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Abstract
We introduce a novel probabilistic shaping (PS) scheme based on bit-weighted distribution matching (BWDM) into a discrete multi-tone wavelength division multiplexing passive optical network (DMT-WDM-PON) employing low-density parity-check-coded 16-ary quadrature amplitude modulation (16QAM). Unlike the prevailing arithmetic coding-class PS schemes with target symbol probability, such as arithmetic distribution matching and constant composition distribution matching, the proposed one realizes Gaussian-like symbol probability distribution emulation merely based on simple bit-class processing, having the advantage of much lower computational complexity. As the key operation in BWDM, the bit weight intervention is implemented in the process of PS-16QAM generation for elevated transmission probability of binary data ‘0’ by cascaded operations of weight bit labelling and bit reconstruction. The experimental results show that, compared with uniformly-distributed signal with the same net rate, significantly-improved receiver power sensitivity and system tolerance to optical fiber nonlinear effect can be obtained in the DMT-WDM-PON system. The proposed PS scheme can be considered as one of promising practical solutions for more available optical network units due to enlarged system power loss budget for the optical distribution network.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In contemporary life, the daily-increasing consumption of high-speed and large-capacity digital information severely challenges modern fiber-optic communication systems [1–2]. As one of the important types of optical access networks, discrete multi-tone wavelength division multiplexing optical passive network (DMT-WDM-PON) with much simpler intensity modulation/direct detection (IM/DD) takes advantage of the impressive balance between transmission capacity and system cost, which is thus considered as a competitive option to be extensively deployed in commercial applications [3]. The DMT modulation technique combined with high-order quadrature amplitude modulation format is commonly used to achieve higher spectral efficiency, stronger resistance capabilities of inter-symbol interference (ISI) and chromatic dispersion (CD) [4]. The conventional WDM-PON suffers from an inherent power constraint bottleneck with the increase of launch fiber power, spelling limited power loss budget for the system to serve optical network units (ONUs) [5]. Unlike geometric rearrangement on the complex plane for geometrically shaped quadrature amplitude modulation (QAM) [6], probabilistic shaping (PS) technique, well known for maximal 1.53-dB shaping gain, has been deeply investigated to change the transmitted symbol probability distribution (SPD) at the aim of a desired probability distribution imitation such as Gaussian distribution (GD) and Maxwell-Boltzmann distribution (MB) [7–10]. Besides, by transmitting high-energy symbols with lower probability as well as low-energy ones with higher probability, the effectively-reduced average power of transmitted signal by PS implementation can contribute to improve system tolerance to fiber nonlinear effect. Recently, some classical PS methods have been studied in optical communication systems, such as Gallager many-to-one (MTO) mapping [11], arithmetic distribution matching (ADM) [12] and constant composition distribution matching (CCDM) [13–15]. For the MTO mapping scheme, despite the remarkable advantage of no extra redundant bits, it takes the system more time and power consumption for forward error correction (FEC) to well address the inherent ambiguity caused by symbol overlapping [8,11]. The classical ADM and CCDM are both derived from arithmetic coding. In order to emulate a desired SPD, it is fundamental and inevitable to refine the probability interval continuously and online. For instance, 4 out of 6 possible binary combinations with Bernoulli (1/2) distribution are selected for the PS-PAM4 generation based on CCDM [13], which turns the input 2 bits into the output 4 bits after interval refinement. Furthermore, considering binary LDPC-based FEC encoding and high-order modulation formats, the final labels symbolizing the desired probabilities should be mapped into binary sequences for the compatibility of optical modulation. The conversion processing certainly makes the complexity of calculation and hardware as well as system power consumption rise.
In this paper, we propose and experimentally demonstrate a DMT-WDM-PON system employing a novel PS scheme based on bit-weighted distribution matching (BWDM). The key operation, bit-weight intervention (BWI), is used to enhance the probability of binary data ‘0’ by joint processing of weight bit labelling and subsequent bit reconstruction before QAM mapping. In this way, compared with ADM and CCDM, the proposed low-complexity PS scheme based on bit-class BWDM can contribute to an available SPD with lower average power. Five-channel 25-GBaud DMT-WDM-PON employing LDPC-coded PS-16QAM DMT signals based on BWDM is investigated in the experiments. The experimental results show that significantly-improved receiver power sensitivity (RPS) and system tolerance to optical fiber nonlinear effect can be obtained compared with the standard uniformly-distributed (UD) signal.
