Abstract

We experimentally and numerically investigated the characteristics of 128 Gb/s dual polarization - quadrature phase shift keying signals received with two types of nonlinear equalizers (NLEs) followed by soft-decision (SD) low-density parity-check (LDPC) forward error correction (FEC). Successful co-operation among SD-FEC and NLEs over various nonlinear transmissions were demonstrated by optimization of parameters for NLEs.

© 2013 Optical Society of America

1. Introduction

The quest for improving the transmission system for fiber communication has encouraged the integration of all transmission techniques: optical modulation formats, digital signal processing (DSP) for channel equalizing, and forward error correction (FEC). Various types of integration have been proposed and investigated, e.g., coded 4-dimensional modulation [13] and a combination of nonlinear equalizers (NLEs) and FEC [4]. Nonlinear equalizer followed by soft-decision (SD) FEC is a straightforward combination since NLEs might be able to contribute to not only the Q-improvement before FEC but also making the noise distribution of the received constellation more Gaussian [5]. However, the characteristics of the system in the nonlinear transmission regime have not been directly mined through an experimental investigation of NLEs followed by SD-FEC to the best of our knowledge. From the first results we previously presented [6], we experimentally demonstrated the characteristics of 128-Gb/s dual polarization (DP) non-return-to-zero (NRZ) quadrature phase shift keying (QPSK) signals received by a digital coherent receiver assisted with SD-FEC and two types of NLEs, back propagation (BP) nonlinear compensator (NLC) [8] and nonlinear polarization crosstalk canceller (NPCC) [9], assuming a nonlinear transmission link consisting of standard single mode fiber (SMF) with 95% dispersion compensation. A low-density parity-check (LDPC) code for the standard of digital video broadcasting - satellite - second generation (DVB-S.2) with an overhead of 12.5% was used a SD-FEC [7]. We demonstrated successful co-operation among SD-FEC and NLEs without a negative impact on either by applying adequate parameters for NLEs.

In this study, we further extend this result and numerically investigate the characteristics of SD-FEC in various types of nonlinear transmission links: (1) standard SMF with 0, 50, and 95% in-line dispersion compensation and (2) non-zero dispersion shifted fiber (NZ-DSF) without in-line dispersion compensation. We present the relationship of the bit error rates (BERs) before and after LDPC SD-FEC decoding under various nonlinear transmissions and discuss a possible change in the relationship due to wrong usage of NLEs. The simulation results suggest the co-operation among SD-FEC and NLEs is also possible under the above practical system conditions.

2. Coding and framing

The coding and framing for this paper is shown in Fig. 1. A standard 112-Gb/s optical-channel transport unit frame including ~7% hard-decision FEC and ~5% protocol overhead are assumed for achieving an effective data rate of 100 Gb/s. Reed Solomon hard-decision outer FEC sets a BER threshold in the range of 3.8 × 10−3 and can be used for guaranteeing low residual BERs required in optical communications. Furthermore, a ~2% header and inner LDPC code with an overhead of 12.5% is implemented. The utilized inner FEC is based on the DVB-S.2 LDPC code with lengths of 64,800 bits including check bits. The resulting total bit rate including all the overheads and FEC is 128 Gb/s. To combat phase slipping, differential QPSK modulation is used. At the receiver, a simplified soft differential log-likelihood decoder [10] computes a posteriori probabilities of the code bits. The LDPC decoder performs 50 iterations.

 figure: Fig. 1

Fig. 1 Coding and framing for experiment and simulation.

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3. Nonlinear equalizer DSPs

Nonlinear distortion generated by propagation through optical fibers can be a major obstacle for fiber optic transmission. In this section, two types of NLEs are recalled to use in DSP operations implemented at the receiver side: (1) back-propagation nonlinear compensator (BP-NLC) and (2) nonlinear polarization crosstalk canceler (NPCC) for the mitigation of intra- and inter-channel nonlinear effects.

