geometrically shaped constellations is analysed. Here, the results show that when optimizing a constellation with respect to mutual information, a minimum number of quantization levels is required to achieve shaping gain. For generalized mutual information, the gain is maintained throughout all of the considered quantization levels. Also, the results imply that the autoencoder can adapt the constellation size to the given channel conditions.
Convolutional LDPC ensembles, introduced by Felstrom and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing as a function of the average degree. Several variations on the basic theme have been proposed to date, all of which share the good performance characteristics of convolutional LDPC ensembles. We describe the fundamental mechanism which explains why "convolutional-like" or "spatially coupled" codes perform so well. In essence, the spatial coupling of the individual code structure has the effect of increasing the belief-propagation (BP) threshold of the new ensemble to its maximum possible value, namely the maximum-a-posteriori (MAP) threshold of the underlying ensemble. For this reason we call this phenomenon "threshold saturation." This gives an entirely new way of approaching capacity. One significant advantage of such a construction is that one can create capacity-approaching ensembles with an error correcting radius which is increasing in the blocklength. Our proof makes use of the area theorem of the BP-EXIT curve and the connection between the MAP and BP threshold recently pointed out by Measson, Montanari, Richardson, and Urbanke. Although we prove the connection between the MAP and the BP threshold only for a very specific ensemble and only for the binary erasure channel, empirically a threshold saturation phenomenon occurs for a wide class of ensembles and channels. More generally, we conjecture that for a large range of graphical systems a similar saturation of the "dynamical" threshold occurs once individual components are coupled sufficiently strongly. This might give rise to improved algorithms as well as to new techniques for analysis.
An upper bound on the capacity of a cascade of nonlinear and noisy channels
is presented. The cascade mimics the split-step Fourier method for computing
waveform propagation governed by the stochastic generalized nonlinear
Schroedinger equation. It is shown that the spectral efficiency of the cascade
is at most log(1+SNR), where SNR is the receiver signal-to-noise ratio. The
results may be applied to optical fiber channels. However, the definition of
bandwidth is subtle and leaves open interpretations of the bound. Some of these
interpretations are discussed.
The FEC limit paradigm is the prevalent practice for designing optical
communication systems to attain a certain bit-error rate (BER) without forward
error correction (FEC). This practice assumes that there is an FEC code that
will reduce the BER after decoding to the desired level. In this paper, we
challenge this practice and show that the concept of a channel-independent FEC
limit is invalid for soft-decision bit-wise decoding. It is shown that for low
code rates and high order modulation formats, the use of the soft FEC limit
paradigm can underestimate the spectral efficiencies by up to 20%. A better
predictor for the BER after decoding is the generalized mutual information,
which is shown to give consistent post-FEC BER predictions across different
channel conditions and modulation formats. Extensive optical full-field
simulations and experiments are carried out in both the linear and nonlinear
transmission regimes to confirm the theoretical analysis.
Lower bounds on mutual information (MI) of long-haul optical fiber systems for hard-decision and soft-decision decoding are studied. Ready-to-use expressions to calculate the MI are presented. Extensive numerical simulations are used to quantify how changes in the optical transmitter, receiver, and channel affect the achievable transmission rates of the system. Special emphasis is put to the use of different quadrature amplitude modulation formats, channel spacings, digital back-propagation schemes and probabilistic shaping. The advantages of using MI over the prevailing Q-factor as a figure of merit of coded optical systems are also highlighted.
In this letter, we present a method for performance estimation of forward error correction (FEC) codes using off-line data without data encoding. Only a few hundred thousand uncoded symbols are used to accurately evaluate post-FEC bit error rate of soft FEC codes decodable by the sum-product algorithm at very low error rates, e.g., 10-8 which is only limited by computer performance and simulation time. The method is applicable to both single and concatenated codes. The demonstration is carried out in optical 128-Gb/s polarization division multiplexed experiments with differentially encoded data and 20% redundancy quasi cyclic low-density parity check code.
