## M-ary pulse-position modulation and frequency-shift keying with additional polarization/phase modulation for high-sensitivity optical transmission |

Optics Express, Vol. 19, Issue 26, pp. B868-B881 (2011)

http://dx.doi.org/10.1364/OE.19.00B868

Acrobat PDF (1642 KB)

### Abstract

We present a new class of optical modulation formats based on the combination of m-ary pulse-position modulation (m-PPM) or m-ary frequency-shift keying (FSK) with additional polarization and/or phase modulation, which is applied on the information carrying pulses in the case of m-PPM or on the information carrying frequency carriers in the case of m-FSK. We describe the principle and implementation of this class of optical modulation formats, and formulate their theoretical receiver sensitivities in optically pre-amplified receivers. Pilot-assisted frequency-domain equalization, similar to that used in coherent optical orthogonal frequency-division multiplexing (CO-OFDM), is used for reliable channel estimation and compensation. CO-OFDM also allows m-FSK to be implemented with high spectral efficiency. As a particular format in this class, m-PPM in combination with polarization-division-multiplexed quadrature phase-shift keying (PDM-QPSK), termed as PQ-mPPM, offers superior receiver sensitivity in optically pre-amplified receivers at bit error ratios (BERs) around the thresholds of common forward-error correction codes. Record receiver sensitivities of 3.5 photons per bit (ppb) at BER = 10^{−3} and 2.7 ppb at BER = 1.5 × 10^{−2} are experimentally demonstrated at 2.5 Gb/s and 6.23 Gb/s using PQ-16PPM and PQ-4PPM, respectively. We further demonstrate the transmission of a 6.23-Gb/s PQ-4PPM signal over a 370-km unrepeatered ultra-large-area-fiber span with 71.7-dB total loss budget.

© 2011 OSA

## 1. Introduction

1. D. O. Caplan, “Laser communication transmitter and receiver design,” J. Opt. Fiber Commun. Rep. **4**(4-5), 225–362 (2007). [CrossRef]

4. B. S. Robinson, A. J. Kerman, E. A. Dauler, R. J. Barron, D. O. Caplan, M. L. Stevens, J. J. Carney, S. A. Hamilton, J. K. W. Yang, and K. K. Berggren, “781 Mbit/s photon-counting optical communications using a superconducting nanowire detector,” Opt. Lett. **31**(4), 444–446 (2006). [CrossRef] [PubMed]

1. D. O. Caplan, “Laser communication transmitter and receiver design,” J. Opt. Fiber Commun. Rep. **4**(4-5), 225–362 (2007). [CrossRef]

6. N. W. Spellmeyer, J. C. Gottschalk, D. O. Caplan, and M. L. Stevens, “High-sensitivity 40 Gb/s RZ-DPSK with forward error correction,” IEEE Photon. Technol. Lett. **16**(6), 1579–1581 (2004). [CrossRef]

8. M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. **16**(2), 674–676 (2004). [CrossRef]

10. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express **16**(2), 804–817 (2008). [CrossRef] [PubMed]

10. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express **16**(2), 804–817 (2008). [CrossRef] [PubMed]

11. M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express **17**(13), 10814–10819 (2009). [CrossRef] [PubMed]

^{−3}, a typical threshold of low-overhead forward-error correction (FEC) codes [12

12. T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron. **10**(2), 376–386 (2004). [CrossRef]

^{−3}, more than 3 dB better than previous Gigabit/sec-class records [14,15]. More recently, a 6.23-Gb/s PQ-4PPM signal was generated and received with a further improved receiver sensitivity of 2.7 ppb [16] assuming the use of a 19.25%-overhead FEC code having a BER threshold of 1.5 × 10

^{−2}[17]. Furthermore, this 6.23-Gb/s PQ-4PPM signal was transmitted over an unrepeatered 370-km ultra-large-area fiber (ULAF) link with a total link loss budget of 71.7 dB using only Erbium-doped fiber amplifiers (EDFAs) at the transmitter and receiver sites [14–16], showing its promise in optical transmission applications that require high receiver sensitivity.