Figure 2(a) shows a schematic diagram of the BP-NLC. The incoming digital data streams correspond to the complex electromagnetic fields of the received optical signal obtained from the digital coherent receiver front-end. The BP-NLC consists of multiple segments of a chromatic dispersion compensator (CDC) and nonlinear phase shifter pair. Each nonlinear phase shifter is responsible for compensation of the the nonlinear phase shift imposed at a certain section of fiber along the transmission line, and each CDC is responsible for CD compensation. Such a multi-stage structure is important for taking into account the evolution of signal intensities due to CD. The detailed structure of a nonlinear phase shifter is shown in Fig. 2(a). The input complex digital data streams Ex and Ey correspond to the orthogonal polarization components of the signal. The nonlinear phase shifter introduces nonlinear phase shift onto each digital stream according to the following formulae:

Exout=Exinexp(j(α|Exin|2+β|Eyin|2)),Eyout=Eyinexp(j(α|Eyin|2+β|Exin|2)).
The BP-NLC parameters α and β introduce a nonlinear phase shift proportional to the optical powers in the same and orthogonal polarizations, respectively.

 figure: Fig. 2

Fig. 2 Nonlinear equalizers (NLEs), (a) back propagation nonlinear compensator (BP-NLC) for self-phase modulation (SPM) compensation, (b) nonlinear polarization crosstalk canceler (NPCC) to mitigate polarization crosstalk between x-and y-polarization.

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The second NLE to mitigate nonlinear polarization crosstalk between x- and y-polarization channels, NPCC, is placed after a DSP of carrier-phase recovery. With the assumption that all linear distortions, together with carrier phase noise, have been compensated, nonlinear polarization crosstalk is modeled as one 2-by-2 matrix, as shown in Eq. (2):

(RxRy)=(1|Wyx|2WxyWyx1|Wxy|2)(SxSy),
where Sx, Sy and Rx, Rv are the transmitted and received symbols for two polarizations, respectively, and Wxy and Wyx are the crosstalk factors between two polarizations. With Eq. (2), nonlinear polarization crosstalk could be measured during the experiments with the knowledge of transmitted and received symbols after digital carrier phase recovery. The polarization crosstalk changes on the order of GHz [9], and this polarization change is too fast for the tracking speed of polarization demultiplexing typically less than sub MHz; on the other hand, such change is still slower than the symbol rate. Therefore, DSP-based nonlinear polarization crosstalk cancellation is feasible. Figure 2(b) shows a block diagram of the NPCC. Because |Wxy|21and |Wyx|21, both 1|Wxy|2 and 1|Wyx|2 are assumed to be 1 for simplicity. The crosstalk factors Wxy and Wyx are then calculated as
Wxy(n)=k=N/2N/2Rx(n+k)Sx(n+k)Sy(n+k),Wyx(n)=k=N/2N/2Ry(n+k)Sy(n+k)Sx(n+k)
with Sx and Sy directly determined from Rx and Ry. N is an averaging parameter for removing amplitude spontaneous emission (ASE) noise. The estimated Wxy and Wyx are multiplied with the received signals from both polarizations to obtain the crosstalk at each symbol. Finally, the nonlinear polarization crosstalk is cancelled by simply subtracting the estimated crosstalk as
Exout=ExinEyinWxy,Eyout=EyinExinWyx.
Note that parameter N impacts NPCC performance through trade-off between noise reduction and following capability of time-changing of polarization crosstalk.

4. System model for experimental and simulation analysis

The system under consideration is shown in Fig. 3. At the transmitter, an external cavity laser with a line-width of ~100 kHz was used as a light source for the channel under study. For the surrounding 79 wavelength-division multiplexed (WDM) channels, distributed feedback lasers with line-widths of <10 MHz were used in the experiment. A total of 80 WDM channels were generated including the probe channel. In the simulation, the number of surrounding channels was 10. The WDM channels were located on the 50-GHz ITU-T grid. The center frequency of the probe channel was 193.4 THz. Even and odd channels were separately modulated with NRZ-QPSK at 64 Gb/s by using two IQ modulators. Polarization division multiplexing was emulated by splitting the signal, delaying one of the outputs, and recombining the signal with a polarization beam combiner. An LDPC code with a rate of 8/9 was implemented as inner FEC. The transmitter-side DSP including the LDPC FEC encoder, differential encoder, and digital pre-distortion to compensate for the non-ideal analogue transfer characteristic was carried out offline and then uploaded into the memory of a two-channel digital analogue converters with a sampling rate of 32 GS/s to generate the drive signals. After modulation, the even and odd channels were combined using a wavelength selective switch (WSS).