We report the successful transmission of ten 494.85 Gbit/s DWDM signals on the standard 50 GHz ITU-T grid over 32 × 100 km of ultra-large-area (ULA) fiber. A net spectral efficiency (SE) of 8.25 b/s/Hz was achieved, after excluding the 20% soft-decision forward-error-correction (FEC) overhead. Such a result was accomplished by the use of a recently proposed polarization-division-multiplexed (PDM) time-domain hybrid 32-64 quadrature-amplitude-modulation (QAM) format, along with improved carrier frequency and phase recovery algorithms. It is shown that time-domain hybrid QAM provides a new degree of design freedom to optimize the transmission performance by fine tuning the SE of the modulation format for a specific channel bandwidth and FEC redundancy requirement. In terms of carrier recovery, we demonstrate that 1) hardware efficient estimation and tracking of the frequency offset between the signal and local-oscillator (LO) can be achieved by using a new feedback-based method, and 2) a training-assisted two-stage phase estimation algorithm effectively mitigates cyclic phase slipping problems. This new phase recovery algorithm not only improves the receiver sensitivity by eliminating the need for differential coding and decoding, but also enables an additional equalization stage following the phase recovery. We have shown that the introduction of this additional equalization stage (with larger number of taps) helps reduce the implementation penalty. This paper also presents the first experimental study of the impact of inphase (I) and quadrature (Q) correlation for a high-order QAM. It is shown that an adaptive equalizer could exploit the correlation between I and Q signal components to artificially boost the performance by up to 0.7 dB for a PDM time-domain hybrid 32-64 QAM signal when the equalizer length is significantly longer than I/Q de-correlation delay.
An analytical discrete-time model is introduced for single-wavelength polarization multiplexed nonlinear fiber-optical channels based on the symmetrized split-step Fourier method (SSFM). According to this model, for high enough symbol rates, a fiber-optic link can be described as a linear dispersive channel with additive white Gaussian noise (AWGN) and a complex scaling. The variance of this AWGN noise and the attenuation are computed analytically as a function of input power and channel parameters. The results illustrate a cubic growth of the noise variance with input power. Moreover, the cross effect between the two polarizations and the interaction of amplifier noise and the transmitted signal due to the nonlinear Kerr effect are described. In particular, it is found that the channel noise variance in one polarization is affected twice as much by the transmitted power in that polarization than by the transmitted power in the orthogonal polarization. The effect of pulse shaping is also investigated through numerical simulations. Finally, it is shown that the analytical performance results based on the new model are in close agreement with numerical results obtained using the SSFM for a symbol rate of 28 Gbaud and above.
Convolutional low-density parity-check (LDPC) ensembles, introduced by Felström and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing functions of the average degree. Several variations on the basic theme have been proposed to date, all of which share the good performance characteristics of convolutional LDPC ensembles. We describe the fundamental mechanism that explains why “convolutional-like” or “spatially coupled” codes perform so well. In essence, the spatial coupling of individual codes increases the belief-propagation (BP) threshold of the new ensemble to its maximum possible value, namely the maximum a posteriori (MAP) threshold of the underlying ensemble. For this reason, we call this phenomenon “threshold saturation.” This gives an entirely new way of approaching capacity. One significant advantage of this construction is that one can create capacity-approaching ensembles with an error correcting radius that is increasing in the blocklength. Although we prove the “threshold saturation” only for a specific ensemble and for the binary erasure channel (BEC), empirically the phenomenon occurs for a wide class of ensembles and channels. More generally, we conjecture that for a large range of graphical systems a similar saturation of the “dynamical” threshold occurs once individual components are coupled sufficiently strongly. This might give rise to improved algorithms and new techniques for analysis.
The performance of bit-interleaved coded modulation (BICM) with shaping (i.e., non-equiprobable bit probabilities) is studied. For the AWGN channel, the rates achievable with BICM and shaping are practically identical to those of coded modulation or multilevel coding, virtually closing the gap that made BICM suboptimal in terms of information rates.
Convolutional LDPC ensembles, introduced by Felström and Zigangirov, have excellent thresholds and these thresholds are rapidly increasing as a function of the average degree. Several variations on the basic theme have been proposed to date, all of which share the good performance characteristics of convolutional LDPC ensembles. We describe the fundamental mechanism which explains why “convolutional-like” or “spatially coupled” codes perform so well. In essence, the spatial coupling of the individual code structure has the effect of increasing the belief-propagation (BP) threshold of the new ensemble to its maximum possible value, namely the maximum-a-posteriori (MAP) threshold of the underlying ensemble. For this reason we call this phenomenon “threshold saturation”. This gives an entirely new way of approaching capacity. One significant advantage of such a construction is that one can create capacity-approaching ensembles with an error correcting radius which is increasing in the blocklength. Our proof makes use of the area theorem of the BP-EXIT curve and the connection between the MAP and BP threshold recently pointed out by Méasson, Montanari, Richardson, and Urbanke. Although we prove the connection between the MAP and the BP threshold only for a very specific ensemble and only for the binary erasure channel, empirically the same statement holds for a wide class of ensembles and channels. More generally, we conjecture that for a large range of graphical systems a similar collapse of thresholds occurs once individual components are coupled sufficiently strongly. This might give rise to improved algorithms as well as to new techniques for analysis.