2. Principle of DMT-WDM-PON employing PS-16QAM based on BWDM
The concise flowchart of DMT-WDM-PON system is illustrated in Fig. 1(a). At the optical line terminal (OLT), binary data streams are firstly processed by a PS distribution matcher based on BWDM. The following LDPC-based FEC encoding, QAM mapping and DMT modulation are carried out orderly. After the electrical-to-optical conversion via optical intensity modulation and WDM signal multiplexing, the optical PS-16QAM DMT-WDM-PON signals are transmitted to the remote terminal over an optical splitter-based optical distribution network (ODN). After the WDM de-multiplexer and the splitter for optical signal routing, the inverse processes at the OLT are performed to retrieve transmitted data from the received downstream PS signals at the ONU.
Fig. 1. (a) Principle of DMT-WDM-PON employing PS-16QAM based on BWDM, (b) PS-16QAM DMT generation based on BWDM, (c) DFT-S DMT modulation, (d) bit weight intervention (k = 4), (e) PS-16QAM mapping. Probability distribution of binary data ‘0’ in the four parallel sequences of PS-16QAM, b(I): before BWI, b(II): after BWI. PS DM: PS distribution matching, Map.: QAM mapping, DMT Mod.: DMT modulation, IM-E/O: intensity modulation-based electrical-to-optical conversion, DD-O/E: direct detection-based optical-to-electrical conversion.
2.1 PS-16QAM DMT generation based on BWDM
Figure 1(b) depicts the PS-16QAM DMT generation based on BWDM. Four parallel pseudo random binary sequences (PRBSs) D1, D2, D3, and D4 with ideal Bernoulli (1/2) distribution, shown as inset b(I) (represented by binary data ‘0’), are used as the data source. The first two binary sequences (D1 and D2) are processed to be D'1 and D'2 by BWI. As the key operation of BWDM, BWI is aimed at elevating the probability weight of binary data ‘0’, which is detailedly illustrated in the next subsection. Then, the four parallel binary data are bitwise processed by the parallel-to-serial conversion (P/S). The following LDPC-based FEC with multiple code rates v is with the contemporary standard of digital video broadcasting-satellite-second generation (DVB-S.2). After the serial-to-parallel conversion (S/P), the four parallel data are permuted by an interleaver for I1, I2, I3, and I4 with reduced burst errors to optimize the LDPC correction performance, which respectively contain the bits originated from D'1, D'2, D'3, and D'4. Within single LDPC block (64800 encoded bits), the four-bit codewords {I1(m), I2(m), I3(m), I4(m)} are mapped into PS-16QAM symbols, which is discussed in subsection 2.3. I1(m) is the most significant bit (MSB) of the four bits and m ∈ [1,16200]. The principle of DMT modulation after PS-16QAM mapping is displayed in Fig. 1(c). There are 288 subcarriers in one DMT frame. Among them, 99-point fast Fourier transform (FFT) and 56-point subcarrier mapping are carried out for DFT-S implementation [16], which is employed for peak-to-average power ratio (PAPR) deduction. Then, DMT modulation is realized by 256-point inverse fast Fourier transform (IFFT) for and 32-point cyclic prefix (CP) insertion for ISI resistance in series. At the end of the process, the serial LDPC-coded PS-16QAM DFT-S DMT is obtained after P/S.
2.2 Bit-weight intervention
In BWI operation mentioned above, the original bits in D1 and D2 are bitwise divided into several k-element subsets. In every subset, the bit-weight calculation for the probability of binary data ‘0’ is carried out to determine the value of weight labelling bit R. We define that R equals to ‘1’ when the probability of binary data ‘0’ in the k-bit subset is smaller than 1/2. In this case, a negation operation is taken to the k bits in the subset. For instance, the subset {1, 1, 1, 1} can be converted into the one {0, 0, 0, 0} under the circumstance. Otherwise, R is set as ‘0’ and all k elements stay unchanged. Then, R is to be the newly-inserted MSB to form a new subset with (k + 1) bits in D'1 and D'2. By this means, the probability distribution of D'1 and D'2 is able to be adjusted by varying the length of subset, i.e. k effective bits in every original subset, defined as the PS parameter.
