## Fiber communications using convolutional coding and bandwidth-efficient modulation

Optics Express, Vol. 14, Issue 2, pp. 542-555 (2006)

http://dx.doi.org/10.1364/OPEX.14.000542

Acrobat PDF (221 KB)

### Abstract

In this paper we evaluate numerically the advantage of combining convolutional coding and bandwidth-efficient modulation. We compare different multilevel modulation formats, line codes, and hard/soft decision decoding. Compared with DPSK modulation (with the same bandwidth and information transmission rate), an improvement of almost 5 dB is observed for bit error rates around 10^{-8}. We also study the robustness to intersymbol interference in the form of chromatic dispersion, and find that the improvement of the coded transmission lines improves over the uncoded even in presence of chromatic dispersion.

© 2006 Optical Society of America

## 1. Introduction

04. I. B. Djordjevic, S. Sankaranarayanan, and B. Vasic, “Irregular Low-Density Parity-Check Codes for Long-Haul Optical Communications,” IEEE Photonics Technol. Lett., vol. **16**, pp. 338–340, 2004. [CrossRef]

12. M. Ohm and J. Speidel, “Quarternary optical ASK-DPSK and receivers with direct detection,” IEEE Photonics Technol. Lett. **15**, 159–161, 2003. [CrossRef]

*et al*. [8] was the first idea in this direction, i.e., to combine multilevel modulation with convolutional coding in optical communications. Using DQPSK and soft decision decoding, an improvement of around 4 dB was found with respect to uncoded DPSK transmission [8]. A later extension with concatenating Reed-Solomon codes with convolutional codes was reported in [9]. The use of multilevel modulation together with low-rate LDPC and RS codes was discussed also in [10

10. G. Kramer, A. Ashikhmin, A. J. van Wijngaarden, and X. Wei, “Spectral efficiency of coded phase-shift keying for fiber-optic communication,” J. Lightwave Technol. **21**, 2438–2445, 2003. [CrossRef]

11. G. Ungerboeck, “Channel coding with mulitlevel/phase signals,” IEEE Transactions of Information Theory **IT-28**, 55–67, 1982. [CrossRef]

12. M. Ohm and J. Speidel, “Quarternary optical ASK-DPSK and receivers with direct detection,” IEEE Photonics Technol. Lett. **15**, 159–161, 2003. [CrossRef]

17. J.-X. Cai, C. R. Davidson, D. G. Foursa, L. Liu, Y. Cai, B. Bakhshi, G. Mohs, W. W. Patterson, P. C. Corbett, A. J. Lucero, W. Anderson, H. Li, M. Nissov, A. N. Pilipetski, and N. S. Bergano, “Experimental comparison of the RZ-DPSK and NRZ-DPSK modulation formats,” *Proc. of Optical Fiber Communication Conference, OFC 2005*, paper OThO1, 2005.

## 2. Simulation setup

*F*is the noise figure of the optical amplifier,

*h*is Planck’s constant,

*v*is the frequency, and G is the amplifier gain. It is assumed that the signal and the noise occur only in one polarization. The EDFA gain is

*G*= 30 dB and the noise figure is

*F*= 5 dB. After amplification, the signal passes an optical bandpass filter (BPF) with Gaussian frequency response and is detected in the receiver. The 3 dB bandwidth of the optical BPF is 40 GHz.

^{-8}and below required several weeks of computation time on a 17-node computer cluster.

### 2.1. RZ-DPSK/ASK transmitter

*et al*. [12

12. M. Ohm and J. Speidel, “Quarternary optical ASK-DPSK and receivers with direct detection,” IEEE Photonics Technol. Lett. **15**, 159–161, 2003. [CrossRef]

*et al*. [13], and further investigated in [14] and [15

15. J. Hansryd, J. van Howe, and C. Xu, “Nonlinear crosstalk and compensation in QDPASK optical communication systems,” IEEE Photonics Technol. Lett. **17**, 232–234, 2005. [CrossRef]

15. J. Hansryd, J. van Howe, and C. Xu, “Nonlinear crosstalk and compensation in QDPASK optical communication systems,” IEEE Photonics Technol. Lett. **17**, 232–234, 2005. [CrossRef]

*a*and

*b*in the figure) shall be chosen so that the bit-error rates of the DPSK and the ASK transmission lines are approximately equal. How this is done will be discussed in more detail in Section 2.3.