We describe a method to estimate the capacity limit of fiber-optic communication systems (or ¿fiber channels¿) based on information theory. This paper is divided into two parts. Part 1 reviews fundamental concepts of digital communications and information theory. We treat digitization and modulation followed by information theory for channels both without and with memory. We provide explicit relationships between the commonly used signal-to-noise ratio and the optical signal-to-noise ratio. We further evaluate the performance of modulation constellations such as quadrature-amplitude modulation, combinations of amplitude-shift keying and phase-shift keying, exotic constellations, and concentric rings for an additive white Gaussian noise channel using coherent detection. Part 2 is devoted specifically to the "fiber channel.'' We review the physical phenomena present in transmission over optical fiber networks, including sources of noise, the need for optical filtering in optically-routed networks, and, most critically, the presence of fiber Kerr nonlinearity. We describe various transmission scenarios and impairment mitigation techniques, and define a fiber channel deemed to be the most relevant for communication over optically-routed networks. We proceed to evaluate a capacity limit estimate for this fiber channel using ring constellations. Several scenarios are considered, including uniform and optimized ring constellations, different fiber dispersion maps, and varying transmission distances. We further present evidences that point to the physical origin of the fiber capacity limitations and provide a comparison of recent record experiments with our capacity limit estimation.
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 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.
We consider a windowed decoding scheme for LDPC convolutional codes that is
based on the belief-propagation (BP) algorithm. We discuss the advantages of
this decoding scheme and identify certain characteristics of LDPC convolutional
code ensembles that exhibit good performance with the windowed decoder. We will
consider the performance of these ensembles and codes over erasure channels
with and without memory. We show that the structure of LDPC convolutional code
ensembles is suitable to obtain performance close to the theoretical limits
over the memoryless erasure channel, both for the BP decoder and windowed
decoding. However, the same structure imposes limitations on the performance
over erasure channels with memory.
We revisit the information-theoretic analysis of bit-interleaved coded modulation (BICM) by modeling the BICM decoder as a mismatched decoder. The mismatched decoding model is well-defined for finite, yet arbitrary, block lengths, and naturally captures the channel memory among the bits belonging to the same symbol. We give two independent proofs of the achievability of the BICM capacity calculated by Caire et al. where BICM was modeled as a set of independent parallel binary-input channels whose output is the bitwise log-likelihood ratio. Our first achievability proof uses typical sequences, and shows that due to the random coding construction, the interleaver is not required. The second proof is based on the random coding error exponents with mismatched decoding, where the largest achievable rate is the generalized mutual information. We show that the generalized mutual information of the mismatched decoder coincides with the infinite-interleaver BICM capacity. We also show that the error exponent -and hence the cutoff rate- of the BICM mismatched decoder is upper bounded by that of coded modulation and may thus be lower than in the infinite-interleaved model. We also consider the mutual information appearing in the analysis of iterative decoding of BICM with EXIT charts. We show that the corresponding symbol metric has knowledge of the transmitted symbol and the EXIT mutual information admits a representation as a pseudo-generalized mutual information, which is in general not achievable. A different symbol decoding metric, for which the extrinsic side information refers to the hypothesized symbol, induces a generalized mutual information lower than the coded modulation capacity.
In this paper, we highlight the class of spatially coupled codes and discuss their applicability to long-haul and submarine optical communication systems. We first demonstrate how to optimize irregular spatially coupled LDPC codes for their use in optical communications with limited decoding hardware complexity and then present simulation results with an FPGA-based decoder where we show that very low error rates can be achieved and that conventional block-based LDPC codes can be outperformed. In the second part of the paper, we focus on the combination of spatially coupled LDPC codes with different demodulators and detectors, important for future systems with adaptive modulation and for varying channel characteristics. We demonstrate that SC codes can be employed as universal, channel-agnostic coding schemes.