## 2. Principle of A-mPPM/FSK

_{2}(m) + p bits, in which the log

_{2}(m) bits are encoded through m-PPM or m-FSK, and the remaining p bits are encoded through additional polarization and/or phase modulation. When the additional modulation involves two orthogonal polarizations, e.g., in the case of PDM or polarization-shift keying (PolSK), a PDM I/Q modulator is used. The two polarization components of this A-mPPM/FSK signal are modulated on an optical carrier through the use of four digital-to-analog convertors (DACs) and two I/Q modulators followed by a polarization-beam combiner (PBC). Figure 1 illustrates the encoding concept in the context of PQ-4PPM/FSK. In each PQ-4PPM/FSK symbol, there are 6 bits, the first two of which are encoded through 4-PPM or 4-FSK and the remaining four are encoded through PDM-QPSK; 4-PPM (4-FSK) encodes 00, 01, 10, 11 at time (frequency) slot position 1, 2, 3, and 4, respectively. For example, the first symbol contains six bits, “010111”. The first two bits “01” are encoded through 4-PPM (4-FSK) so the pulse (frequency) in the 4-PPM (4-FSK) symbol is located in the second time (frequency) slot. The remaining 4 bits “0111” are encoded via PDM-QPSK, i.e., “01” and “11” are encoded on the x- and y-polarization components, respectively. The above process repeats for the remaining PQ-4PPM/FSK symbols.

_{2}(m) bits associated with m-PPM or m-FSK, and the recovered optical field in this slot is used to recover the remaining 4 bits associated with the PDM-QPSK modulation. More details on the receiver signal processing can be found in Refs [14–16].

18. H. Sugiyama and K. Nosu, “MPPM: A method for improving the band-utilization efficiency in optical PPM,” J. Lightwave Technol. **7**(3), 465–472 (1989). [CrossRef]

_{2}(m) bits can be transmitted per symbol. For k-pulse m-PPM, the number of pulse patterns in each symbol is

_{2}(120) = 6.9 bits per symbol, which is ~73% higher than that carried by 16-PPM. Note that the increase data rate is at the expense of reduced receiver sensitivity or reduced immunity to noise. Using more than 2 pulses per PPM symbol further increases the data rate carried by the PPM, but at further reduced receiver sensitivity. The A-mPPM/FSK concept can be extended by using multiple pulses (carriers) in each symbol and additionally modulate these pulses (carriers) in their polarizations/phases.

19. I. S. Reed and R. A. Scholtz, “N-orthogonal phase-modulated codes,” IEEE Trans. Inf. Theory **12**(3), 388–395 (1966). [CrossRef]

20. W. C. Lindsey and M. K. Simon, “L–Orthogonal Signal Transmission and Detection,” IEEE Trans. Commun. **20**(5), 953–960 (1972). [CrossRef]

## 3. Theoretical performance

### 3.1 General formularization

1. D. O. Caplan, “Laser communication transmitter and receiver design,” J. Opt. Fiber Commun. Rep. **4**(4-5), 225–362 (2007). [CrossRef]

_{m-PPM}and BER

*are respectively the SER of m-PPM and BER of the additional modulation format at a given signal-to-noise ratio per symbol (SNR*

_{AddM}_{sym}). The first term on the R.H.S. of Eq. (2) accounts for the bit errors caused by incorrectly identifying the m-PPM pulse or m-FSK frequency, which on average leads to p/2 bit errors in the decoding of the additional modulation, and m/[2(m-1)]log

_{2}(m) errors in m-PPM or m-FSK decoding. The second term on the R.H.S. of Eq. (2) accounts for the bit errors caused by incorrectly decoding the PDM-QAM, even when the m-PPM time slot or m-FSK frequency slot is correctly identified.