 figure: Fig. 3

Fig. 3 System setup. LD: laser diode, AWG: arrayed waveguide grating, PPG: pulse pattern generator, DAC: digital analogue converter, Pol. Mux: polarization multiplexing emulator, WSS: wavelength selective switch, VOA: variable optical attenuator, OBPF: optical band pass filter, LSPS: loop-synchronous polarization scrambler, SW: optical switch, DCM: dispersion compensation module, ASE: amplified spontaneous emission, LO: local oscillator, DSO: digital storage oscilloscope, BP-NLC: back propagation nonlinear compensator, AEQ: adaptive equalizer, FOC: frequency offset compensator, CPR: carrier phase recovery, NPCC: nonlinear polarization crosstalk canceller, and LLR: log-likelihood ratio detector.

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In the experiment, the transmission recirculating loop consisted of five spans of 60-km SSMF, and all signals traveled twice around the loop. In each node, a loop-synchronous polarization scrambler (LSPS) and a WSS for power equalization were installed. Amplification was provided using erbium-doped fiber amplifiers with a dispersion compensation module (DCM) in-between for 95% partial dispersion compensation. After transmission with a signal power of 4 dBm/channel and loading additional ASE noise, the signal was inputted to a receiver. In the simulation, several transmission lines were tested: (1) standard SMF with 0, 50, and 95-% in-line dispersion compensation, (2) NZ-DSF without in-line dispersion compensation. The fiber parameters in the simulation are described in the caption of Fig. 6.

At the receiving end, the signal went through an optical demultiplexing filter and combined with the local oscillator light in a polarization and 90° phase diversity hybrid, followed by four balanced photo detectors. The four signal components—XI, XQ, YI, and YQ—were digitized by a four-channel 80-GS/s digital storage oscilloscope, resulting in 2M complex signal samples per polarization. After re-sampling at 2.5 to 2 times the symbol rate, the BP-NLC was applied. The number of activated BP-NLC stages was set to be the same as the number of spans (i.e., 10). After polarization de-multiplexing by a 4 × 11 taps butterfly-structured FIR, frequency offset compensation and Viterbi-Viterbi carrier recovery, the NPCC was used. After LDPC SD-FEC decoding, BERs were measured.

5. Results and discussion

For experimental investigation of the SD-FEC characteristics with digital coherent reception including NLEs, we picked up a transmission link of a 95% dispersion compensated standard SMF link as a typical terrestrial system. The BERs before and after SD-FEC decoding are labeled “pre-SD-FEC BER” and “post-SD-FEC BER,” respectively. In this experimental investigation, fiber input power was set to + 4dBm/channel. To obtain an FEC cliff, the loading ASE value after transmission was varied. First, we turned off all NLEs. Open circles indicate the SD-FEC characteristics after 10-span transmission in Fig. 4(a). In this case, the transmission should be in the XPM/SPM-limited regime due to the high fiber input power of + 4dBm/channel. The experimental results imply that nonlinear transmission including XPM does not affect the characteristics of SD-FEC, as Leoni et al. discussed [11]. Next, the NLEs, including BP-NLC and NPCC, were turned on, and the parameters of BP-NLC and NPCC were optimized to minimize post-SD-FEC BER. In this case, the transmission should still be in the XPM-limited regime even with improvement by NLEs. The minimization of the post-FEC BER for optimization of NLEs was equivalently the same to minimize the pre-FEC BER in this case. The resulting BERs (open squares in Fig. 4(a)) show that there was no impact on the SD-FEC of the activation of NLEs with optimal parameters. On the other hand, when we detuned the averaging parameter N of the NPCC to 3 (non opt.) from 39 (opt.), the effect on SD-FEC performance was observed, as shown by the closed triangles in Fig. 4(a). The wrong usage of the NPCC introduced additional distortion into the received waveform, and the characteristic of the waveform was far from the simple XPM-limited situation. These results suggest that we should take into account the parameter settings of NLEs to derive maximum benefit from SD-FEC.

 figure: Fig. 4

Fig. 4 (a) Measured pre-SD-FEC BER vs. post-SD-FEC BER after transmission, (b) cumulative distribution function (CDF) of normalized noise, Solid line: Gaussian fit, crosses: back-to-back, open squares: after transmission w/o NLEs, open circles: after transmission w/ NLE (optimal parameters), and closed triangles: after transmission w/ NLEs (non-optimal parameters).

