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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 16 — Aug. 2, 2010
  • pp: 16883–16889
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428-Gb/s single-channel coherent optical OFDM transmission over 960-km SSMF with constellation expansion and LDPC coding

Qi Yang, Abdullah Al Amin, Xi Chen, Yiran Ma, Simin Chen, and William Shieh  »View Author Affiliations


Optics Express, Vol. 18, Issue 16, pp. 16883-16889 (2010)
http://dx.doi.org/10.1364/OE.18.016883


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Abstract

High-order modulation formats and advanced error correcting codes (ECC) are two promising techniques for improving the performance of ultrahigh-speed optical transport networks. In this paper, we present record receiver sensitivity for 107 Gb/s CO-OFDM transmission via constellation expansion to 16-QAM and rate-1/2 LDPC coding. We also show the single-channel transmission of a 428-Gb/s CO-OFDM signal over 960-km standard-single-mode-fiber (SSMF) without Raman amplification.

© 2010 OSA

1. Introduction

2. Experiment setup and system configuration

The primary goal of this report is to demonstrate significant improvement of the receiver sensitivity through the use of LDPC without requiring higher optoelectronic bandwidth. Namely, we present a system design based on 16-QAM to provide coding overhead for LDPC, achieving enhanced receiver sensitivity while maintaining the same spectral efficiency of 3.3 b/s/Hz as the uncoded 4-QAM modulation [1

1. Q. Yang, Y. Ma, and W. Shieh, “107 Gb/s coherent optical OFDM reception using orthogonal band multiplexing,” in Proc. Optical Fiber Commun. Conf., 2008, Paper PDP 7.

]. For ECC, we choose LDPC in this work as it provides flexibility of arbitrary rate coding compared to relatively rigid coding rate in TCM. Figure 1
Fig. 1 Experimental setup for 400 Gb/s LDPC coded CO-OFDM transmission.
shows the system configuration for 400 Gb/s LDPC coded 16-QAM CO-OFDM system. Although longer block length can improve the coding performance, it also increases the hardware complexity. We use the practical length of LDPC code that is close to what have been demonstrated in real-time using state-of-art FPGA [17

17. I. B. Djordjevic, M. Arabaci, and L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightwave Technol. 27(16), 3518–3530 (2009). [CrossRef]

,18

18. T. Mizuochi, Y. Konishi, Y. Miyata, T. Inoue, K. Onohara, S. Kametani, T. Sugihara, K. Kubo, H. Yoshida, T. Kobayashi, and T. Ichikawa, “Experimental demonstration of concatenated LDPC and RS codes by FPGAs emulation,” IEEE Photon. Technol. Lett. 21(18), 1302–1304 (2009). [CrossRef]

]. We use Reed-Solomon codes as outer code to eliminate possible error-floor in LDPC [19

19. T. Mizuochi, “Next Generation FEC for optical communication,” Optical Fiber communication/National Fiber Optic Engineers Conference, 2008. OFC/NFOEC 2008. Conference on, vol., no., pp.1–33, 24–28 Feb. 2008.

]. The data is first fed into RS (255, 239) and then the LDPC (4000, 2000) [23

23. D. J. C. Mackay, Ldpc database. Available at http://www.inference.phy.cam.ac.uk/mackay/codes/data.html.

] encoder. In order to eliminate the influence of burst-errors, an interleaver is placed between the two serially-concatenated FEC codes [24

24. A. Tychopoulos, O. Koufopavlou, and I. Tomkos, “FEC in optical communications - A tutorial overview on the evolution of architectures and the future prospects of outband and inband FEC for optical communications,” IEEE Circuits Devices Mag. 22(6), 79–86 (2006). [CrossRef]

