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

Xing Xu; Bo Liu; Xiangyu Wu; Lijia Zhang; Yaya Mao; Jianxin Ren; Ying Zhang; Lei Jiang; Xiangjun Xin

doi:10.1364/OE.26.026576

1. Introduction

We are entering an era of information, when various high-end and booming network technologies, including virtual reality (VR), Internet of Things (IoT) and Distributed Data Center, are being employed to facilitate people’s daily communication, to enhance the interconnectivity worldwide, and to revolutionarily change the blueprint for life experience in the future. Meanwhile, in order to accommodate the exponential growth of traffic generated by these emerging network technologies and applications, it is imperative for us to upgrade the current network into a higher level, which features higher speed, longer haul and larger capacity. Specifically, with respect to access network, passive optical network (PON) has been proven to be an effective and future-proof network architecture with such unparalleled advantages as lower power consumption, higher data transmission rate and wider coverage for access compared to those of the traditional cable modems or xDSL [1–5]. There have been extensive researches on the modulation formats applied in the PON system. A 5 Gb/s DQPSK signal transmission per wavelength channel in the range of 50 km fiber, which allowed for a splitting ratio of up to 1:1024 with total capacity of 1.28 Tb/s, was demonstrated experimentally [6]. Also an UDWDM-PON architecture with 2.5 Gbaud 16-QAM data transmission over 50 km of SSMF without the need for inline amplification was presented [7]. Besides, a 40 Gbps data transmission at −19 dBm after 10 km SMF at a BER of $4.6 \times 10^{- 3}$ employing DMT technology was demonstrated [8]. All these modulation formats combined with multi-domain and multiplexing technology have significantly improved the spectral efficiency and data transmission rate in the system. However, the complexity in digital signal processing and challenges in system implementation have massively increased, which weakens the scalability and flexibility of PON system. Consequently, CAP (carrier-less amplitude and phase) modulation has been introduced as an alternative due to its low power consumption, easy implementation and low complexity in data processing. This technique, regarded as quite promising, has drawn widespread attention, and can be applied in the high-speed PON communication system. Specifically, a 10x70 Gb/s dynamic filter bank multi-band CAP-PON to fulfill dynamic wavelength scheduling with different split ratios and multi-granularity bandwidth allocation was realized [9]. And a 10 Gb/s 4-dimensional CAP data transmission over 25 km SSMF in PON system was successfully demonstrated [10]. In addition, 10 Gb/s symmetrical rate of bidirectional CAP signals is evidently transmitted over 20 km MCF [11]. It is notable that our proposed scheme employed CAP technology for data modulation format.

Recently, how to improve the data transmission rate and channel capacity, as known as approaching the Shannon limit, has become a hot topic widely pursued by plenty of researchers [12–18], wherein probabilistic shaping (PS) stands out as a potent and easy-to-implement technique. Compared with conventional signaling schemes, in which signal points are uniformly distributed in the constellation, probabilistic shaping adjusts the distribution of various constellation signal points by means of intentionally and dynamically reducing the transmitting probabilities of the outer constellation signal points with larger energy, while in turn increasing the chances of the inner signal points being transmitted. Such a method can reduce the average transmitted signal power and enlarge channel capacity to a large degree, which will produce an improved bit error rate (BER) performance. It’s worth mentioning that the ultimate theoretical gain of 1.53 dB can be expected in Gaussian channel in a Maxwell-Boltzmann distribution [19]. For practical application, probability shaping scheme for APSK constellation in BICM system is employed [20] and an enhanced scheme for Gray mapping in APSK constellation, which can be adjusted according to the signal-to-noise ratio is presented [21]. Also, a construction method for APSK constellation with uniform distribution was put forward [22]. However, current probabilistic shaping schemes, primarily aimed at signal shaping and mapping between regular constellations, such as 8-PSK, 16-QAM, 32-QAM, etc., and featuring relatively low space utilization and large spatial gap in the case of same Euclidean distance, can result in the deterioration of system performance, rising of transmitting optical power and lowering of transmission rate and channel capacity.