Figure 1(d) shows the specific case of k = 4 in BWI. The n-th and (n + 1)-th subsets containing a total of 8 bits in D1 and D2 are converted to two 5-bit new subsets in D'1 and D'2. Rn and Rn+1 are respectively introduced as the new MSBs after the bit-weight calculation and bit reconstruction to enhance the probability of binary data ‘0’. It is not tough to infer that the subsets {0, 0, 0, 1, 0}, {0, 1, 0, 1, 0}, {1, 0, 0, 1, 0} and {1, 0, 0, 0, 0}are the corresponding BWI outputs from {0, 0, 1, 0}, {1, 0, 1, 0}, {1, 1, 0, 1} and {1, 1, 1, 1} in the process of PS-16QAM generation. Inset b(II) portrays the probability distribution for PS-16QAM with the k values of 4, 9 and 39. Evidently, the smaller k is, the higher probability of binary data ‘0’ can be obtained. It is because the MSB in every subset plays a less influential role in the probability recombination of binary data ‘0’ as the k value increases.
2.3 PS-16QAM mapping
Provided that the transmitted data source is ideal and infinite, the definite probability of pre-LDPC PS-16QAM symbol mapped from the codeword {D'1(d’), D'2(d’), D'3(d’), D'4(d’)} can be defined as
Considering the uniformly-distributed binary FEC [15], the probability of LPDC-coded PS-16QAM mapped from the codeword {I1(m), I2(m), I3(m), I4(m)} can be expressed as
According to Eqs. (1)-4, it is known that with different k, various symbol probabilities can be attained without and with LDPC encoding. For purpose of a Gaussian-like SPD imitation, the PS-16QAM mapping scheme optimized by the bit-level BWDM is given in Fig. 1(e). In short, the codewords with greater transmission probabilities are mapped into the symbols with less energy, and the equiprobability codewords are arranged to be the symbols with the same energy. In addition, the maximum Hamming distance (HD) is taken into consideration, designed and minimized to be 1 between the adjacent symbols. It is evident that the innermost constellation points with minimal energy, (±1 ± 1i) on the complex plane, are clearly allocated from the four codewords “0000”, “0001”, “0010”, and “0011” with the highest transmission probability. Thus, once the value of k is given in cooperation with the PS-16QAM mapping scheme as specified, the available Gaussian-like SPD can solely be guaranteed. In other words, the value of k and the attainable SPD share a one-to-one correspondence. The specific mapping rule is performed in the experiment for both the UD-16QAM and the PS-16QAM for comparison.
Figures 2(a) and (b) show the bar charts for the probability of binary data ‘0’ in the four input sequences of PS-16QAM. We can see that the probability of ‘0’ in the first two binary sequences can be significantly enhanced by BWI. The SPD for pre- and post-LDPC PS-16QAM with ideal source (Figs. 2(c) and (d)) and practically-transmitted data (Figs. 2(e) and (f)) clearly supports Eqs. (1)–4 following the PS-16QAM mapping law. Although there exists certain deviation between the ideal (infinite) and practically-transmitted (finite) sources, the SPD in Figs. 2(c) and (d) by BWDM matches well with the one in Figs. 2(e) and (f) correspondingly. Namely, the divergence is acceptable and can be negligible. Besides, with the addition of LDPC-based FEC to improve transmission reliability, the SPD for PS-16QAM varies from the pre-LDPC shape acceptably and controllably, according to the comparisons of Figs. 2(c-f). Thus, it can be easily proved that the BWDM scheme is feasible and compatible with the practical LDPC-based FEC in optical communication system.
Fig. 2. Probability distribution of binary data ‘0’ (k = 4 and v = 3/4) in the four input sequences (a) without and (b) with LDPC, SPD for ideal PS-16QAM (c) pre- and (d) post-LDPC cases, SPD for practical PS-16QAM (e) pre- and (f) post-LDPC cases.
2.4 Channel capacity
Assuming that the signal X is transmitted in the channel with additive white Gaussian noise (AWGN), and the vector Y represents the received signal. $p(x)$ stands for the input SPD. Based on the information theory, the mutual information (MI) can be obtained by
For the PS-16QAM based on BWDM, the SPD of transmitted signal is designed to emulate GD, which has been proved to be the optimal input SPD in AWGN channel [17–18]. Accordingly, C can be further optimized and the shaping gain can be obtained since the SPD changes to Gaussian-like distribution from UD. The constrained channel capacity analyses for standard UD-16QAM and proposed PS-16QAM based on the ideal pre-LDPC SPD in the case of k = 4 are shown in Fig. 3. It is intuitive that up to 0.44-dB shaping gain can be obtained based on the SPD in Fig. 2(c). It indicates the reduced gap to the Shannon capacity limit in certain low SNR region.