], where the input signal is filled symbol by symbol, and output is sent subcarrier by subcarrier. The encoded data are then fed into 16-QAM OFDM base band generator to obtain digital OFDM time-domain signal, including procedures of serial-to-parallel conversion, data mapping to 16 QAM constellation, IDFT and guard interval insertion. The parameters for the OFDM baseband generation are as follows: 128 total subcarriers; guard interval is 1/8 of the symbol period. Middle 102 subcarriers out of 128 are filled, from which 4 pilot subcarriers are used for phase estimation. The middle two subcarriers are fed with zeros, where the frequency signal and local lasers are located. Polarization multiplexing doubles the raw rate to 53.3 Gb/s per band. After LDPC decoding, the net data rate is 26.7 Gb/s (10 GHz · log2(16QAM) · 2 pols · 96) / (128 · 1.125GI)· 50%LDPC), excluding the cyclic prefix, pilot tones, and unused middle two subcarriers. The real and imaginary parts of the OFDM waveforms are uploaded into an AWG operated at 10 GS/s to generate IQ analog signals, and subsequently fed into I and Q ports of an optical IQ modulator respectively. The optical input to the optical IQ modulator is derived from a recirculating frequency shifter (RFS), essentially a recirculating loop including an IQ modulator and optical amplifiers [11

11. S. Y. Chung, G. D. Forney, T. J. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5(2), 58–60 (2001). [CrossRef]

]. A multitone-source is generated by using a CW laser light replicated 16 times via the RFS [10

10. Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express 17(11), 9421–9427 (2009). [CrossRef] [PubMed]

], and is modulated into a 16-band CO-OFDM signal after being driven by a complex electrical OFDM signal, carrying a data rate of 428 Gb/s. The number of tones in the RFS is controlled by the bandwidth of the optical bandpass filter in the RFS loop, and the RF tone frequency is 7.96875 GHz, phase-locked with the AWG using a 10 MHz reference clock. This is to ensure that all the subcarriers across the entire OFDM spectrum are at the correct uniform frequency grids. There is no frequency guard band between each sub-band. The optical OFDM signal from the RFS is then inserted into a polarization splitter, with one branch delayed by one OFDM symbol period (14.4 ns) to emulate the polarization multiplexing, resulting in a total line rate of 856 Gb/s. The signal is then coupled into a recirculation loop comprising of 2x80 km SSMF fiber (span loss of 18.5 dB and 17.5 dB) and three EDFAs to compensate the loss. The signal is coupled out from the loop and received with a polarization diversity coherent optical receiver [1

1. Q. Yang, Y. Ma, and W. Shieh, “107 Gb/s coherent optical OFDM reception using orthogonal band multiplexing,” in Proc. Optical Fiber Commun. Conf., 2008, Paper PDP 7.

,2

2. S.L. Jansen, I. Morita, H. Tanaka, “10×121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz spectral efficiency over 1,000 km of SSMF,” in Proc. Optical Fiber Commun. Conf., 2008, Paper PDP 2.

]. The performance is detected on a per-band basis by aligning the local laser to the center of each band, and the detected RF signal is anti-alias filtered with a 7-GHz low-pass filter. The four RF signals for the two IQ components are then input into a Tektronix Time Domain-sampling Scope (TDS) and are acquired at 20 GS/s and processed with a MATLAB program using 2x2 MIMO-OFDM models, which are detailed in [1

1. Q. Yang, Y. Ma, and W. Shieh, “107 Gb/s coherent optical OFDM reception using orthogonal band multiplexing,” in Proc. Optical Fiber Commun. Conf., 2008, Paper PDP 7.

,2

2. S.L. Jansen, I. Morita, H. Tanaka, “10×121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz spectral efficiency over 1,000 km of SSMF,” in Proc. Optical Fiber Commun. Conf., 2008, Paper PDP 2.

]. Finally the complex symbol values are input to the LDPC soft-decoder for data recovery.