In this paper, we propose to our best knowledge a probabilistic shaping PON based on symbol-level labeling and rhombus-shaped modulation. In such an appropriate combination of the probability adjustment and rhombus-shaped constellation mapping of the signal points, the space utilization in this novel constellation can be increased and signal transmission power be reduced remarkably, thus improving the transmission rate and capacity of the system. Numerical analysis is also given to elaborate the proposed scheme from a mathematical perspective. Moreover, an experiment demonstrating 33.3 Gb/s 16-to-9 probabilistic-shaped mapping CAP transmission over 25 km standard single-mode fiber (SSMF) in PON system is successfully carried out to validate the performance.

2. Principle of probabilistic shaping scheme based on symbol-level labeling and rhombus-shaped modulation

Probabilistic shaping in principle is to alter the distribution pattern of signal points in certain constellation, by which the probabilities of those outer constellation signal points with large energy are declined to achieve a considerably favorable performance in terms of average signal power. In order to realize this result, marginal signal points have to be reassigned and mapped to those in the middle region of the constellation. However, this will pose a problem as to many-to-one mapping for certain signal points, which can lead to bit-wise redundancy for the original information. To minimize the side effects of this extra overhead, a probabilistic shaping scheme based on symbol-level labeling for 16 signal points to 9 signal points constellation mapping is proposed in this paper, which takes full account of the distribution pattern of constellation signal points and coding advantages of the information format, as well as the intensity and probability of newly generated signal points. Moreover, the proposed probabilistic shaping scheme can be flexible and reversible, and thus allowing the decoding procedure in the receiver much more efficient.

Suppose the distribution mapping for probabilistic shaping as an array of $M_{0} \times L_{0}$ , where $M_{0}$ is the number of signal points after probabilistic shaping, and $L_{0}$ denotes the maximum overlapping of every signal point, which will be filled with the proposed symbol-level labels. Then the symbol-level labels will be concatenated to the pre-defined and well-designed modulated symbol to form the newly-generated signal points, which will be the composed element of the array of $M_{0} \times L_{0}$ . The information, carried in the format of bits composed of “0” or “1”, when grouped and modulated in the form of m bits input and n bits output ( $n > m$ ), will accordingly bring about $2^{m}$ and $2^{n}$ signal points in the constellation. Whereas, for the purpose of reversible mapping, only some of the $2^{n}$ signal points will be employed for mapping of the original $2^{m}$ signal points. Therefore, symbol-level labelling is added to determine and distinguish the overlapping of the original signal points, which makes the decoding in the receiver accurate and efficient at the same time. In the case where $\log_{2} M_{0}$ is not an integral ( $2^{n} > M_{0}$ ), which means that the bit information is not complete enough to describe $M_{0}$ . In this occasion, the traditional $2^{⌈ \log_{2} L_{0} ⌉}$ is not applicable for labelling. Instead, the encoded bit information of $M_{0}$ needs to be considered for the mapping scheme. To expatiate this principle, this paper elaborates on the mapping scheme of 16-to-9 signal points employing symbol-level labeling probabilistic shaping.

As illustrated in Fig. 1, input signal points are firstly identified to recognize the coding format before being analyzed to compute the probability distribution. Then a notification mechanism is used to transfer this probability information to the symbol-level label generator, which will determine the optimal label aimed to distinguish the signal points in preparation for probabilistic shaping. Following the above procedure, the signal points are filled with the predefined label in the probability distribution mapper to determine the final output signal points. Figure. 2 illustrates 16-to-9 signal points mapping employing the proposed symbol-level labeling based probabilistic shaping. Considering the number of output signal points, which is 9, a 4-bits information is required for signal shaping. In addition, to distinguish the original 16 signal points, part of the output 9 signal points are chosen to provide the overlapping functionality due to the fact that $⌈ 16 / 9 ⌉ = 2$ . Therefore, to bring the 4-bits information into full play, 2-bits symbol-level label is employed to make a unique distinction of the original 16 signal points. Particularly, the “11” label is not chosen because its code weight is 2, which is larger than that of “00”, “01” and “10”. Besides, the code weight can be an index of the inner ring in the constellation. The reason that 1 parity bit is not added for probabilistic shaping is the inconveniency in decoding and difficulty in the constellation shaping. In summary, the output signal points can be generated through concatenation between the 4-bits information and the 2-bits labels, and then be mapped into the constellation with different probabilities. To be specific, for the code weight of 0, $C_{4}^{0}$ is given to correspond to the symbol of “0000”; for the code weight of 1, is given to reflect on the symbols of “1000”, “0100”, “0010” and “0001”. Finally, for the code weight of 2, the symbol of “1010”, “0101”, “1001”, and “0110” are employed to convey signal points information, which are a subset of $C_{4}^{2}$ options. Apart from that, the signal points labelled by the symbol of “00” are much more likely to be shaped, and then are mapped to the inner space in the constellation with lower energy.