_{b}[7]. The above formulas provide a basis to analytically calculate the BER performance of an A-mPPM/FSK signal as a function of SNR

_{b}. Note that the above BER performances presented in this paper are practically realizable through essentially a 2-stage detector, which may be suboptimal [20

20. W. C. Lindsey and M. K. Simon, “L–Orthogonal Signal Transmission and Detection,” IEEE Trans. Commun. **20**(5), 953–960 (1972). [CrossRef]

**4**(4-5), 225–362 (2007). [CrossRef]

### 3.2 A-mPPM/FSK with the additional modulation being PDM-QPSK

_{b}assuming no polarization filtering (PF) of the amplified spontaneous emission (ASE) noise at the receiver. At BER = 10

^{−3}, the required ppb for 16-PPM is 6.7 dB. Figure 3 shows the theoretical BER performance of PQ-mPPM as a function of SNR

_{b}. The required ppb at BER = 10

^{−3}for PQ-16PPM is 3.9 dB, which is 2.8 dB better than 16-PPM.

_{b}. The analytical results obtained using the approximation of Eq. (2) match well with those obtained using Eq. (1). The simulated results also match well with the analytical results with a small constant additional SNR penalty of ~0.2 dB, probably due to imperfect channel compensation. The theoretical results were further verified through experiments reported in Refs [14] and [15]. Figure 5 shows the receiver sensitivity improvement of PQ-mPPM over BPSK (or PDM-QPSK) at BER = 10

^{−3}as a function of m, where m = 2

^{i}(i = 1,2,3,…10). Evidently, PQ-mPPM outperforms PDM-QPSK for all the values of m, and the improvement increases with the increases of m, and approaches ~4 dB at m = 1024.

### 3.3 A-mPPM/FSK with the additional modulation being PS-QPSK

_{PS-PQSK}is the BER of PS-QPSK, which itself can be expressed as [15]where BER

_{QPSK}is the BER of QPSK, and SER

_{PS}is the SER of polarization switching (equivalent to 2-PPM with PF to obtain single-polarization ASE noise), both of which can be analytically calculated [7,21]. The BER performances of both PS-QPSK and PS-QPSK-4PPM as a function of SNR

_{b}are shown in Fig. 3. PS-QPSK and PS-QPSK-4PPM require ~6 dB and ~4.9 dB ppb at BER = 10

^{−3}, respectively, which are ~2 dB and ~1 dB worse than PQ-16PPM. We note that the asymptotic BER performance of PS-QPSK-4PPM (e.g., at BER<10

^{−9}) is better than PQ-16PPM, which is in agreement with a recent study conducted on PS-QPSK-PPM by Karlsson and Agrell [22]. In the BER range between 10

^{−2}and 10

^{−3}, around the BER thresholds of commonly used FEC codes for optical communications, the sensitivity of PS-QPSK-4PPM is similar to that of PQ-4PPM, but is much less bandwidth efficient.

### 3.4 A-mFSK with CO-OFDM

**4**(4-5), 225–362 (2007). [CrossRef]

25. W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come?” J. Opt. Netw. **7**(3), 234–255 (2008). [CrossRef]

**4**(4-5), 225–362 (2007). [CrossRef]

26. X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s reduced-guard-interval CO-OFDM transmission over 2000 km of ultra-large-area fiber and five 80-GHz-grid ROADMs,” J. Lightwave Technol. **29**(4), 483–490 (2011). [CrossRef]

## 4. Experimental performance of PQ-mPPM

^{15}-1. The four field components of the encoded PQ-4PPM signal, corresponding to the I and Q components of both x- and y-polarizations, were stored in two synchronized arbitrary waveform generators (AWGs), each having two 10-GS/s digital-to-analog converters (DACs). Twofold oversampling was used, leading to a 4-PPM slot rate of 5 GHz (a symbol rate of 1.25 GHz), which resulted in a raw data rate of 7.5 Gb/s for PQ-4PPM. The DAC outputs were amplified to a peak-to-peak voltage swing of 3.5 V before driving the modulator. The signal has a 3-dB spectral bandwidth of ~6 GHz.