LDPC codes was first invented by R. G. Gallager in 1960s [25

25. R. G. Gallager, Low Density Parity Check Codes, MIT Press, Cambridge, Mass., 1963.

], and rediscovered in 1990s by MacKay [26

26. D. J. C. MacKay and R. M. Neal, “Near Shannon limit performance of low density parity check codes,” Electron. Lett. 32(18), 1645–1646 (1996). [CrossRef]

]. It was introduced to the optical communications during the last decade by Djordjevic and Mizuochi [12

12. I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Using LDPC-coded modulation and coherent detection for ultra high-speed optical transmission,” IEEE/OSA, J. Lightwave Technol. 25(11), 3619–3625 (2007). [CrossRef]

19

19. T. Mizuochi, “Next Generation FEC for optical communication,” Optical Fiber communication/National Fiber Optic Engineers Conference, 2008. OFC/NFOEC 2008. Conference on, vol., no., pp.1–33, 24–28 Feb. 2008.

]. The soft-decision algorithm for LDPC can be best described using the Tanner graph [27

27. S. J. Johnson, S. R. Weller, “Low-density parity-check codes: design and decoding”, Wiley Encyclopedia of Telecommunications, John Wiley and Sons, 2003.

]. The name of ‘low density parity’ is derived from the fact that the number of ‘1’s in each column (or row) of the parity check matrix H (dimension of m times n) is very small compared to the block length. Tanner graph consists of m check nodes (the number of parity bits) and n variable nodes (the number of bits in a codeword) [12

12. I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Using LDPC-coded modulation and coherent detection for ultra high-speed optical transmission,” IEEE/OSA, J. Lightwave Technol. 25(11), 3619–3625 (2007). [CrossRef]

].The connection between ci and fj is made if the parity check matrix element (H)ij is a 1. Figure 2
Fig. 2 The Tanner graph representation of the parity-check matrix
shows a typical Tanner graph. The number of edges in the Tanner graph is equal to the number of ones in the parity-check matrix. The inserted H in the figure is the corresponding parity check matrix.

The LDPC soft decoding algorithm is based on so-called belief propagation where the message is passed between the check and variable nodes [28

28. Bernhard M. J. Leiner, “LDPC codes - a Brief Tutorial,” April 2005.

]. The message sent by the variable node to the check node contains the pair of probability (qij) for the ‘belief’ that the variable node should be ‘0’ or ‘1’. qij(0) and qij(1) stands for the two probabilities. Similarly, the message sent by the check node to the variable node also contains another probability (rij) for the ‘belief’ that the variable node should be ‘0’ or ‘1’. At the beginning, the bit codes send their qij to check nodes. qij(0) and qij(1) stands for the amount of belief that received yi is a 0 or 1. Then the check nodes will compute the response rji as
rji(0)=12+12i'Vj\i(12qi'j(1)),rji(1)=1rji(0)
(1)
The variable nodes then will send the calculated response to bit node by

qij(0)=Kij(1Pi)j'Cj\irj'i(0),qij(1)=Kijj'Cj\irj'i(1) (2)where the Kij is used to ensure that qij(0) +qij(1)=1. The updating procedures of qij and rij are illustrated in Fig. 2 (b) and (c). At this stage, the estimated c^jof the current variable cjis using

Qi(0)=Ki(1Pi)j'Cirji(0),Qi(1)=KiPijCirji(1)
(3)

3. Experimental results and discussion

To identify net effective coding gain and the resultant improvement of the receiver sensitivity for the LDPC coded 16-QAM OFDM signal, we first measure the receiver performance for 107 Gb/s at back-to-back and the result is shown in Fig. 3
Fig. 3 Back-to-back OSNR sensitivity for 107 Gb/s and 428 Gb/s signal. All the data rates shown are before 7% RS FEC
. Since we are comparing the two signals with the same net data rate, this coding gain is equivalent to the coding gain per bit if Fig. 3 is re-plotted as BER versus SNR per bit Because of the sharp drop off of the BER after LDPC and maximum number of bits (1,500,000 bits per data point) measured, we defined the receiver sensitivity as the OSNR for the BER of 1x10−3 before RS decoding (BER of 1x10−3 or lower always results in zero error count after RS outer decoder in the experiment). Any error floor due to LDPC can be effectively eliminated by the interleaver/deinterleaver and RS FEC. It can be seen that the OSNR sensitivity for rate ½ LDPC coded 16-QAM signal is 12.5 dB OSNR compared with 15.5 dB OSNR in conventional 4-QAM signal, indicating a 3 dB improvement. We stress again this is achieved with the same electrical and optical bandwidth for all the optical and electrical components encountered. In contrast to the application of using high-order modulation for ultra-high spectral efficiency [6