Fig. 1 Principle of symbol-level labeling based probabilistic shaping.

Download Full Size | PDF

Fig. 2 Schematic of probabilistic shaping employing symbol-level labeling for 16-to-9 signal points mapping.

Download Full Size | PDF

Furthermore, in a mathematical viewpoint, the chances are the same for “0” or “1” information to be generated before probabilistic shaping, which can be shown as follows:

{\begin{cases} P (0) = 0.5 \\ P (1) = 0.5 \end{cases}

Hence, the probabilities of the original 16 signal points carrying 4 bits are uniformly distributed as illustrated in Table 1.

Table 1. Probability distribution of the original 16 signal points.

View Table | View all tables in this article

The distribution pattern of the proposed probabilistic shaping can be expressed as follows:

\begin{array}{l} P (x_{i + j}) = \sum_{i, j \in {00, 01, 10}} {γ_{i + j} \times P (l e n g t h (x_{i + j})) + γ_{i j} \times P (i) \times P (j)} \\ i, j \in {00, 01, 10} i + j \in {0000, 0001, 0010, 0100, 1000, 0101, 1010, 0110, 1001} \end{array}

where $x_{i + j}$ represents the newly-generated signal points after probabilistic shaping, which can be mapped to the constellation. And $l e n g t h (x_{i + j})$ indicates the pre-defined and well-designed modulated symbol without the extra information of the symbol-level labels, $P (l e n g t h (x_{i + j}))$ is the corresponding probability. $P (i), P (j)$ is the probability of the generated symbol-level labels. $γ_{i + j}$ and $γ_{i j}$ are the weighting coefficients related to the proportion of the label information to the shaped signal points in the constellation and the grouping of the symbol-level label, which meets the criterion of $γ_{i + j} + γ_{i j} = 1$ . In our 16-to-9 CAP probabilistic shaping scheme, as can be seen in Fig. 2, the input 4-bits 16-CAP is mapped to the output 6-bits 9-CAP. The 6-bits information is composed of the 4-bits pre-defined modulated symbol and the 2-bits symbol-level label. By means of grouping and mapping of two 2-bits well-designed labels into a 4-bits signal points, along with the mapping of 4-bits pre-defined modulated symbol, we can implement the probability distribution of the newly-generated 9-CAP signal points. Wherein $P (i) \times P (j)$ indicates the probability of the signal points generated by the grouping of two 2-bits labels. Thereby the probability of newly-generated 9 signal points are distributed as shown in Table 2.

Table 2. Distribution of newly generated 9 signal points after probabilistic shaping.

View Table | View all tables in this article

It can be seen that after the functioning of the proposed probabilistic shaping, the uniform distribution of the original 16 signal points has been transferred fundamentally to a new distribution of 9 signal points, during which the chances of those signal points of high energy being generated have been reduced significantly. This will bring out the outstanding performance in terms of average signal power in the transmitter.

Right now the most widely adopted constellation modulation schemes are MQAM, MASK and MPSK, among which MQAM has a relatively appropriate distribution in two-dimensional constellation. Yet MQAM still lacks flexibility and is unable to fully utilize the inner space of the constellation. This paper hence proposes a novel rhombus-shaped constellation modulation based on the geometrical principle that if the minimum Euclidean distance is fixed, regular hexagon is the optimal pattern, where the signal points are evenly located. Figure. 3 illustrates the proposed rhombus-shaped constellation modulation.