The FEC limit paradigm is the prevalent practice for designing optical communication systems to attain a certain bit error rate (BER) without forward error correction (FEC). This practice assumes that there is an FEC code that will reduce the BER after decoding to the desired level. In this paper, we challenge this practice and show that the concept of a channel-independent FEC limit is invalid for soft-decision bit-wise decoding. It is shown that for low code rates and high-order modulation formats, the use of the soft-decision FEC limit paradigm can underestimate the spectral efficiencies by up to 20%. A better predictor for the BER after decoding is the generalized mutual information, which is shown to give consistent post-FEC BER predictions across different channel conditions and modulation formats. Extensive optical full-field simulations and experiments are carried out in both the linear and nonlinear transmission regimes to confirm the theoretical analysis.
We report the current status of forward error correction schemes and show how close we can operate to some theoretical limits taking into account the size of the codes. Finally, we compare some spatially-coupled codes.
We analyze the performance of different left-terminated, infinitely extended spatially coupled LDPC codes for optical communications using an FPGA-based emulator. We find codes that are able to realize conjectured net coding gains of more than 12.1 dB.
We developed time-domain hybrid-modulation with adaptive symbolrates to optimize the reach and margin of WSS routed 400 Gb/s systems. Experimental comparisons show, that a DP-8QAM/16QAM hybrid format can outperform the benchmark DP-8QAM and DP-16QAM formats in distance when up to 18 WSS are incorporated.
We implemented a flexible transmission system operating at adjustable data
rate and fixed bandwidth, baudrate, constellation and overhead using
probabilistic shaping. We demonstrated in a transmission experiment up to 15%
capacity and 43% reach increase versus 200 Gbit/s 16-QAM.
A compound channel is characterized by a set of permissible transition probabilities (which depend on the state of the channel). We focus on a class of compound channels for which the state sequence has a stochastic characterization and with mismatched decoding. Three levels of receiver side information on the state sequence are addressed, namely known state, known statistics, and mismatch. First, we develop some new relations of error exponents and achievable rates in this general context, and for completeness, review relevant known results. We then apply some of these general results to the specific case of binary PSK modulation operating in a fading channel with ideal interleaving under the above-mentioned different levels of side information. We address two variants of the Rician model, as well as the Nakagami-m model, and compare their similarities and differences.
In this paper, we highlight the class of spatially coupled codes and discuss
their applicability to long-haul and submarine optical communication systems.
We first demonstrate how to optimize irregular spatially coupled LDPC codes for
their use in optical communications with limited decoding hardware complexity
and then present simulation results with an FPGA-based decoder where we show
that very low error rates can be achieved and that conventional block-based
LDPC codes can be outperformed. In the second part of the paper, we focus on
the combination of spatially coupled LDPC codes with different demodulators and
detectors, important for future systems with adaptive modulation and for
varying channel characteristics. We demonstrate that SC codes can be employed
as universal, channel-agnostic coding schemes.
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.
Asymptotically in the blocklength, the encoder achieves the maximum rate,
namely the entropy of the desired distribution. Furthermore, the normalized
divergence of the encoder output and the desired distribution goes to zero in
the blocklength.
In this letter, the fiber-optic communication channel with a quadrature amplitude modulation (QAM) input constellation is treated. Using probabilistic shaping, we show that high-order QAM constellations can achieve and slightly exceed the lower bound on the channel capacity, set by ring constellations. We then propose a mapping function for turbo-coded bit-interleaved coded modulation based on optimization of the mutual information between the channel input and output. Using this mapping, spectral efficiency as high as 6.5 bits/s/Hz/polarization is achieved on a simulated single channel long-haul fiber-optical link excluding the pilot overhead, used for synchronization, and taking into account frequency and phase mismatch impairments, as well as laser phase noise and analog-to-digital conversion quantization impairments. The simulations suggest that major improvements can be expected in the achievable rates of optical networks with high-order QAM.
In this paper, we discuss and present some recent advances in the field of error correcting codes and discuss their applicability for lightwave transmission systems. We introduce several classes of spatially coupled codes and discuss several design options for spatially coupled codes and show how rapidly decodable codes can be constructed by careful selection of the degree distribution. We confirm the good performance of some spatially coupled codes at very low bit error rates using an FPGA-based simulation. Finally, we compare all proposed schemes and show how spatially coupled Low-Density Parity-Check (LDPC) codes outperform conventional LDPC and polar codes with similar receiver complexity and memory requirements.