6. H. Takahashi, A. Al Amin, S.L Jansen, I. Morita, and H. Tanaka, “DWDM transmission with 7.0-bit/(s1Hz) spectral efficiency using 8×65.1-Gbit/s coherent PDM-OFDM signals,” in Proc. Optical Fiber Commun. Conf. 2009, PDPB7.

,7

7. X. Yi, W. Shieh, and Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008). [CrossRef]

], the proposed rate ½ LDPC coded 16-QAM signal does not require higher OSNR, and the net coding gain could be utilized to increase transmission reach and/or reduce the required bit resolution for DAC/ADC compared to 4-QAM modulation case. The back-to-back 428 Gb/s BER performance is also shown at Fig. 3 and the sensitivity is measured at 20.2 dB OSNR for LDPC coded 16-QAM. The inset shows for 16-QAM CO-OFDM signal at the OSNR of 19 dB.

Table 1

Table 1. Detailed BER for the worst band of 428 Gb/s LDPC-coded 16-QAM signal at reaches of 960 km and 800 km.

table-icon
View This Table
shows the detailed BERs for 400-Gb/s LDPC-coded OFDM signal at different reaches. At the reach of 960 km with a launch power of 3dBm, only the performance of the worst band, the 8th band of the 400-Gb/s is shown including its raw BER for the 16-QAM signal or the input BER to LDPC decoder, BER after LDPC decoding, and BER after both LDPC and RS decoding. It can be seen that LDPC-coded 16-QAM signal can be received successfully (zero error counts for both polarizations) after 960-km transmission. We also measure transmission performance in various reaches below 960 km, all error-free after LDPC and RS decoding. Table 1 only shows one instance of the reach below 960 which is 800 km. Figure 4
Fig. 4 spectrum for 428 Gb/s LDPC-coded 16-QAM at reaches of 960 km.
shows the spectrum of the 400 Gb/s CO-OFDM signal at the reach of 960 km. Although each band is uniformly modulated with the same data, the chromatic dispersion induces rapid inter-band walk off and de-correlate the multi-band signal. In fact, the nonlinearity performance of such configuration is slightly conservative compared to the truly uncorrelated multiband signal [1

1. Q. Yang, Y. Ma, and W. Shieh, “107 Gb/s coherent optical OFDM reception using orthogonal band multiplexing,” in Proc. Optical Fiber Commun. Conf., 2008, Paper PDP 7.

]. We note this is the first experimental demonstration of LDPC coding for long-haul transmission.

4. Conclusion

We have shown record receiver sensitivity for 100 Gb/s CO-OFDM transmission via constellation expansion from 4-QAM to 16-QAM and rate 1/2 LDPC coding. As a result, transmission of 400 Gb/s single-channel CO-OFDM signal over 960-km SSMF is demonstrated without Raman amplification.

Acknowledgement

The authors would like to thank Dr. Tetsuya Kawanishi from National Institute of Information and Communications Technology (NICT), Japan for providing the optical IQ modulator in the experiment.

References and links

1.

Q. Yang, Y. Ma, and W. Shieh, “107 Gb/s coherent optical OFDM reception using orthogonal band multiplexing,” in Proc. Optical Fiber Commun. Conf., 2008, Paper PDP 7.

2.

S.L. Jansen, I. Morita, H. Tanaka, “10×121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz spectral efficiency over 1,000 km of SSMF,” in Proc. Optical Fiber Commun. Conf., 2008, Paper PDP 2.

3.