Fig. 3 Principle of rhombus-shaped constellation modulation.

Download Full Size | PDF

According to Fig. 3, the transformation from the tradition square-shaped constellation to the rhombus-shaped constellation can be formulated as follows:

(X_{n}, Y_{n}) = (X_{0}, Y_{0}) (\begin{array}{l} 1 \\ \sin α \end{array} \begin{array}{l} 0 \\ \cos α \end{array}), \sin α = - \frac{1}{2}, \cos α = \frac{\sqrt{3}}{2}

Where $(X_{n}, Y_{n})$ and $(X_{0}, Y_{0})$ stand for the signal points coordinates in the rhombus-shaped constellation and square-shaped constellation respectively, and $α$ denotes the rotating angle in the transformation, which will be used in the following analysis in terms of CFM (figure of merit) of the constellation [23,24].

C F M (C) = C F M_{0} \times γ_{c} (Λ) \times γ_{s} (R)

Where $C F M (C)$ is the overall gain of the constellation and $C F M_{0}$ represents the primitive gain related to the dimensions of the constellation. $γ_{c}$ and $γ_{s}$ are the coding and shaping gain of constellation respectively.

γ_{c} = d_{m i n}^{2} (Λ) / V {(Λ)}^{\frac{2}{n}}

Where $γ_{c}$ denotes the coding gain of the constellation and $d_{\min}$ denotes the minimum Euclidean distance. $V (Λ)$ is the reciprocal of the number of signal points per unit area in the constellation [23,24]. In other words, $V (Λ)$ can be expressed as the average area occupied by the signal points in the constellation per unit area. In our paper, we choose square for square-shaped 9-CAP and regular hexagon for rhombus-shaped 9-CAP for computation. Because the decision regions of the signal points in the center is smaller than those of the signal points in the border, we need to take the weighted average of the signal points into consideration. Therefore, the average area occupied by the signal points in the square-shaped constellation is 1, while the average area in the rhombus-shaped constellation can be computed as ${(1 / 2)}^{3} \times (\sqrt{3} / 2) \times 6 = 3 \sqrt{3} / 8$ . And $n$ represents the dimensions of the constellation. (in our proposed scheme, $n = 2$ ) As $\cos α$ is introduced in the constellation transformation and the minimum Euclidean distance is fixed, the below formula can be deduced:

\begin{array}{l} γ_{c_n e w} / γ_{c_o l d} = \frac{d_{\min}^{2} (Λ_{n e w}) / V (Λ_{n e w})}{d_{\min}^{2} (Λ_{o l d}) / V (Λ_{o l d})} = \frac{V (Λ_{o l d})}{V (Λ_{n e w})} \approx 1.5 \\ γ_{s} = \frac{V {(R)}^{\frac{2}{n}}}{6 E_{a v g}} \end{array}

Where $γ_{s}$ represents the shaping gain of the constellation, $R$ denotes the border diameter of the constellation, $V (R)$ is the area covered by the signal points and $E_{a v g}$ is the average energy of the signal points. Similarly, the formula below can be deduced:

\begin{array}{l} E_{n e w_a v g} = \frac{1}{9} (0 + 6 \times {(\frac{\sqrt{3}}{2})}^{2} + 4 \times {(\frac{1}{2})}^{2} + 2 \times 1 + 2 \times {(\frac{3}{2})}^{2}) d_{\min}^{2} = \frac{4}{3} d_{\min}^{2} \\ E_{o l d_a v g} = \frac{1}{9} (0 + 6 \times 1 + 6 \times 1) d_{\min}^{2} = \frac{4}{3} d_{\min}^{2} \\ γ_{s_n e w} / γ_{s_o l d} = \frac{V {(R_{n e w})}^{\frac{2}{n}} / 6 E_{n e w_a v g}}{V {(R_{o l d})}^{\frac{2}{n}} / 6 E_{o l d_a v g}} = \frac{{(V (R_{o l d}) \times \cos α)}^{\frac{2}{n}} / 6 \times \frac{4}{3} d_{\min}^{2}}{V {(R_{o l d})}^{\frac{2}{n}} / 6 \times \frac{4}{3} d_{\min}^{2}} = \frac{\sqrt{3}}{2} \end{array}