^{2}.

26. X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s reduced-guard-interval CO-OFDM transmission over 2000 km of ultra-large-area fiber and five 80-GHz-grid ROADMs,” J. Lightwave Technol. **29**(4), 483–490 (2011). [CrossRef]

26. X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s reduced-guard-interval CO-OFDM transmission over 2000 km of ultra-large-area fiber and five 80-GHz-grid ROADMs,” J. Lightwave Technol. **29**(4), 483–490 (2011). [CrossRef]

^{−2}to below 10

^{−15}, the net data rate of the signal is 6.23 Gb/s.

*net*information bit). The theoretical performance is also shown for comparison. At BER = 1.5 × 10

^{−2}, the system requires 2.7 ppb, which is 1.8 dB away from theory. In the 1.8-dB overall penalty, ~0.8 dB is due to the 19.25% FEC overhead, 0.4 dB is due to the excess EDFA noise, 0.2 dB is due to the pilot sequences used for synchronization and CE, and 0.1 dB is due to the pilot symbols used for PE, leaving only ~0.3 dB to account for the hardware implementation penalty. As a reference, PDM-QPSK performance was also measured by turning off the PPM modulation. The net data rate of the PDM-QPSK signal was 4.15 Gb/s. At BER = 2 × 10

^{−2}, the system requires ~4 ppb for PDM-QPSK, which is essentially the same as that recently reported in Ref [27]. The 2.7-ppb sensitivity obtained for the PQ-4PPM signal is better than that obtained for the PDM-QPSK signal by 1.9 dB. The theoretical performance of PQ-4PPM and PDM-QPSK are also shown in Fig. 12 for comparison. It can be seen that PQ-4PPM suffers ~0.6 dB less implementation penalty than PDM-QPSK, probably because the implementation penalty associated with demodulating PPM is lower than with demodulating PDM-QPSK. Compared to the PQ-16PPM demonstration at 2.5 Gb/s [14], this PQ-4PPM demonstration offers a 2.5-fold increase in net data rate and a 1.1-dB reduction in ppb.

^{−2}when the signal launch power is between 12.5 dBm and 17.5 dBm, indicating a substantial power margin of 5 dB. The optimum signal launch power was 15.5 dBm, corresponding to a mean nonlinear phase shift of 2.7 radians for each PPM pulse. At the optimum power, the signal Q factor (derived from the BER) is 8.5 dB, which is 1.7 dB higher than the FEC threshold (1.5 × 10

^{−2}). To assess the maximum allowable link loss, we added 2.7 dB of additional loss after the 370-km ULAF, increasing the total link loss to 71.7 dB. The optimum signal launch power was found to be 16.5 dBm, at which the measured BER is just below the BER threshold. At the optimum power, the transmission penalty is estimated to be ~1.5 dB. This allowable link loss budget (71.7 dB) compares reasonably well with the 71.5 dB recently obtained with return-to-zero PDM-BPSK and third-order Raman pumping [3]. This experiment has shown good nonlinear tolerance of the PQ-4PPM signal in single-channel transmission, and it would be of interest to study its nonlinear tolerance in wavelength-division multiplexed (WDM) transmission, which is beyond the scope of this paper. We expect that with the return-to-zero (RZ) like pulse format for PQ-mPPM, it could have high nonlinear tolerance to WDM nonlinear effects, e.g., inter-channel cross-phase modulation, when the dispersion-induced pulse broadening is sufficiently high.