E. Yamada, A. Sano, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, K. Yonenaga, Y. Miyamoto, K. Ishihara, Y. Takatori, T. Yamada, and H.Yamazaki, “1Tb/s (111Gb/s/ch × 10ch) no-guard-interval OOFDM transmission over 2100 km DSF,” OECC/ACOFT Conf. 2008, paper PDP6.

4.

S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15(5), 2120–2126 (2007). [CrossRef] [PubMed]

5.

H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express 16(2), 873–879 (2008). [CrossRef] [PubMed]

6.

H. Takahashi, A. Al Amin, S.L Jansen, I. Morita, and H. Tanaka, “DWDM transmission with 7.0-bit/(s1Hz) spectral efficiency using 8×65.1-Gbit/s coherent PDM-OFDM signals,” in Proc. Optical Fiber Commun. Conf. 2009, PDPB7.

7.

X. Yi, W. Shieh, and Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008). [CrossRef]

8.

R. Dischler, and F. Buchali, “Transmission of 1.2 Tb/s continuous waveband PDM‐OFDM‐FDM signal with spectral efficiency of 3.3 bit/s/Hz over 400 km of SSMF,” in Proc. Optical Fiber Commun. Conf. 2009, PDP C2.

9.

S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of ultra-large-area fiber,” ECOC’09, post-deadline paper PD2.6.

10.

Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express 17(11), 9421–9427 (2009). [CrossRef] [PubMed]

11.

S. Y. Chung, G. D. Forney, T. J. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5(2), 58–60 (2001). [CrossRef]

12.

I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Using LDPC-coded modulation and coherent detection for ultra high-speed optical transmission,” IEEE/OSA, J. Lightwave Technol. 25(11), 3619–3625 (2007). [CrossRef]

13.

I. B. Djordjevic, and H. G. Batshon, Lei Xu and T. Wang, “Coded polarization-multiplexed iterative polar modulation (PM-IPM) for beyond 400 Gb/s serial optical transmission,” in Proc. OFC/NFOEC 2010, Paper No. OMK2, San Diego, CA, March 21–25, 2010.

14.

I. B. Djordjevic and B. Vasic, “Multilevel Coding in M-ary DPSK/Differential QAM High-Speed Optical Transmission with Direct Detection,” IEEE/OSA J, Lightw. Technol. 24(1), 420–428 (2006). [CrossRef]

15.

M. Arabaci, I. B. Djordjevic, R. Saunders, and R. M. Marcoccia, “Non-binary Quasi-Cyclic LDPC based coded modulation for beyond 100 Gb/s transmission,” IEEE Photon. Technol. Lett. 22(6), 434–436 (2010). [CrossRef]

16.

I. B. Djordjevic, L. Xu, and T. Wang, “Beyond 100 Gb/s optical transmission based on polarization multiplexed coded-OFDM with coherent detection,” J. Opt. Commun. Netw. 1(1), 50–56 (2009). [CrossRef]

17.

I. B. Djordjevic, M. Arabaci, and L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightwave Technol. 27(16), 3518–3530 (2009). [CrossRef]

18.

T. Mizuochi, Y. Konishi, Y. Miyata, T. Inoue, K. Onohara, S. Kametani, T. Sugihara, K. Kubo, H. Yoshida, T. Kobayashi, and T. Ichikawa, “Experimental demonstration of concatenated LDPC and RS codes by FPGAs emulation,” IEEE Photon. Technol. Lett. 21(18), 1302–1304 (2009). [CrossRef]

19.

T. Mizuochi, “Next Generation FEC for optical communication,” Optical Fiber communication/National Fiber Optic Engineers Conference, 2008. OFC/NFOEC 2008. Conference on, vol., no., pp.1–33, 24–28 Feb. 2008.

20.

G. Ungerboeck, “Trellis-coded modulation with redundant signal sets Part I&II: Introduction,” Communications Magazine, IEEE 25(2), 5–11 (1987). [CrossRef]

21.