A new coded modulation scheme is proposed. At the transmitter, the concatenation of a distribution matcher and a systematic binary encoder performs probabilistic signal shaping and channel coding. At the receiver, the output of a bitwise demapper is fed to a binary decoder. No iterative demapping is performed. Rate adaption is achieved by adjusting the input distribution and the transmission power. The scheme is applied to bipolar amplitude shift keying (ASK) constellations with equidistant signal points and it is directly applicable to two-dimensional quadrature amplitude modulation (QAM). The scheme is implemented by using the DVB-S2 low-density parity-check (LDPC) codes. At a frame error rate of 1e-3, the new scheme operates within less than 1 dB of the AWGN capacity 0.5log2(1+SNR) at any spectral efficiency between 1 and 5 bits/s/Hz by using only 5 modes, i.e., 4-ASK with code rate 2/3, 8-ASK with 3/4, 16-ASK and 32-ASK with 5/6 and 64-ASK with 9/10.
A protograph-based low-density parity-check (LDPC) code design technique for bandwidth-efficient coded modulation is presented. The approach jointly optimizes the LDPC code node degrees and the mapping of the coded bits to the bit-interleaved coded modulation (BICM) bit-channels. For BICM with uniform input and for BICM with probabilistic shaping, binary-input symmetric-output surrogate channels are constructed and used for code design. The constructed codes perform as good as multi-edge type codes of Zhang and Kschischang (2013). For 64-ASK with probabilistic shaping, a blocklength 64800 code is constructed
that operates within 0.69 dB of 0.5log(1+SNR) at a spectral efficiency of 4.2 bits/channel use and a frame error rate of 1e-3.
An LDPC coded modulation scheme with probabilistic shaping, optimized
interleavers and noniterative demapping is proposed. Full-field simulations
show an increase in transmission distance by 8% compared to uniformly
distributed input.
Fiber's nonlinearity fundamentally bounds the achievable information rates in fiber-optic communication systems. In a wavelength-division multiplexed system it induces a nonlinear interference between adjacent channels, an interference that was recently shown to have a strong dependance on the input distribution. In this work we show that a ball shaped input constellation may significantly reduce the nonlinear effects. We study the shaping gains in the fiber-optic channel and show that in certain scenarios the maximum gains may be higher than the 1.53dB ultimate shaping gain in linear additive white Gaussian noise channels. Furthermore, the maximum gain is achieved with a finite-dimensional ball shaping region.
A new achievable rate for bit-metric decoding (BMD) is derived using random coding arguments. The rate expression can be evaluated for any input distribution, and in particular the bit-levels of binary input labels can be stochastically dependent. Probabilistic shaping with dependent bit-levels (shaped BMD), shaping of independent bit-levels (bit-shaped BMD) and uniformly distributed independent bit-levels (uniform BMD) are evaluated on the additive white Gaussian noise (AWGN) channel with bipolar amplitude shift keying (ASK). For 32-ASK at a rate of 3.8 bits/channel use, the gap to 32-ASK capacity is 0.008 dB for shaped BMD, 0.46 dB for bit-shaped BMD, and 1.42 dB for uniform BMD. These numerical results illustrate that dependence between the bit-levels is beneficial on the AWGN channel. The relation to the generalized mutual information (GMI) is discussed.
The paper contains an approach to the problems of universal encoding and decoding which is based on the concept of inaccuracy. The areas of noiseless source coding, source coding for noisy channels and channel coding and decoding are covered. Another purpose of the paper is to get a deeper understanding of the role of inaccuracy in the theory of information transmission.
In this paper, we present the design and analysis of an adaptive cost-effective discrete multitone transponder (DMT) using direct detection (DD) suitable for data center interconnections. Levin Campello margin adaptive (LC-MA) algorithm is applied to the transponder digital signal processing modules to enhance fiber chromatic dispersion (CD) resilience, while achieving high-data rate transmission. The bit error rate (BER) performance and the rate/distance adaptive capabilities of the proposed transponder have been numerically analyzed and compared to bandwidth variable uniform loading, taking into account the transmission impairments at the varying of the fiber length. Specifically, the performance of the designed transponder has been assessed from $20$ to $112$ Gb/s, extending the achievable reach at $50$ Gb/s beyond $80$ km of standard single mode fiber (SSMF). The numerical simulations have been compared with experimental results, evidencing good agreement in presence of transmission impairments.