Hence we can deduce the comparison of overall gain between the square-shaped constellation and rhombus-shaped constellation as follow:

C F M (C_{n e w}) / C F M (C_{o l d}) = (γ_{c_n e w} / γ_{c_o l d}) \times (γ_{s_n e w} / γ_{s_o l d}) \approx 1.35 \approx 1.3 d B > 1

In conclusion, the proposed rhombus-shaped constellation modulation has a favorable performance with respect to overall gain of the constellation, which can produce the improvement of bit error rate (BER), thus enhancing the robustness of the transmission system.

The advantages of symbol-level labeling based probabilistic shaping and rhombus-shaped constellation modulation are so immense that it is natural for us to consider the option of integrating these two methods together in the transmitting side. Figure. 4 illustrates the proposed architecture and probability distribution, as well as those of the conventional ones. Such an approach can sharply reduce the transmitting signal power, in order to improve the energy efficiency and bit error ratio (BER), thus supporting the expansion of channel capacity.

Fig. 4 The proposed and the conventional constellations and their probability distributions.

Download Full Size | PDF

As can be seen in the Fig. 4 (c), signal points of “0100” and “0001”, “0010” and “1000”, “0101” and “0110”, as well as “1010” and “1001” are selected to be centrally symmetrical respectively so as to realize the symmetry of probability distribution in general.

To evaluate the performance, the average energy is taken into consideration in the formula as

E_{a v g} = \sum_{i} p_{i} \times E_{i}

Where $i$ denotes the signal points and $E_{i}$ is the corresponding energy. The detailed calculation is shown as follows:

\begin{array}{l} E_{16} = \sum_{i} p_{i} \times E_{i} \\ = \frac{1}{16} {4 \times [{(\frac{1}{2})}^{2} + {(\frac{1}{2})}^{2}] + 8 \times [{(\frac{1}{2})}^{2} + {(\frac{3}{2})}^{2}] + 4 \times [{(\frac{3}{2})}^{2} + {(\frac{3}{2})}^{2}]} d_{\min}^{2} = 2.5 d_{\min}^{2} \\ E_{9} = \sum_{i} p_{i} \times E_{i} \\ = \frac{1}{9} {0 + 6 \times 1 + 2 \times [{(\frac{3}{2})}^{2} + {(\frac{\sqrt{3}}{2})}^{2}]} d_{\min}^{2} = \frac{4}{3} d_{\min}^{2} > d_{\min}^{2} \\ E_{p s 9} = \sum_{i} p_{i} \times E_{i} \\ = {0 + (\frac{20}{512} + \frac{26}{512}) [{(\frac{3}{2})}^{2} + {(\frac{\sqrt{3}}{2})}^{2}] + [1 - (\frac{20}{512} + \frac{26}{512}) - \frac{129}{512}]} d_{\min}^{2} = \frac{475}{512} d_{\min}^{2} < d_{\min}^{2} \end{array}

Where $E_{16}$ is the average energy of the conventional 16 uniformly-distributed signal points, $E_{9}$ denotes the average energy of the conventional 9 uniformly-distributed signal points, and $E_{p s 9}$ is the average energy of the proposed 9 signal points employing probabilistic shaping based on symbol-level labeling and rhombus-shaped constellation modulation. By comparison, we can see that there has been a significant decrease in average energy, which greatly improves the system performance.