## 5. Summary

^{−2}has been experimentally demonstrated at 6.23 Gb/s using PQ-4PPM. We have also demonstrated the transmission of a 6.23-Gb/s PQ-4PPM signal over a 370-km unrepeatered ULAF span with a total loss budget of 71.7 dB. Another particular format, m-FSK in combination with PolSK, is also of interest due to its constant-power profile and its ability to operate without the need for phase tracking. This class of power-efficient modulation formats is expected to be attractive in applications where photon efficiency is of critical importance, such as in deep-space communications and unrepeatered fiber transmission.

## Acknowledgments

## References and links

1. | D. O. Caplan, “Laser communication transmitter and receiver design,” J. Opt. Fiber Commun. Rep. |

2. | D. O. Caplan, M. L. Stevens, and B. S. Robinson, “Free-space laser communications: global communications and beyond,” European Conference on Optical Communication (ECOC), Tutorial, Paper 9.6.1, Vienna, Austria, September 2009. |

3. | P. Bousselet, H. Bissessur, J. Lestrade, M. Salsi, L. Pierre, and D. Mongardien, “High capacity (64 x 43 Gb/s) unrepeatered transmission over 440 km,” OFC’11, OMI2. |

4. | B. S. Robinson, A. J. Kerman, E. A. Dauler, R. J. Barron, D. O. Caplan, M. L. Stevens, J. J. Carney, S. A. Hamilton, J. K. W. Yang, and K. K. Berggren, “781 Mbit/s photon-counting optical communications using a superconducting nanowire detector,” Opt. Lett. |

5. | D. O. Caplan, B. S. Robinson, R. J. Murphy, and M. L. Stevens, “Demonstration of 2.5 Gslot/sec optically-preamplified M-PPM with 4 photons/bit receiver sensitivity,” OFC’05, Postdeadline paper PDP32. |

6. | N. W. Spellmeyer, J. C. Gottschalk, D. O. Caplan, and M. L. Stevens, “High-sensitivity 40 Gb/s RZ-DPSK with forward error correction,” IEEE Photon. Technol. Lett. |

7. | X. Liu, S. Chandrasekhar, and A. Leven, “Self-Coherent Optical Transport Systems,” in |

8. | M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. |

9. | K. Kikuchi, “Coherent Optical Communication Systems,” in |

10. | S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express |

11. | M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express |

12. | T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron. |

13. | H. Bülow and E. Masalkina, “Coded modulation in optical communications,” OFC’11, paper OThO1. |

14. | X. Liu, T. H. Wood, R. W. Tkach, and S. Chandrasekhar, “Demonstration of record sensitivity in an optically pre-amplified receiver by combining PDM-QPSK and 16-PPM with pilot-Assisted digital coherent detection,” OFC’11, PDB1. |

15. | X. Liu, T. H. Wood, R. W. Tkach, and S. Chandrasekhar, “Demonstration of record sensitivities in optically pre-amplified receivers by combining PDM-QPSK and m-ary pulse-position modulation,” J. Lightwave Technol. (accepted for publication) (invited paper). |

16. | X. Liu, S. Chandrasekhar, T. H. Wood, R. W. Tkach, E. C. Burrows, and P. J. Winzer, “Demonstration of 2.7-PPB receiver sensitivity using PDM-QPSK with 4-PPM and unrepeatered transmission over a single 370-km unamplified ultra-large-area fiber span,” ECOC’11, paper Tu.3.B.4. |

17. | F. Chang, “Application aspects of enhanced HD-FEC for 40/100G systems,” ECOC’10, workshop talk WS11–6. |

18. | H. Sugiyama and K. Nosu, “MPPM: A method for improving the band-utilization efficiency in optical PPM,” J. Lightwave Technol. |

19. | I. S. Reed and R. A. Scholtz, “N-orthogonal phase-modulated codes,” IEEE Trans. Inf. Theory |

20. | W. C. Lindsey and M. K. Simon, “L–Orthogonal Signal Transmission and Detection,” IEEE Trans. Commun. |

21. | J. G. Proakis, |

22. | M. Karlsson and E. Agrell, “Generalized pulse-position modulation for optical power-efficient communication,” ECOC’11, paper Tu.6.B.6. |