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To analyze these phenomena, the cumulative distribution function (CDF) of the real part of the normalized noise is shown in Fig. 4(b). The noise was obtained from the constellation points in the upper-right corner (first quadrant of constellation plane) with a pre-SD-FEC BER of around 1.5 × 10−2. The noise of the constellation points was normalized so that the means were zero and the standard deviations were 1. As shown in Fig. 4(b), the CDF for back-to-back, after transmission without NLEs, and after transmission with NLEs (opt. parameters) agreed well with the standard normal distribution, whereas the deviation started from 10−2 CDF for case after transmission with NLEs (non-opt. parameters). These results imply that the noise generated in the fiber could be treated as moderated Gaussian-like noise in terms of a usage of given LDPC in this case. However, the detuned NPCC directly inserts distortion on the waveform after all fiber transmission. This is the reason the measured CDF in the case with a detuned NPCC deviated from the CDF in other cases. Nevertheless, with the optimization of the NLE parameters, a CDF after the NLEs has the same function as a CDF at back-to-back, and allow the SD-FEC offer the same input/output BER performance together with co-operative NLEs.

We also experimentally demonstrated successful co-operation among LDPC SD-FEC and two-types of NLEs by measuring BERs. Figure 5 depicts the measured BERs before and after the SD-FEC decoder as a function of optical signal-to-noise ratio (OSNR) after 10-span transmission at a fiber launched power of 4 dBm/channel. Although SD-FEC was working, the NLEs, including BP-NLC and NPCC, successfully reduced the transmission penalty of ~2 dB in terms of the required OSNR at the BER of the outer FEC threshold of 3.8 × 10−3. The results suggest that the application of NLEs is beneficial for not only pre-SD-FEC BERs but also post SD-FEC BERs.

 figure: Fig. 5

Fig. 5 Measured BERs vs. OSNR after 10-span transmission with and without NLEs and LDPC SD-FEC.

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To extend the experimental results to various practical systems, we numerically investigated the characteristics of the post-SD-FEC BER as a function of the pre-SD-FEC BER after various types of nonlinear transmission. Four types of transmission links were considered: (1) standard SMF with 95-% in-line dispersion compensation (95% DC link), (2) standard SMF with 50-% in-line dispersion compensation (50% DC link), (3) dispersion uncompensated (UC) standard SMF, and (4) UC NZ-DSF. The fiber span length was 60 km for all conditions, and additional ASE noise was loaded at the receiver to obtain the cliff of measured BER curves. The fiber launched power was + 3 dBm/channel for (4) and + 4dBm/channel for the others. (See caption of Fig. 6 for detailed fiber parameters in the simulation.) First, all NLEs were turned off. Figure 6(a) shows the SD-FEC characteristics over the four types of links after 10-span transmission. All results in Fig. 6(a) agree with the simulated results with AWGN. These nonlinear transmissions over various links did not affect the characteristics of SD-FEC for all cases. In these practical cases, the balance of the dispersion map, fiber input power, and symbol rate of signal provided an acceptable situation for given SD-FEC for the QPSK modulation format.

 figure: Fig. 6

Fig. 6 Numerical simulated pre SD-FEC BER vs post SD-FEC BER after various nonlinear transmission links (a) without all nonlinear equalizers, and (b) with all NLEs including BP-NLC and NPCC (opt. parameters). Fiber parameters in simulation, standard SMF: Loss = 0.2 dB/km, dispersion = 16.8 ps/nm/km, nonlinear refractive index = 2.7 × 10−20 m2/W, Aeff = 86 μm2, NZ-DSF: Loss = 0.2 dB/km, dispersion = 2.4 ps/nm/km, nonlinear refractive index = 2.5 × 10−20 m2/W, Aeff = 55 μm2.