### 2.2. RZ-DQPSK transmitter

### 2.3. RZ-DPSK/ASK receiver

*a*and

*b*in Fig. 2, deserves a special discussion. In a system limited by optical noise, such as, e.g., an optically preamplified system in the limit of high signal-to-noise ratio, the system behaves as with an additive white Gaussian noise channel, where the bit error rate will be a function of the separation between the signal levels in the complex plane, and the optimum case will be when the separation is equal, i.e.,

*a*/

*b*= 1/3. In terms of the optical extinction ratio

*ER*this equals

*ER*= 20log

_{10}(

*b*/

*a*) = 9.5 dB as noted in [13] and [15

15. J. Hansryd, J. van Howe, and C. Xu, “Nonlinear crosstalk and compensation in QDPASK optical communication systems,” IEEE Photonics Technol. Lett. **17**, 232–234, 2005. [CrossRef]

*b*

^{2}-

*a*

^{2}) and the DPSK signal (which is proportional to 2

*a*

^{2}) to be equal, which gives

*a*/

*b*= 1/√3, or

*ER*= 4.8 dB.

*a*/

*b*ratio to be somewhat higher than the predicted value of 1/3, and we found, numerically, an optimum value of

*a*/

*b*= 0.398, or

*ER*= 8.0 dB, which is actually exactly the same optimum values that was found in the experiments [13,14]. It is this optimum value of the

*a*/

*b*ratio that we use in the simulations.

#### 2.4. RZ-DQPSK receiver

#### 2.5. The convolutional encoder and decoder

*K*= 10 input bits. Specifically, the “data 1” stream can be obtained, at any time instant, by multiplying these 10 bits with the binary mask 1001110111 and adding the results using binary addition, i.e., an exclusive-or operation. The standard nomenclature for identifying convolutional encoders is to use the octal form of the binary masks, so in our case, “data 1” is identified by the octal number 1167. Similarly, the “data 2” output corresponds to 1545 in octal form, and the convolutional code is thus denoted (1167,1545).

**15**, 159–161, 2003. [CrossRef]

^{K-1}states. This implies that the decoding complexity of the (1167,1545)-code is too high to be attractive in practice, since the Viterbi algorithm needs to keep track of 2

^{9}states. The today more reasonable (with respect to decoding complexity) code (133,171) is therefore also studied.

*coding gain*, which is the ratio (usually in dB) between the power needed in an uncoded and coded system, resp., to attain the same bit error rate (BER). Furthermore, the

*asymptotic coding gain*(ACG) is defined as the limit of the coding gain as the BER approaches zero. It can be shown [7, pp. 17–18, 531–534] that the ACG (in dB) for transmission over an AWGN channel with optimal detection is simply

*ACG*= 10log

_{10}(

*Rd*) for soft decision and

_{f}*ACG*= 10log

_{10}(

*Rd*/2) for hard decision, compared to an uncoded reference system with the same energy per information bit. For example, the (1167,1545) convolutional code has

_{f}*R*= 1/2 and

*d*= 12, implying that

_{f}*ACG*= 7.8 dB for soft decision and 4.8 dB for hard decision. Since the ACG denotes an asymptotic limit, we can interpret it as the best coding gain one can expect to find, but it says nothing about how fast (in terms of, e.g., the signal-to-noise ratio) one will reach this limit. To answer that issue, simulations were performed.

### 3. Results

#### 3.1. Back to back

*b*-

*a*= Δ) yields the same BER. We find that the average power required to get

*a*/

*b*= 0.398 (as was explained in Sec. 2.3) and

*b*-

*a*= Δ is (

*b*

^{2}+

*a*

^{2})/2 = 1.60Δ

^{2}. Since the average power of NRZ-OOK is Δ

^{2}/2, a power penalty of 1.60/0.5 = 3.2 = 5.0 dB can be expected for RZ-DPSK/ASK compared with RZ-ASK. The remaining 2 dB difference with respect to the observed 3 dB penalty, we attribute to the well-known performance difference between NRZ and RZ, which is in the order of 2 dB in favor of RZ, see, e.g., [22

22. P. J. Winzer and A. Kalmár, “Sensitivity enhancement of optical receivers by impulsive coding,” J. Lightwave Technol. **17**, 171–177, 1999. [CrossRef]

23. M. Pauer and P. Winzer, “Impact of extinction ratio on return-to-zero coding gain in optical noise limited receivers,” IEEE Photonics Technol. Lett. **15**, 879–881, 2004. [CrossRef]