23. | D. O. Caplan, J. J. Carney, and S. Constantine, “Parallel direct modulation laser transmitters for high-speed high-sensitivity laser communications,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (Optical Society of America, 2011), paper PDPB12. |

24. | K. Kikuchi and M. Osaki, “Highly-sensitive coherent optical detection of M-ary frequency-shift keying signal,” ECOC’11, paper Tu.5.A.1. |

25. | W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come?” J. Opt. Netw. |

26. | X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s reduced-guard-interval CO-OFDM transmission over 2000 km of ultra-large-area fiber and five 80-GHz-grid ROADMs,” J. Lightwave Technol. |

27. | D. Lavery, E. Torrengo, and S. J. Savory, “Bidirectional 10 Gbit/s long-reach WDM-PON using digital coherent receivers,” OFC’11, OTuB4. |

**OCIS Codes**

(060.1660) Fiber optics and optical communications : Coherent communications

(060.2330) Fiber optics and optical communications : Fiber optics communications

(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems

**ToC Category:**

Transmission Systems and Network Elements

**History**

Original Manuscript: October 13, 2011

Revised Manuscript: November 22, 2011

Manuscript Accepted: November 29, 2011

Published: December 7, 2011

**Virtual Issues**

European Conference on Optical Communication 2011 (2011) *Optics Express*

**Citation**

Xiang Liu, S. Chandrasekhar, T. H. Wood, R. W. Tkach, P. J. Winzer, E. C. Burrows, and A. R. Chraplyvy, "M-ary pulse-position modulation and frequency-shift keying with additional polarization/phase modulation for high-sensitivity optical transmission," Opt. Express **19**, B868-B881 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-26-B868