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Next, we turned on all NLEs including BP-NLC and NPCC with optimum parameters, which were selected to minimize the post-SD-FEC BERs. Figure 6(b) shows the post-SD-FEC BER as a function of pre-SD-FEC BER. All curves of the pre- and post-SD-FEC BERs in Fig. 6(b) are also in good agreement with the AWGN case, and no negative impact was observed in SD-FEC performance by use of NLEs. These results suggest that co-operation among SD-FEC and NLEs is also possible under various fiber link conditions.

6. Conclusions

We experimentally and numerically investigated the characteristics of 50-GHz-spaced WDM 128-Gb/s DP-QPSK signals received using a digital coherent receiver with SD-FEC and nonlinear equalizers in a nonlinear transmission regime. By applying adequate parameters for nonlinear equalizers, we demonstrated successful co-operation among LDPC SD-FEC and nonlinear equalizers over various transmission links including (1) standard SMF with 0, 50, and 95-% in-line dispersion compensation and (2) NZ-DSF without in-line dispersion compensation.

Acknowledgments

We would like to thank Mr. Yohei Koganei for his useful discussion about FEC implementation and Mr. Kiichi Sugitani for implementing the program code used in the simulation. This work was partly supported by “The research and development project for the ultra-high speed and green photonic networks” of the Ministry of Internal Affairs and Communications, Japan.

References and links

1. J. Renaudier, A. Voicila, O. Bertran-Pardo, O. Rival, M. Karlsson, G. Charlet, and S. Bigo, “Comparison of Set-Partitioned Two-Polarization 16QAM Formats with PDM-QPSK and PDM-8QAM for Optical Transmission Systems with Error-Correction Coding,” in Proc.Eur. Conf. Opt. Commun. (2012), paper We.1.C.5. [CrossRef]  

2. B. Krongold, T. Pfau, N. Kaneda, and S. C. J. Lee, “Comparison between PS-QPSK and PDM-QPSK With Equal Rate and Bandwidth,” IEEE Photon. Technol. Lett. 24(3), 203–205 (2012). [CrossRef]  

3. J. K. Fischer, S. Alreesh, R. Elschner, F. Frey, C. Meuer, L. Molle, C. Schmidt-Langhorst, T. Tanimura, and C. Schubert, “Experimental Investigation of 126-Gb/s 6PolSK-QPSK signals,” Opt. Express 20(26), B232–B237 (2012). [CrossRef]   [PubMed]  

4. T. Koike-Akino, C. Duan, K. Parsons, K. Kojima, T. Yoshida, T. Sugihara, and T. Mizuochi, “High-order statistical equalizer for nonlinearity compensation in dispersion-managed coherent optical communications,” Opt. Express 20(14), 15769–15780 (2012). [CrossRef]   [PubMed]  

5. S. Oda, T. Tanimura, T. Hoshida, Y. Akiyama, H. Nakashima, K. Sone, Y. Aoki, W. Yan, Z. Tao, L. Dou, L. Li, J. C. Rasmussen, Y. Yamamoto, and T. Sasaki, “Experimental Investigation on Nonlinear Distortions with Perturbation Back-propagation Algorithm in 224 Gb/s DP-16QAM Transmission,” in Proc.Opt. Fiber Commun. Conf. (2012), paper OM3A.2. [CrossRef]  

6. T. Tanimura, S. Oda, T. Hoshida, Y. Aoki, Z. Tao, and J. C. Rasmussen, “ Co-operation of Digital Nonlinear Equalizers and Soft-Decision LDPC FEC in Nonlinear Transmission,” in Proc.Eur. Conf. Opt. Commun. (2013), paper Mo.3.D.3.

7. DVB-S.2 Standard Specification, ETSI EN 302 307 V1.1.1 (2005–03).

8. T. Tanimura, T. Hoshida, S. Oda, T. Tanaka, C. Ohsima, Z. Tao, and J. C. Rasmussen, “Systematic analysis on multi-segment dual-polarisation nonlinear compensation in 112 Gb/s DP-QPSK coherent receiver,” in Proc.Eur. Conf. Opt. Commun. (2009) (2009), paper 9.4.5.