3. Experimental setup
The proof-of-concept experimental setup of 5-channel 25-GBaud DMT-WDM-PON system employing LDPC-coded PS-16QAM based on BWDM is elaborated in Fig. 4. At the OLT, the 25-GBaud PS-16QAM DMT electrical signal is generated by a digital-to-analog convertor (DAC, Tek70001A) with a sampling rate of 50 GSa/s and 3-dB bandwidth of 18 GHz. Five external cavity lasers (ECLs) with the linewidth of less than 100 kHz are deployed to generate the 5 downstream optical channels with an equal wavelength spacing of 50 GHz. At the output of the two polarization-maintenance optical couplers (PM-OCs), the odd and even channels are combined by the optical channels from #1, #3, #5 and #2, #4 ECLs. Two PS-16QAM DMT electrical signals are used to drive the two group channels via two sets of Mach-Zehnder modulators (MZMs) after power boosting by two electrical amplifiers (EAs) with the broadband bandwidth of 45 GHz. The MZMs are with the 3-dB bandwidth of 40 GHz and half-wave voltage of 3 V. Then the two group channels are amplitude-shaped and coupled via a programmable wavelength selective switch (WSS). At the ODN, the downstream WDM signal is fed into 20-km SSMF after being boosted by an Erbium-doped fiber amplifier (EDFA) for launch fiber power investigation. Subsequently, an optical tunable filter (OTF) with 3-dB bandwidth of 23 GHz is equipped for WDM channel selection. At the ONU, a photodetector (PD) with 40-GHz 3-dB bandwidth is applied for signal optical/electrical conversion. A digital real-time storage oscilloscope with 50-GSa/s sampling rate and 17-GHz 3-dB electrical bandwidth is adopted for A/D and signal capture. Then digital signal is fed into the offline DSP module including 2-samples/symbol down-sampling, training synchronization, DFT-S DMT demodulation, PS-16QAM de-mapping, LDPC decoding, inverse BWDM and final BER calculation. Note that the pre-equalization based on the reference signal of UD-16QAM DMT is employed in order to compensate for the signal distortion at high frequency, which is incurred by the limited bandwidth of optical/electrical components, such as the arbitrary waveform generator (AWG), optical modulator, electrical drivers, PD and analog-to-digital convertor (ADC) [4].
Fig. 4. Proof-of-concept experimental setup of DMT-WDM-PON employing LDPC-coded PS-16QAM based on BWDM.
4. Experimental result
Figure 5(a) shows the BER performance for the optical PS-16QAM DMT-WDM-PON signal before and after 20-km SSMF transmission. The measured 25-GBaud ${(\textrm{net}\; \textrm{rate}\; }({\textrm{GBd}} ){ = \textrm{Baud}\; \textrm{rate} \times }\left( {{1 - }\frac{{1}}{{{2}({{\textrm{k} + 1}} )}}} \right)\textrm{)}$ LDPC-coded PS-16QAM DMT is with the PS parameter k = 4 and LDPC v = 3/4, and thus, a 22.5-GBaud UD-16QAM DMT with the same net rate is transmitted in the same optical link for fair comparison. One can see that over 20-km SSMF transmission, there exists 0.97- and 0.24-dB power penalty for the UD-16QAM and the PS-16QAM at post-FEC BER of 1×10−4. Receiver power sensitivity (RPS) improvement of 2.22 dB can be obtained by PS implementation based on BWDM. It is worth noting that the BER performance by inverse bit-weight distribution matching processing (IDM) is obtained without any LDPC or PS codes, and it becomes gradually worse than the corresponding post-FEC BER performance only if the error-free state cannot be achieved any longer after bit correction by LDPC decoding. In this case, this can be ascribed to the wrong MSBs after LDPC decoding, which results in the error bits of entire subsets after IDM.
Fig. 5. BER performance with the launch fiber power of 4 dBm, (a) versus ROP with k = 4 and LDPC v = 3/4, (b) versus ROP with k = 4, 9, 39, and LDPC v = 3/4 over 20-km SSMF transmission, (c) versus ROP with LDPC v = 1/2, 3/4, 5/6, and k = 4, (d) versus launch fiber power with k = 4 with the ROP of -17 dBm. Insets (I)-(III): constellation diagrams for PS-16QAM (k = 4, 9, 39 and v = 3/4) over 20-km SSMF transmission with the ROP of -17 dBm.