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### References

- D. O. Caplan, “Laser communication transmitter and receiver design,” J. Opt. Fiber Commun. Rep. 4(4-5), 225–362 (2007). [CrossRef]
- D. O. Caplan, M. L. Stevens, and B. S. Robinson, “Free-space laser communications: global communications and beyond,” European Conference on Optical Communication (ECOC), Tutorial, Paper 9.6.1, Vienna, Austria, September 2009.
- P. Bousselet, H. Bissessur, J. Lestrade, M. Salsi, L. Pierre, and D. Mongardien, “High capacity (64 x 43 Gb/s) unrepeatered transmission over 440 km,” OFC’11, OMI2.
- B. S. Robinson, A. J. Kerman, E. A. Dauler, R. J. Barron, D. O. Caplan, M. L. Stevens, J. J. Carney, S. A. Hamilton, J. K. W. Yang, and K. K. Berggren, “781 Mbit/s photon-counting optical communications using a superconducting nanowire detector,” Opt. Lett. 31(4), 444–446 (2006). [CrossRef] [PubMed]
- D. O. Caplan, B. S. Robinson, R. J. Murphy, and M. L. Stevens, “Demonstration of 2.5 Gslot/sec optically-preamplified M-PPM with 4 photons/bit receiver sensitivity,” OFC’05, Postdeadline paper PDP32.
- N. W. Spellmeyer, J. C. Gottschalk, D. O. Caplan, and M. L. Stevens, “High-sensitivity 40 Gb/s RZ-DPSK with forward error correction,” IEEE Photon. Technol. Lett. 16(6), 1579–1581 (2004). [CrossRef]
- X. Liu, S. Chandrasekhar, and A. Leven, “Self-Coherent Optical Transport Systems,” in Optical Fiber Telecommunications V B, Systems and Networks, I. P. Kaminow, T. Li, and A. E. Willner, eds. (Academic Press, Burlington, MA, 2008) Chapter 4.
- M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subsequent equalization of propagation impairments,” IEEE Photon. Technol. Lett. 16(2), 674–676 (2004). [CrossRef]
- K. Kikuchi, “Coherent Optical Communication Systems,” in Optical Fiber Telecommunications V B, Systems and Networks, I. P. Kaminow, T. Li, and A. E. Willner, eds. (Academic Press, Burlington, MA, 2008), Chapter 3.
- S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16(2), 804–817 (2008). [CrossRef] [PubMed]
- M. Karlsson and E. Agrell, “Which is the most power-efficient modulation format in optical links?” Opt. Express 17(13), 10814–10819 (2009). [CrossRef] [PubMed]
- T. Mizuochi, Y. Miyata, T. Kobayashi, K. Ouchi, K. Kuno, K. Kubo, K. Shimizu, H. Tagami, H. Yoshida, H. Fujita, M. Akita, and K. Motoshima, “Forward error correction based on block turbo code with 3-bit soft decision for 10 Gb/s optical communication systems,” IEEE J. Sel. Top. Quantum Electron. 10(2), 376–386 (2004). [CrossRef]
- H. Bülow and E. Masalkina, “Coded modulation in optical communications,” OFC’11, paper OThO1.
- X. Liu, T. H. Wood, R. W. Tkach, and S. Chandrasekhar, “Demonstration of record sensitivity in an optically pre-amplified receiver by combining PDM-QPSK and 16-PPM with pilot-Assisted digital coherent detection,” OFC’11, PDB1.
- X. Liu, T. H. Wood, R. W. Tkach, and S. Chandrasekhar, “Demonstration of record sensitivities in optically pre-amplified receivers by combining PDM-QPSK and m-ary pulse-position modulation,” J. Lightwave Technol. (accepted for publication) (invited paper).
- X. Liu, S. Chandrasekhar, T. H. Wood, R. W. Tkach, E. C. Burrows, and P. J. Winzer, “Demonstration of 2.7-PPB receiver sensitivity using PDM-QPSK with 4-PPM and unrepeatered transmission over a single 370-km unamplified ultra-large-area fiber span,” ECOC’11, paper Tu.3.B.4.
- F. Chang, “Application aspects of enhanced HD-FEC for 40/100G systems,” ECOC’10, workshop talk WS11–6.
- H. Sugiyama and K. Nosu, “MPPM: A method for improving the band-utilization efficiency in optical PPM,” J. Lightwave Technol. 7(3), 465–472 (1989). [CrossRef]
- I. S. Reed and R. A. Scholtz, “N-orthogonal phase-modulated codes,” IEEE Trans. Inf. Theory 12(3), 388–395 (1966). [CrossRef]
- W. C. Lindsey and M. K. Simon, “L–Orthogonal Signal Transmission and Detection,” IEEE Trans. Commun. 20(5), 953–960 (1972). [CrossRef]
- J. G. Proakis, Digital Communications, 4th ed. (Boston, MA 2001).
- M. Karlsson and E. Agrell, “Generalized pulse-position modulation for optical power-efficient communication,” ECOC’11, paper Tu.6.B.6.
- D. O. Caplan, J. J. Carney, and S. Constantine, “Parallel direct modulation laser transmitters for high-speed high-sensitivity laser communications,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest (Optical Society of America, 2011), paper PDPB12.
- K. Kikuchi and M. Osaki, “Highly-sensitive coherent optical detection of M-ary frequency-shift keying signal,” ECOC’11, paper Tu.5.A.1.
- W. Shieh, X. Yi, Y. Ma, and Q. Yang, “Coherent optical OFDM: has its time come?” J. Opt. Netw. 7(3), 234–255 (2008). [CrossRef]
- X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s reduced-guard-interval CO-OFDM transmission over 2000 km of ultra-large-area fiber and five 80-GHz-grid ROADMs,” J. Lightwave Technol. 29(4), 483–490 (2011). [CrossRef]
- D. Lavery, E. Torrengo, and S. J. Savory, “Bidirectional 10 Gbit/s long-reach WDM-PON using digital coherent receivers,” OFC’11, OTuB4.

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