The problem of analytical evaluation of the maximum rate at which information can be reliably transmitted on a nonlinear wavelength division multiplexing fiber-optic channel with a given modulation format and detection strategy is addressed. An approximate solution of the nonlinear Schrödinger equation is adopted to obtain an accurate analytical discrete-time channel model, valid for arbitrary link configurations and modulation formats. By exploiting the concept of mismatched decoding, considering a sub-optimum detection strategy that accounts for intra-channel nonlinearities, the proposed model is employed to derive closed-form expressions of the achievable information rate with various modulation formats. All the analytical results are verified through comparison with numerical simulations in different scenarios.
A scheme is proposed that combines probabilistic signal shaping with bit-metric decoding. The transmitter generates symbols according to a distribution on the channel input alphabet. The symbols are labeled by bit strings. At the receiver, the channel output is decoded with respect to a bit-metric. An achievable rate is derived using random coding arguments. For the 8-ASK AWGN channel, numerical results show that at a spectral efficiency of 2 bits/s/Hz, the new scheme outperforms bit-interleaved coded modulation (BICM) without shaping and BICM with bit shaping (i Fabregas and Martinez, 2010) by 0.87 dB and 0.15 dB, respectively, and is within 0.0094 dB of the coded modulation capacity. The new scheme is implemented by combining a distribution matcher with a systematic binary low-density parity-check code. The measured finite-length gains are very close to the gains predicted by the asymptotic theory.
We propose a novel coded modulation scheme for coherent optical orthogonal frequency-division multiplexing (CO-OFDM) to achieve high-speed transmission at spectral-efficiencies near the Shannon limit. The proposed coding scheme relies on the concept of bit interleaved coded modulation with iterative decoding (BICM-ID), low-density parity-check (LDPC) codes, and shaped iterative polar modulation (IPM). To further increase the transmission spectral efficiency, reduced guard interval (RGI) CO-OFDM is used, in which fiber chromatic dispersion (CD) is digitally compensated prior to OFDM demultiplexing at the receiver. We experimentally demonstrate the generation and forward error correction (FEC) decoding of a 231.5-Gb/s RGI-CO-OFDM signal with 256-IPM subcarrier modulation, occupying a bandwidth of 20.75 GHz. The coded 256-IPM signal offers a coding gain of 15.1-dB compared to uncoded 256-point quadrature amplitude modulation (256-QAM) at a post-FEC bit error ratio of 10- 15. Transmission was demonstrated over an 800-km ultra-large-area fiber (ULAF) link with a record intrachannel spectral efficiency of 11.15-b/s/Hz.
We propose a tool for assessing the performance of soft-input forward-error-correction codes with recorded optical transmission experiments. This tool, which can be used to evaluate the performance of any linear coding scheme, is especially suited for higher order modulation schemes. Without having to redo the channel measurements, recorded data can be used to perform offline evaluation of various coding schemes. This is facilitated by the linearity of the code. We demonstrate the usefulness of the tool by applying it in a 16-quadrature amplitude modulation (QAM) experiment, where recorded channel data is used to compare the performance of two different low-density parity-check coding schemes using differentially encoded 16-QAM modulation.
We propose a coded polarization-multiplexed iterative polar modulation (PM-IPM) as an enabling coded-modulation scheme for beyond 400 Gb/s serial optical transmission. We demonstrate that the proposed scheme can achieve 400 Gb/s optical transmission over 2250 km (for M = 3D16).
We successfully applied layered decoding algorithm in decoding LDPC convolutional codes designed for applications in high speed optical transmission systems. A relatively short code was FPGA-emulated with a Q factor of 5.7dB at BER of 10-15.
We address perturbative models for the impact of non- linear propagation in uncompensated links. We concentrate on a re- cently-proposed model which splits up the signal into spectral com- ponents 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 val- idation by addressing an ample and significant set of formats en- compassing 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 simu- lation 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.