3. Experiment and results

An experiment is carried out to evaluate the performance of the proposed scheme by employing the system setup illustrated in Fig. 5, where IM/DD is adopted for demonstration [25]. In the transmitting side, CAP modulation is implemented offline in the DSP module integrated with the proposed probabilistic shaping scheme. To be specific, firstly the raw input bit stream with length of $2^{15} - 1$ goes through the S/P (serial-to-parallel) conversion. And then the generated 4-parallelled bit data undergoes the procedure of the proposed symbol-level labeling and rhombus-shaped mapping to form the corresponding symbol signals, which are used for up-sampling. Afterwards, the real and imaginary part of the signals are split for according shaping filtering before wave forming by AWG (AWG70002A) with 25 Gs/s sampling rate. After the application of electrical amplifier (EA), the generated waveform is loaded on the Mach-Zehnder modulator (MZM) to fulfil the intensity modulation of the continuous wave laser operated at 1550 nm with power of 10 dBm. Finally, the generated optical signal carrying the data is amplified by an erbium-doped fiber amplifier (EDFA) and injected into a 25 km standard single-mode fiber (SSMF) for transmission. In our experiment, the roll-off coefficient of the shaping filters is set as 0.2 and the number of sampling per symbol is 3. Besides, data transmission rate is set as 33.3 Gb/s.

Fig. 5 Experimental Setup (AWG: arbitrary waveform generator; EA: electrical amplifier, EDFA: erbium-doped optical fiber amplifier; OF: optical fiber; VOA: variable optical attenuator; PD: photodiode; MSO: mixed signal oscilloscope).

Download Full Size | PDF

In the receiving side, ASE noise is suppressed by a 25 GHz optical filter and a variable optical attenuator (VOA) is employed to adjust the received optical power before the detection of a 40 GHz photodiode (PD).

A mixed signal oscilloscope (MSO73304DX) with sampling rate of 100 Gs/s is put in place to resample the received signal, which are subsequently split into the real and imaginary parts. Matched filtering and down-sampling are employed accordingly. Then after the procedure of rhombus-shaped demapping and symbol-level label removing, the signal is converted to the serial bits data for further performance analysis.

Figure. 6 depicts the measured BER as the received optical power changes for back-to-back (b2b) and after 25 km transmission of the proposed probabilistic shaping 16-to-9 CAP signal. We can learn that the required optical power is −18 dBm in back-to-back transmission at the threshold of $1 \times 10^{- 3}$ BER, while the power penalty is within the range of 0.3 dB after 25 km transmission. In short, the system performance has been consistent after 25 km optical line transmission.

Fig. 6 The measured BER curves of probabilistic shaping 16-to-9 CAP before and after 25 km transmission (b2b: back-to-back).

Download Full Size | PDF

Also, the performance of the probabilistic shaping 16-to-9 CAP signal after 25 km transmission is illustrated in Fig. 7 in the cases of different data rates. Specifically, the data rate of 4.2 Gb/s, 8.3 Gb/s, 16.7 Gb/s and 33.3 Gb/s can be obtained by means of adjusting the related parameters in AWG. It can be observed that the BER performance deteriorates as the data rate gradually increases. The extra power penalty of 1 dB is needed to achieve the $1 \times 10^{- 3}$ BER performance in 33.3 Gb/s transmission when compared with 16.7 Gb/s transmission.

Fig. 7 The measured BER curves of probabilistic shaping 16-to-9 CAP under different data rates after 25 km transmission.

Download Full Size | PDF

Moreover, to show the superiority of the proposed probabilistic shaping scheme, we make a comprehensive comparison between the conventional 16-CAP, the square-shaped probabilistic shaping 16-to-9 CAP, the conventional star-shaped 8-CAP, and finally the proposed rhombus-shaped probabilistic shaping 16-to-9 CAP, which is illustrated in Fig. 8. As can be observed, the proposed rhombus-shaped probabilistic shaping 16-to-9 CAP largely outperforms the conventional 16-CAP by 2 dB at the threshold of $1 \times 10^{- 3}$ BER, which has an outstanding advantage in energy efficiency. Compared with square-shaped probabilistic shaping 16-to-9 CAP, the proposed rhombus-shaped probabilistic shaping 16-to-9 CAP has a slightly favorable performance of decreasing the optical power by 0.4 dB at the threshold of $1 \times 10^{- 3}$ BER, which can be attributed to the overall gain obtained by the rhombus-shaped constellation modulation. The result coincides with the theoretical analysis mentioned above. In addition, we can see that the BER performance of the proposed scheme approaches that of the conventional star-shaped 8-CAP, while having a much larger information capacity.

Fig. 8 The measured BER curve of different modulation schemes after 25 km transmission and corresponding constellations.