24. P. Humblet and M. Azioglou, “On the bit error rate of lightwave systems with optical amplifiers,” J. Lightwave Technol. , **9**, 1576–1582, 1991. [CrossRef]

24. P. Humblet and M. Azioglou, “On the bit error rate of lightwave systems with optical amplifiers,” J. Lightwave Technol. , **9**, 1576–1582, 1991. [CrossRef]

^{-8}as a reference. This means that we measure the input power required to get a BER of 10

^{-8}relative to -43.6 dBm. By using the RZ-ASK/DPSK transmission scheme, we find a gain of 0.7 dB for hard decision decoding, and about 3.4 dB for soft decision decoding. For the RZ-DQPSK transmission scheme, the coding gain is slightly better, being about 2.2 dB for hard decision and about 4.4 dB for soft decision, compared with DPSK. We can thus see that the RZ-DQPSK performs better than the RZ-ASK/DPSK, which we attribute to the larger separation between the modulation levels in signal space for DQPSK.

^{-9}) we obtain in the simulations is -43 dBm, or only 3 dB from the quantum limit of 20 photons per bit (which corresponds to -46 dBm). This is not unrealistic, as experiments have reported sensitivities of 30 photons per bit at 10 Gb/s [25] and 38 photons per bit at 42.7 Gb/s [26].

#### 3.2. Influence of dispersion

^{-4}) BER’s for RZ-DPSK over 75 km of fiber. This transmission limit applies also for coded transmission and hard decision Viterbi decoding. By using soft decision Viterbi decoding, the transmission length can be increased to 75 km.

^{-5}(which is -45.8 dBm according to Fig. 7). As we can see from Fig. 9, the dispersion penalty at the 10

^{-9}- level is the same for small distances, but for the longer distances the penalty is underestimated due to the BER floors. The penalties are plotted in Fig. 10.

^{-5}, where DPSK and DPSK/ASK(hard) have their crossover point (as shown in Fig. 8), and for lower BERs the coded transmission would be around 0.8 dB better. For soft decision decoding we can see that the power gain is 2 dB at 0 km and increases to 2.4 dB at 75 km.

^{-5}, the penalty will approach infinity, and there the coding gain will also be infinite. We can observe that transmission lengths of 75 km can only be reached with the soft decision decoded systems, but then at fairly large transmission penalties.

#### 3.3. Reed-Solomon and alternative coding

*n*,

*k*) code, the rate is

*R*=

*k*/

*n*and the minimum distance is

*d*=

*n*-

*k*+ 1. Thus

*ACG*= 10log

_{10}(

*k*(

*n*-

*k*+ 1)/2

*n*) with hard decision decoding, and for the often used RS(255,239) code, we find

*ACG*= 9.0 dB. This seems more impressive than the convolutional code, which has

*ACG*= 7.8 dB with soft decision. The fact that the RS code is applied to DPSK and the convolutional code to DQPSK to maintain approximately the same bandwidth contributes an additional 2.3 dB to the advantage of RS [20, pp. 274–276]. To verify this, we performed simulations of RS(255,239)-coded data using the RZ-DPSK modulation format, at a 10 Gb/s information rate (i.e., a 10.7 Gb/s encoded data rate). The result is shown in Fig. 11. All optical and electrical filter bandwidths remained the same as in the previous simulations. Extrapolation of our data to BER around 10

^{-9}in Fig. 11 nevertheless show that the convolutional code with soft decision performs similarly to the conventional RS coded system. The reason is that the asymptotic limits are reached faster for DQPSK with convolutional coding than for DPSK with RS coding. This shows clearly the importance of using both simulations and asymptotic theories when comparing different systems.

10. G. Kramer, A. Ashikhmin, A. J. van Wijngaarden, and X. Wei, “Spectral efficiency of coded phase-shift keying for fiber-optic communication,” J. Lightwave Technol. **21**, 2438–2445, 2003. [CrossRef]

27. A. Agata, K. Tanaka, and N. Edagawa, “Study on the optimum ReedĐSolomon-based FEC codes for 40-Gb/s-based ultralong-distance WDM transmission,” J. Lightwave Technol. , **20**, 2189–2195, 2002. [CrossRef]

### 4. Conclusions and outlook

^{-8}) of -39.8 dBm for NRZ-OOK. This can be improved to - 43.6 dBm by using the RZ-DPSK modulation format. By using four-level modulation in form of RZ-DPSK/ASK and the (1167,1545)convolutional code, the sensitivity is improved to -44.4 dBm, and with the better RZ-DQPSK modulation format, -45.7 dBm can be reached. Finally, by using soft decision decoding on the convolutional code, we reach -48 dBm, which is an impressive 8.2 dB improvement over the conventional NRZ transmission, and a 4.4 dB improvement over RZ-DPSK.