By adjusting the values of PS parameter k to obtain various SPD, we investigate the BER performance of PS-16QAM DMT over 20km SSMF shown in Fig. 5(b). We can see that there is 2.22-, 1.59- and 0.75-dB RPS improvement for the three cases of k = 4, 9 and 39 compared with the 22.5-, 23.75-, and 24.6875-GBaud unshaped UD-16QAM DMT signals. Regardless of v, the average power of PS-16QAM DMT decrease sharply with the decline of k. Since higher-energy QAM DMT signal is more susceptible to optical fiber nonlinear effect, the diminishment of average power by PS with induced SPD arrangement is an efficient way to improve system performance, especially the tolerance to optical fiber nonlinear effect. The received constellation diagrams for the PS-16QAM in the cases of k = 4, 9 and 39 over 20-km SSMF transmission with the ROP of -17 dBm are shown as insets Fig. 5(I)-(III).
Figure 5(c) illustrates the BER performance of diverse LDPC code rates of v = 1/2, 3/4 and 5/6 with the fixed k value of 4. One can see that 1.52-, 2.24-, and 1.52-dB RPS improvement in the cases of v = 1/2, 3/4, and 5/6, at the post-FEC of 1×10−4. It might infer that the combination of k = 4 and v = 3/4 leads to a superior input SPD for the experimental AWGN channel. Figure 5(d) shows the pre-FEC BER performance versus launch fiber power over 20-km SSMF transmission with the fixed ROP of -17 dBm. By the comparison of the two curves, optimized system tolerance to optical fiber nonlinear effect can be obtained significantly. In contrast with the 22.5-GBaud UD-16QAM adopting the same mapping scheme, there exists 4.59-dB superior nonlinear effect tolerance for the 25-GBaud BWDM-based PS-16QAM with k = 4 at the BER of 3.37×10−2.
5. Discussion
5.1 Implementation complexity
The ADM and CCDM schemes based on arithmetic coding have to online and continuously refine probability intervals for target symbol probability emulation according to the desired distribution, which necessarily introduces multiple bits in the both fixed-to-variable and fixed-to-fixed mapping processes [12–13]. Taking the binary LDPC-based FEC into consideration, the labels indicating output probabilities from PS matcher need to be mapped into bits following the Gray rule for compatibility. As the key technology of the proposed BWDM, the BWI processing can be realized by simple bit-weight calculation, weight bit labelling and bit reconstruction. The mapping bits can also be directly and seamlessly compatible with the binary FEC encoding and optical/electrical modulation. Thus, the BWDM scheme is expected to be implemented with much less complexity in practical systems.
5.2 Symbol probability distribution
The intensively-studied PS schemes based on arithmetic coding are the shaping ways from bits (data source) to the target SPD. At the cost of time, power consumption and hardware complexity, the output SPD from input binary data with Bernoulli (1/2) distribution and the desired SPD are expected to be as similar as possible. The proposed PS scheme based on bit-class BWDM in this work is feasible to find the SPD approximating the target one. As stated in the former subsections, regardless of the LDPC code rate v, k as a key parameter in BWDM can directly determine the available SPD with infinite data source. Thus, for practical usage, a look-up table (LUT) can be established including k, ideal SPD and even PS overhead. In other words, the divergence entropy can be used to pick out the existing SPD and the corresponding k in the LUT closest to the target one.
For instance, if a desired SPD following GD is given as Fig. 6(a), a simple LUT containing five cases of k = 1, 4, 9, 19, and 39 is formed as Table 1. Figures 6(b)–(f) illustrate the SPD obtained by the five k values, respectively. Clearly, according to Fig. 6(d) and the corresponding information divergence (relative entropy) in the case of k = 9, PS-16QAM with k = 9 is closest to the desired GD as Fig. 6(a) among the five examples of k value.
Table 1. Look-up Table (based on pre-LDPC PS-16QAM SPDs with 5 k values)
6. Conclusion
A simple and practicable PS scheme based on BWDM is introduced into DMT-WDM-PON system for the first time. In contrast with the standard uniformly-distributed signal, considerable receiver power sensitivity improvement can be obtained for the PS-16QAM DMT signal in addition to the shaping gain. Owing to the decreasing average normalized signal power, the significantly-enhanced system tolerance to optical fiber nonlinear effect can be obtained to help with the power budget enlargement for ODN and resultantly more ONUs to be served. Thus, the PS scheme based on BWDM can be well implemented in the power-constraint WDM-PON for the more cost-efficient and competitive benefits.
Funding
Distinguished Young Scientific Research Talents Plan in Universities of Fujian Province (2016J06015); National Natural Science Foundation of China (61401166, 61302095); Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications) (IPOC2019A002); Quanzhou City Science & Technology Program of China (2018C108R, 2018C116R).
Disclosures
The authors declare no conflicts of interest.
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