Download Full Size | PDF

4. Conclusion

We have proposed a robust probabilistic shaping PON based on symbol-level labeling and rhombus-shaped modulation, which can remarkably improve the system performance in terms of transmission signal power and bit error rate compared with traditional signaling scheme. Numerical analysis also indicates that the proposed scheme has an incomparable superiority by means of adjusting the probability distribution pattern of the transmitted signal and increasing the overall gain of the new constellation modulation. An experiment demonstrating a 33.3 Gb/s rhombus-shaped probabilistic shaping 16-to-9 CAP data transmission over 25 km SSMF is successfully conducted, in which the 2 dB improvement of the optical power can be obtained compared with the traditional 16-CAP signaling scheme. The experiment results suggest that our proposed scheme can have a promising and future-proof application in next generation PON system.

Funding

National Natural Science Foundation of China (NSFC) (61522501, 61475024, 61675004, 61705107, 61727817, 61775098, and 61720106015); Program 863 (2015AA015501 and 2015AA015502); Beijing Young Talent (2016000026833ZK15); Fund of State Key Laboratory of IPOC (BUPT).

References

1. K. Ohara, A. Tagami, H. Tanaka, M. Suzuki, T. Miyaoka, T. Kodate, T. Aoki, K. Tanaka, H. Uchinao, S. Aruga, H. Ohnishi, H. Akita, Y. Taniguchi, and K. Arai, “Traffic analysis of Ethernet-PON in FTTH trial service,” in 2003 Optical Fiber Communications Conference, (2003), 607–608 vol.602.

2. F. J. Effenberger, “Next generation PON: lessons learned from G-PON and GE-PON,” in 2009 35th European Conference on Optical Communication, (2009), 1–3.

3. Y. Luo, X. Zhou, F. Effenberger, X. Yan, G. Peng, Y. Qian, and Y. Ma, “Time- and Wavelength-Division Multiplexed Passive Optical Network (TWDM-PON) for Next-Generation PON Stage 2 (NG-PON2),” J. Lightwave Technol. 31(4), 587–593 (2013). [CrossRef]

4. A. M. Mikaeil, W. Hu, T. Ye, and S. B. Hussain, “Performance evaluation of XG-PON based mobile front-haul transport in cloud-RAN architecture,” J. Opt. Commun. Netw. 9(11), 984–994 (2017). [CrossRef]

5. C. Zhang, H. Li, N. Song, and H. Li, “High-stability algorithm in white-light phase-shifting interferometry for disturbance suppression,” IEEE Photonics J. 10(5), 6900718 (2018).

6. I. N. Cano, A. Lerín, V. Polo, and J. Prat, “Flexible D(Q)PSK 1.25–5 Gb/s UDWDM-PON with directly modulated DFBs and centralized polarization scrambling,” in 2015 European Conference on Optical Communication (ECOC), (2015), 1–3.

7. P. M. Anandarajah, H. Tam, V. Vujicic, Z. Rui, and L. P. Barry, “UDWDM PON with 6 × 2.5Gbaud 16-QAM multicarrier transmitter and phase noise tolerant direct detection,” in 2015 Optical Fiber Communications Conference and Exhibition (OFC), (2015), 1–3.

8. C. Qin, V. Houtsma, D. V. Veen, J. Lee, H. Chow, and P. Vetter, “40 Gbps PON with 23 dB power budget using 10 Gbps optics and DMT,” in 2017 Optical Fiber Communications Conference and Exhibition (OFC), (2017), 1–3.

9. L. Zhang, B. Liu, X. Xin, and Y. Wang, “10 × 70.4-Gb/s dynamic FBMB/CAP PON based on remote energy supply,” Opt. Express 22(22), 26985–26990 (2014). [CrossRef] [PubMed]

10. J. He, L. Shi, L. Deng, M. Cheng, M. Tang, S. Fu, M. Zhang, P. P. Shum, and D. Liu, “Novel design of N-dimensional CAP filters for 10 Gb/s CAP-PON system,” Opt. Lett. 40(10), 2409–2412 (2015). [CrossRef] [PubMed]

11. J. He, L. Deng, B. Li, M. Tang, S. Fu, D. Liu, and P. P. Shum, “Experimental demonstration of MCF enabled bidirectional colorless CAP-PON system with wavelength reuse technique,” in 2017 Opto-Electronics and Communications Conference (OECC) and Photonics Global Conference (PGC), (2017), 1–3.