9. L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Nonlinear Polarization Crosstalk Canceller for Dual-Polarization Digital Coherent Receivers,” in Proc.Opt. Fiber Commun. Conf. (2010), paper OWE3. [CrossRef]  

10. A. Bisplinghoff, C. Cabirol, S. Langenbach, W. Sauer-Greff, and B. Schmauss, “Soft Decision Metrics for Differentially Encoded QPSK,” in Proc.Eur. Conf. Opt. Commun. (2011), paper Tu.6.A.2. [CrossRef]  

11. P. Leoni, V. Sleiffer, S. Calabrò, V. Veljanovski, M. Kuschnerov, S. L. Jansen, and B. Lankl, “Impact of Interleaving on SD-FEC Operating in Highly Non-Linear XPM-Limited Regime,” in Proc.Opt. Fiber Commun. Conf. (2013), paper OW1E.6. [CrossRef]  

12. A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightwave Technol. 30(10), 1524–1539 (2012). [CrossRef]  

References

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  1. J. Renaudier, A. Voicila, O. Bertran-Pardo, O. Rival, M. Karlsson, G. Charlet, and S. Bigo, “Comparison of Set-Partitioned Two-Polarization 16QAM Formats with PDM-QPSK and PDM-8QAM for Optical Transmission Systems with Error-Correction Coding,” in Proc.Eur. Conf. Opt. Commun. (2012), paper We.1.C.5.
    [Crossref]
  2. B. Krongold, T. Pfau, N. Kaneda, and S. C. J. Lee, “Comparison between PS-QPSK and PDM-QPSK With Equal Rate and Bandwidth,” IEEE Photon. Technol. Lett. 24(3), 203–205 (2012).
    [Crossref]
  3. J. K. Fischer, S. Alreesh, R. Elschner, F. Frey, C. Meuer, L. Molle, C. Schmidt-Langhorst, T. Tanimura, and C. Schubert, “Experimental Investigation of 126-Gb/s 6PolSK-QPSK signals,” Opt. Express 20(26), B232–B237 (2012).
    [Crossref] [PubMed]
  4. T. Koike-Akino, C. Duan, K. Parsons, K. Kojima, T. Yoshida, T. Sugihara, and T. Mizuochi, “High-order statistical equalizer for nonlinearity compensation in dispersion-managed coherent optical communications,” Opt. Express 20(14), 15769–15780 (2012).
    [Crossref] [PubMed]
  5. S. Oda, T. Tanimura, T. Hoshida, Y. Akiyama, H. Nakashima, K. Sone, Y. Aoki, W. Yan, Z. Tao, L. Dou, L. Li, J. C. Rasmussen, Y. Yamamoto, and T. Sasaki, “Experimental Investigation on Nonlinear Distortions with Perturbation Back-propagation Algorithm in 224 Gb/s DP-16QAM Transmission,” in Proc.Opt. Fiber Commun. Conf. (2012), paper OM3A.2.
    [Crossref]
  6. T. Tanimura, S. Oda, T. Hoshida, Y. Aoki, Z. Tao, and J. C. Rasmussen, “ Co-operation of Digital Nonlinear Equalizers and Soft-Decision LDPC FEC in Nonlinear Transmission,” in Proc.Eur. Conf. Opt. Commun. (2013), paper Mo.3.D.3.
  7. DVB-S.2 Standard Specification, ETSI EN 302 307 V1.1.1 (2005–03).
  8. T. Tanimura, T. Hoshida, S. Oda, T. Tanaka, C. Ohsima, Z. Tao, and J. C. Rasmussen, “Systematic analysis on multi-segment dual-polarisation nonlinear compensation in 112 Gb/s DP-QPSK coherent receiver,” in Proc.Eur. Conf. Opt. Commun. (2009) (2009), paper 9.4.5.
  9. L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Nonlinear Polarization Crosstalk Canceller for Dual-Polarization Digital Coherent Receivers,” in Proc.Opt. Fiber Commun. Conf. (2010), paper OWE3.
    [Crossref]
  10. A. Bisplinghoff, C. Cabirol, S. Langenbach, W. Sauer-Greff, and B. Schmauss, “Soft Decision Metrics for Differentially Encoded QPSK,” in Proc.Eur. Conf. Opt. Commun. (2011), paper Tu.6.A.2.
    [Crossref]
  11. P. Leoni, V. Sleiffer, S. Calabrò, V. Veljanovski, M. Kuschnerov, S. L. Jansen, and B. Lankl, “Impact of Interleaving on SD-FEC Operating in Highly Non-Linear XPM-Limited Regime,” in Proc.Opt. Fiber Commun. Conf. (2013), paper OW1E.6.
    [Crossref]
  12. A. Carena, V. Curri, G. Bosco, P. Poggiolini, and F. Forghieri, “Modeling of the impact of nonlinear propagation effects in uncompensated optical coherent transmission links,” J. Lightwave Technol. 30(10), 1524–1539 (2012).
    [Crossref]