H. Bülow, F. Buchali, G. Thielecke, ”Optical Trellis-coded modulation ”, in Proc. Optical Fiber Commun. Conf. 2004, WM5.

22.

X. Liu, Q. Yang, S. Chandrasekhar, W. Shieh, Y. K. Chen “Transmission of 44-Gb/s coherent optical OFDM signal with Trellis-cded 32-QAM subcarrier modulation”, in Proc. Optical Fiber Commun. Conf. 2010, OMR3.

23.

D. J. C. Mackay, Ldpc database. Available at http://www.inference.phy.cam.ac.uk/mackay/codes/data.html.

24.

A. Tychopoulos, O. Koufopavlou, and I. Tomkos, “FEC in optical communications - A tutorial overview on the evolution of architectures and the future prospects of outband and inband FEC for optical communications,” IEEE Circuits Devices Mag. 22(6), 79–86 (2006). [CrossRef]

25.

R. G. Gallager, Low Density Parity Check Codes, MIT Press, Cambridge, Mass., 1963.

26.

D. J. C. MacKay and R. M. Neal, “Near Shannon limit performance of low density parity check codes,” Electron. Lett. 32(18), 1645–1646 (1996). [CrossRef]

27.

S. J. Johnson, S. R. Weller, “Low-density parity-check codes: design and decoding”, Wiley Encyclopedia of Telecommunications, John Wiley and Sons, 2003.

28.

Bernhard M. J. Leiner, “LDPC codes - a Brief Tutorial,” April 2005.

OCIS Codes
(060.1660) Fiber optics and optical communications : Coherent communications

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: April 1, 2010
Revised Manuscript: May 23, 2010
Manuscript Accepted: June 7, 2010
Published: July 26, 2010

Citation
Qi Yang, Abdullah Al Amin, Xi Chen, Yiran Ma, Simin Chen, and William Shieh, "428-Gb/s single-channel coherent optical OFDM transmission over 960-km SSMF with constellation expansion and LDPC coding," Opt. Express 18, 16883-16889 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-16883