We present a family of protograph based LDPC codes that can be derived from permutation matrix based regular (J,K) LDPC convolutional codes by termination. In the terminated protograph, all variable nodes still have degree J but some check nodes at the start and end of the protograph have degrees smaller than K. Since the fraction of these stronger nodes vanishes as the termination length L increases, we call the codes asymptotically regular. The density evolution thresholds of these protographs are better than those of regular (J, K) block codes. Interestingly, this threshold improvement gets stronger with increasing node degrees (at a fixed rate) and it does not decay as L increases. Terminated convolutional protographs can also be derived from standard irregular protographs and may exhibit a significant threshold improvement.
A pragmatic coded modulation system is presented that incorporates signal
shaping and exploits the excellent performance and efficient high-speed
decoding architecture of staircase codes. Reliable communication within 0.62
bits/s/Hz of the estimated capacity (per polarization) of a system with L=2000
km is provided by the proposed system, with an error floor below 1E-20. Also,
it is shown that digital backpropagation increases the achievable spectral
efficiencies---relative to linear equalization---by 0.55 to 0.75 bits/s/Hz per
polarization.
A scheme for the construction of m -out-of- n
codes based on the arithmetic coding technique is described. For
appropriate values of n , k , and m , the scheme
can be used to construct an ( n , k ) block code in which
all the codewords are of weight m . Such codes are useful, for
example, in providing perfect error detection capability in asymmetric
channels such as optical communication links and laser disks. The
encoding and decoding algorithms of the scheme perform simple arithmetic
operations recursively, thereby facilitating the construction of codes
with relatively long block sizes. The scheme also allows the
construction of optimal or nearly optimal m -out-of- n
codes for a wide range of block sizes limited only by the arithmetic
precision used
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
We design multilevel coding (MLC) and bit-interleaved coded modulation (BICM) schemes based on low-density parity-check (LDPC) codes. The analysis and optimization of the LDPC component codes for the MLC and BICM schemes are complicated because, in general, the equivalent binary-input component channels are not necessarily symmetric. To overcome this obstacle, we deploy two different approaches: one based on independent and identically distributed (i.i.d.) channel adapters and the other based on coset codes. By incorporating i.i.d. channel adapters, we can force the symmetry of each binary-input component channel. By considering coset codes, we extend the concentration theorem based on previous work by Richardson et al. ( see ibid., vol.47, p.599-618, Feb. 2001) and Kavcˇic´ et al.(see ibid., vol.49, p.1636-52, July 2003) We also discuss the relation between the systems based on the two approaches and show that they indeed have the same expected decoder behavior. Next, we jointly optimize the code rates and degree distribution pairs of the LDPC component codes for the MLC scheme. The optimized irregular LDPC codes at each level of MLC with multistage decoding (MSD) are able to perform well at signal-to-noise ratios (SNR) very close to the capacity of the additive white Gaussian noise (AWGN) channel. We also show that the optimized BICM scheme can approach the parallel independent decoding (PID) capacity as closely as does the MLC/PID scheme. Simulations with very large codeword length verify the accuracy of the analytical results. Finally, we compare the simulated performance of these coded modulation schemes at finite codeword lengths, and consider the results from the perspective of a random coding exponent analysis.
A fixed-to-fixed length distribution matcher in C/MATLAB
- P Schulte
P. Schulte, "A fixed-to-fixed length distribution matcher in C/MATLAB."
[Online]. Available: http://www.beam.to/ccdm
Pulse code communication
- gray
F. Gray, "Pulse code communication," U. S. Patent 2 632 058, 1953.
Evaluation of leftterminated spatially coupled LDPC codes for optical communications
- L Schmalen
- D Suikat
- D Rosener
- A Leven
L. Schmalen, D. Suikat, D. Rosener, and A. Leven, "Evaluation of leftterminated spatially coupled LDPC codes for optical communications,"
in European Conference on Optical Communication (ECOC), 2014,
th.2.3.4.
Hybrid modulation formats outperforming 16QAM and 8QAM in transmission distance and filtering with cascaded WSS
- W Idler
- F Buchali
- L Schmalen
- K Schuh
- H Bülow
W. Idler, F. Buchali, L. Schmalen, K. Schuh, and H. Bülow, "Hybrid
modulation formats outperforming 16QAM and 8QAM in transmission
distance and filtering with cascaded WSS," in Optical Fiber Communication Conference (OFC), 2015, paper M3G.4.