2012 (4)

Alreesh, S.

Bosco, G.

Carena, A.

Curri, V.

Duan, C.

Elschner, R.

Fischer, J. K.

Forghieri, F.

Frey, F.

Kaneda, N.

B. Krongold, T. Pfau, N. Kaneda, and S. C. J. Lee, “Comparison between PS-QPSK and PDM-QPSK With Equal Rate and Bandwidth,” IEEE Photon. Technol. Lett. 24(3), 203–205 (2012).
[Crossref]

Koike-Akino, T.

Kojima, K.

Krongold, B.

B. Krongold, T. Pfau, N. Kaneda, and S. C. J. Lee, “Comparison between PS-QPSK and PDM-QPSK With Equal Rate and Bandwidth,” IEEE Photon. Technol. Lett. 24(3), 203–205 (2012).
[Crossref]

Lee, S. C. J.

B. Krongold, T. Pfau, N. Kaneda, and S. C. J. Lee, “Comparison between PS-QPSK and PDM-QPSK With Equal Rate and Bandwidth,” IEEE Photon. Technol. Lett. 24(3), 203–205 (2012).
[Crossref]

Meuer, C.

Mizuochi, T.

Molle, L.

Parsons, K.

Pfau, T.

B. Krongold, T. Pfau, N. Kaneda, and S. C. J. Lee, “Comparison between PS-QPSK and PDM-QPSK With Equal Rate and Bandwidth,” IEEE Photon. Technol. Lett. 24(3), 203–205 (2012).
[Crossref]

Poggiolini, P.

Schmidt-Langhorst, C.

Schubert, C.

Sugihara, T.

Tanimura, T.

Yoshida, T.

IEEE Photon. Technol. Lett. (1)

B. Krongold, T. Pfau, N. Kaneda, and S. C. J. Lee, “Comparison between PS-QPSK and PDM-QPSK With Equal Rate and Bandwidth,” IEEE Photon. Technol. Lett. 24(3), 203–205 (2012).
[Crossref]

J. Lightwave Technol. (1)

Opt. Express (2)

Other (8)

S. Oda, T. Tanimura, T. Hoshida, Y. Akiyama, H. Nakashima, K. Sone, Y. Aoki, W. Yan, Z. Tao, L. Dou, L. Li, J. C. Rasmussen, Y. Yamamoto, and T. Sasaki, “Experimental Investigation on Nonlinear Distortions with Perturbation Back-propagation Algorithm in 224 Gb/s DP-16QAM Transmission,” in Proc.Opt. Fiber Commun. Conf. (2012), paper OM3A.2.
[Crossref]

T. Tanimura, S. Oda, T. Hoshida, Y. Aoki, Z. Tao, and J. C. Rasmussen, “ Co-operation of Digital Nonlinear Equalizers and Soft-Decision LDPC FEC in Nonlinear Transmission,” in Proc.Eur. Conf. Opt. Commun. (2013), paper Mo.3.D.3.

DVB-S.2 Standard Specification, ETSI EN 302 307 V1.1.1 (2005–03).

T. Tanimura, T. Hoshida, S. Oda, T. Tanaka, C. Ohsima, Z. Tao, and J. C. Rasmussen, “Systematic analysis on multi-segment dual-polarisation nonlinear compensation in 112 Gb/s DP-QPSK coherent receiver,” in Proc.Eur. Conf. Opt. Commun. (2009) (2009), paper 9.4.5.