12. Y. Nishino, M. Tanahashi, and H. Ochiai, “A new bit-labeling for trellis-shaped PSK with improved PAPR reduction capability,” in 2010 International Symposium On Information Theory & Its Applications, (2010), 747–751. [CrossRef]

13. R. Dischler, “Experimental comparison of 32-and 64-QAM constellation shapes on a coherent PDM burst mode capable system,” in 2011 37th European Conference and Exhibition on Optical Communication, 2011), 1–3.

14. C. Pan and F. R. Kschischang, “Probabilistic 16-QAM Shaping in WDM Systems,” J. Lightwave Technol. 34(18), 4285–4292 (2016). [CrossRef]

15. M. P. Yankovn, F. Da Ros, E. P. da Silva, S. Forchhammer, K. J. Larsen, L. K. Oxenlowe, M. Galili, and D. Zibar, “Constellation Shaping for WDM Systems Using 256QAM/1024QAM With Probabilistic Optimization,” J. Lightwave Technol. 34(22), 5146–5156 (2016). [CrossRef]

16. L. Fay, L. Michael, D. Gomez-Barquero, N. Ammar, and M. W. Caldwell, “An Overview of the ATSC 3.0 Physical Layer Specification,” IEEE Trans. Broadcast 62(1), 159–171 (2016). [CrossRef]

17. T. Fehenberger, A. Alvarado, G. Böcherer, and N. Hanik, “On Probabilistic Shaping of Quadrature Amplitude Modulation for the Nonlinear Fiber Channel,” J. Lightwave Technol. 34(21), 5063–5073 (2016). [CrossRef]

18. L. Bertignono, D. Pilori, A. Nespola, F. Forghieri, and G. Bosco, “Experimental comparison of PM-16QAM and PM-32QAM with probabilistically shaped PM-64QAM,” in 2017 Optical Fiber Communications Conference and Exhibition (OFC), (2017), 1–3.

19. F. R. Kschischang and S. Pasupathy, “Optimal nonuniform signaling for Gaussian channels,” IEEE Trans. Inf. Theory 39(3), 913–929 (1993). [CrossRef]

20. F. Yang, K. Yan, Q. Xie, and J. Song, “Non-Equiprobable APSK Constellation Labeling Design for BICM Systems,” IEEE Commun. Lett. 17(6), 1276–1279 (2013). [CrossRef]

21. D. He, Y. Shi, Y. Guan, Y. Xu, Y. Wang, W. Zhang, and H. Yin, “Improvements to APSK constellation with gray mapping,” in 2014 IEEE International Symposium on Broadband Multimedia Systems and Broadcasting, (2014), 1–4.

22. H. Méric, “Approaching the Gaussian Channel Capacity With APSK Constellations,” IEEE Commun. Lett. 19(7), 1125–1128 (2015). [CrossRef]

23. G. D. Forney and L. Wei, “Multidimensional constellations. I. Introduction, figures of merit, and generalized cross constellations,” IEEE J. Sel. Areas Comm. 7(6), 877–892 (1989). [CrossRef]

24. G. D. Forney, “Multidimensional constellations. II. Voronoi constellations,” IEEE J. Sel. Areas Comm. 7(6), 941–958 (1989). [CrossRef]

25. T. Liu, C. Lin, and I. B. Djordjevic, “Advanced GF(3₂) nonbinary LDPC coded modulation with non-uniform 9-QAM outperforming star 8-QAM,” Opt. Express 24(13), 13866–13874 (2016). [CrossRef] [PubMed]

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

Abstract

1. Introduction

2. Principle of probabilistic shaping scheme based on symbol-level labeling and rhombus-shaped modulation

3. Experiment and results

4. Conclusion

Funding

References

Cited By

Figures (8)

Tables (2)

Equations (10)

Optics Express