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References

  1. Q. Yang, Y. Ma, and W. Shieh, “107 Gb/s coherent optical OFDM reception using orthogonal band multiplexing,” in Proc. Optical Fiber Commun. Conf., 2008, Paper PDP 7.
  2. S.L. Jansen, I. Morita, H. Tanaka, “10×121.9-Gb/s PDM-OFDM transmission with 2-b/s/Hz spectral efficiency over 1,000 km of SSMF,” in Proc. Optical Fiber Commun. Conf., 2008, Paper PDP 2.
  3. E. Yamada, A. Sano, H. Masuda, E. Yamazaki, T. Kobayashi, E. Yoshida, K. Yonenaga, Y. Miyamoto, K. Ishihara, Y. Takatori, T. Yamada, and H.Yamazaki, “1Tb/s (111Gb/s/ch × 10ch) no-guard-interval OOFDM transmission over 2100 km DSF,” OECC/ACOFT Conf. 2008, paper PDP6.
  4. S. J. Savory, G. Gavioli, R. I. Killey, and P. Bayvel, “Electronic compensation of chromatic dispersion using a digital coherent receiver,” Opt. Express 15(5), 2120–2126 (2007). [CrossRef] [PubMed]
  5. H. Sun, K.-T. Wu, and K. Roberts, “Real-time measurements of a 40 Gb/s coherent system,” Opt. Express 16(2), 873–879 (2008). [CrossRef] [PubMed]
  6. H. Takahashi, A. Al Amin, S.L Jansen, I. Morita, and H. Tanaka, “DWDM transmission with 7.0-bit/(s1Hz) spectral efficiency using 8×65.1-Gbit/s coherent PDM-OFDM signals,” in Proc. Optical Fiber Commun. Conf. 2009, PDPB7.
  7. X. Yi, W. Shieh, and Y. Ma, “Phase noise effects on high spectral efficiency coherent optical OFDM transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008). [CrossRef]
  8. R. Dischler, and F. Buchali, “Transmission of 1.2 Tb/s continuous waveband PDM‐OFDM‐FDM signal with spectral efficiency of 3.3 bit/s/Hz over 400 km of SSMF,” in Proc. Optical Fiber Commun. Conf. 2009, PDP C2.
  9. S. Chandrasekhar, X. Liu, B. Zhu, and D. W. Peckham, “Transmission of a 1.2-Tb/s 24-carrier no-guard-interval coherent OFDM superchannel over 7200-km of ultra-large-area fiber,” ECOC’09, post-deadline paper PD2.6.
  10. Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express 17(11), 9421–9427 (2009). [CrossRef] [PubMed]
  11. S. Y. Chung, G. D. Forney, T. J. Richardson, and R. Urbanke, “On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit,” IEEE Commun. Lett. 5(2), 58–60 (2001). [CrossRef]
  12. I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Using LDPC-coded modulation and coherent detection for ultra high-speed optical transmission,” IEEE/OSA, J. Lightwave Technol. 25(11), 3619–3625 (2007). [CrossRef]
  13. I. B. Djordjevic, and H. G. Batshon, Lei Xu and T. Wang, “Coded polarization-multiplexed iterative polar modulation (PM-IPM) for beyond 400 Gb/s serial optical transmission,” in Proc. OFC/NFOEC 2010, Paper No. OMK2, San Diego, CA, March 21–25, 2010.
  14. I. B. Djordjevic and B. Vasic, “Multilevel Coding in M-ary DPSK/Differential QAM High-Speed Optical Transmission with Direct Detection,” IEEE/OSA J, Lightw. Technol. 24(1), 420–428 (2006). [CrossRef]
  15. M. Arabaci, I. B. Djordjevic, R. Saunders, and R. M. Marcoccia, “Non-binary Quasi-Cyclic LDPC based coded modulation for beyond 100 Gb/s transmission,” IEEE Photon. Technol. Lett. 22(6), 434–436 (2010). [CrossRef]
  16. I. B. Djordjevic, L. Xu, and T. Wang, “Beyond 100 Gb/s optical transmission based on polarization multiplexed coded-OFDM with coherent detection,” J. Opt. Commun. Netw. 1(1), 50–56 (2009). [CrossRef]
  17. I. B. Djordjevic, M. Arabaci, and L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightwave Technol. 27(16), 3518–3530 (2009). [CrossRef]
  18. T. Mizuochi, Y. Konishi, Y. Miyata, T. Inoue, K. Onohara, S. Kametani, T. Sugihara, K. Kubo, H. Yoshida, T. Kobayashi, and T. Ichikawa, “Experimental demonstration of concatenated LDPC and RS codes by FPGAs emulation,” IEEE Photon. Technol. Lett. 21(18), 1302–1304 (2009). [CrossRef]
  19. T. Mizuochi, “Next Generation FEC for optical communication,” Optical Fiber communication/National Fiber Optic Engineers Conference, 2008. OFC/NFOEC 2008. Conference on, vol., no., pp.1–33, 24–28 Feb. 2008.
  20. G. Ungerboeck, “Trellis-coded modulation with redundant signal sets Part I&II: Introduction,” Communications Magazine, IEEE 25(2), 5–11 (1987). [CrossRef]
  21. H. Bülow, F. Buchali, G. Thielecke, ”Optical Trellis-coded modulation ”, in Proc. Optical Fiber Commun. Conf. 2004, WM5.
  22. X. Liu, Q. Yang, S. Chandrasekhar, W. Shieh, Y. K. Chen “Transmission of 44-Gb/s coherent optical OFDM signal with Trellis-cded 32-QAM subcarrier modulation”, in Proc. Optical Fiber Commun. Conf. 2010, OMR3.
  23. D. J. C. Mackay, Ldpc database. Available at http://www.inference.phy.cam.ac.uk/mackay/codes/data.html .
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