L. Li, Z. Tao, L. Liu, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Nonlinear Polarization Crosstalk Canceller for Dual-Polarization Digital Coherent Receivers,” in Proc.Opt. Fiber Commun. Conf. (2010), paper OWE3.
[Crossref]

A. Bisplinghoff, C. Cabirol, S. Langenbach, W. Sauer-Greff, and B. Schmauss, “Soft Decision Metrics for Differentially Encoded QPSK,” in Proc.Eur. Conf. Opt. Commun. (2011), paper Tu.6.A.2.
[Crossref]

P. Leoni, V. Sleiffer, S. Calabrò, V. Veljanovski, M. Kuschnerov, S. L. Jansen, and B. Lankl, “Impact of Interleaving on SD-FEC Operating in Highly Non-Linear XPM-Limited Regime,” in Proc.Opt. Fiber Commun. Conf. (2013), paper OW1E.6.
[Crossref]

J. Renaudier, A. Voicila, O. Bertran-Pardo, O. Rival, M. Karlsson, G. Charlet, and S. Bigo, “Comparison of Set-Partitioned Two-Polarization 16QAM Formats with PDM-QPSK and PDM-8QAM for Optical Transmission Systems with Error-Correction Coding,” in Proc.Eur. Conf. Opt. Commun. (2012), paper We.1.C.5.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Coding and framing for experiment and simulation.
Fig. 2
Fig. 2 Nonlinear equalizers (NLEs), (a) back propagation nonlinear compensator (BP-NLC) for self-phase modulation (SPM) compensation, (b) nonlinear polarization crosstalk canceler (NPCC) to mitigate polarization crosstalk between x-and y-polarization.
Fig. 3
Fig. 3 System setup. LD: laser diode, AWG: arrayed waveguide grating, PPG: pulse pattern generator, DAC: digital analogue converter, Pol. Mux: polarization multiplexing emulator, WSS: wavelength selective switch, VOA: variable optical attenuator, OBPF: optical band pass filter, LSPS: loop-synchronous polarization scrambler, SW: optical switch, DCM: dispersion compensation module, ASE: amplified spontaneous emission, LO: local oscillator, DSO: digital storage oscilloscope, BP-NLC: back propagation nonlinear compensator, AEQ: adaptive equalizer, FOC: frequency offset compensator, CPR: carrier phase recovery, NPCC: nonlinear polarization crosstalk canceller, and LLR: log-likelihood ratio detector.
Fig. 4
Fig. 4 (a) Measured pre-SD-FEC BER vs. post-SD-FEC BER after transmission, (b) cumulative distribution function (CDF) of normalized noise, Solid line: Gaussian fit, crosses: back-to-back, open squares: after transmission w/o NLEs, open circles: after transmission w/ NLE (optimal parameters), and closed triangles: after transmission w/ NLEs (non-optimal parameters).
Fig. 5
Fig. 5 Measured BERs vs. OSNR after 10-span transmission with and without NLEs and LDPC SD-FEC.
Fig. 6
Fig. 6 Numerical simulated pre SD-FEC BER vs post SD-FEC BER after various nonlinear transmission links (a) without all nonlinear equalizers, and (b) with all NLEs including BP-NLC and NPCC (opt. parameters). Fiber parameters in simulation, standard SMF: Loss = 0.2 dB/km, dispersion = 16.8 ps/nm/km, nonlinear refractive index = 2.7 × 10−20 m2/W, Aeff = 86 μm2, NZ-DSF: Loss = 0.2 dB/km, dispersion = 2.4 ps/nm/km, nonlinear refractive index = 2.5 × 10−20 m2/W, Aeff = 55 μm2.

Equations (4)

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E x out = E x in exp( j( α | E x in | 2 +β | E y in | 2 ) ), E y out = E y in exp( j( α | E y in | 2 +β | E x in | 2 ) ).
( R x R y )=( 1 | W yx | 2 W xy W yx 1 | W xy | 2 )( S x S y ),
W xy (n)= k=N/2 N/2 R x (n+k) S x (n+k) S y (n+k) , W yx (n)= k=N/2 N/2 R y (n+k) S y (n+k) S x (n+k)
E x out = E x in E y in W xy , E y out = E y in E x in W yx .

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