^{-}5) is limited to 62.5 km. This is increased to 75 km by using coded RZ-DQPSK transmission and soft decision Viterbi decoding. In this case, the improvement over RZ-DPSK varies from 3.9 dB (back-to-back transmission) to 5.2 dB (62.5 km SMF).

## References and links

01. | O. Vassilieva, T. Hoshida, S. Choudhary, G. Castanon, H. Kuwahara, T. Terahara, and H. Onaka, “Numerical comparison of NRZ, CS-RZ and IM-DPSK formats in 43 Gbit/s WDM transmission”, |

02. | W. Kaiser, G. Mohs, T. Wuth, R. Neuhauser, W. Rosenkranz, and C. Glingener, “225 km repeaterless 10 Gb/s transmission over uncompensated SSMF using duobinary modulation and Raman amplification,” |

03. | T. Mizuochi, K. Kubo, H. Yoshida, H. Fujita, H. Tagami, M. Akita, and K. Motoshima, “Next generation FEC for optical networks,” |

04. | I. B. Djordjevic, S. Sankaranarayanan, and B. Vasic, “Irregular Low-Density Parity-Check Codes for Long-Haul Optical Communications,” IEEE Photonics Technol. Lett., vol. |

05. | E. Forestieri, R. Gangopadhyay, and G. Prati, “Performance of convolutional codes in a direct-detection PPM channel,” IEEE Transactions on Communications, |

06. | K. Seki, “Single-chip FEC codec LSI using iterative CSOC decoder for 10 Gb/s long-haul optical transmisison systems,” IEEE Custom Integrated Circuits Conference,Orlando, USA,155–158, May 12-15, 2002. |

07. | S. Lin and D. J. Costello Jr., |

08. | H. Bülow, G. Thielecke, and F. Buchali, “Optical Trellis-Coded Modulation,” |

09. | P. Faraj, S. Schöllmann, J. Leibrich, and W. Rosenkranz, “8.4 dB net coding gain achieved with a serially concatenated coding scheme for differential quadrature phase shift keyed optical systems,” |

10. | G. Kramer, A. Ashikhmin, A. J. van Wijngaarden, and X. Wei, “Spectral efficiency of coded phase-shift keying for fiber-optic communication,” J. Lightwave Technol. |

11. | G. Ungerboeck, “Channel coding with mulitlevel/phase signals,” IEEE Transactions of Information Theory |

12. | M. Ohm and J. Speidel, “Quarternary optical ASK-DPSK and receivers with direct detection,” IEEE Photonics Technol. Lett. |

13. | X. Liu, X. Wei, Y.-H. Kao, J. Leuthold, C. R. Doerr, and L. F. Mollenauer, “Quartenary differential-phase amplitude-shift-keying for DWDM transmission,” |

14. | X. Liu, X. Wei, Y.-H. Kao, J. Leuthold, C. R. Doerr, Y. Su, and L. F. Mollenauer, “Return-to-zero quaternary differential-phase amplitude-shift-keying for long-haul transmission,” |

15. | J. Hansryd, J. van Howe, and C. Xu, “Nonlinear crosstalk and compensation in QDPASK optical communication systems,” IEEE Photonics Technol. Lett. |

16. | C. Wree, J. Leibrich, and W. Rosenkranz, “RZ-DQPSK Format with High Spectral Efficiency and High Robustness Towards Fiber Nonlinearities,” |

17. | J.-X. Cai, C. R. Davidson, D. G. Foursa, L. Liu, Y. Cai, B. Bakhshi, G. Mohs, W. W. Patterson, P. C. Corbett, A. J. Lucero, W. Anderson, H. Li, M. Nissov, A. N. Pilipetski, and N. S. Bergano, “Experimental comparison of the RZ-DPSK and NRZ-DPSK modulation formats,” |

18. | M. Ohm and J. Speidel, “Optimal receiver bandwidths, bit error probabilities and chromatic dispersion tolerance of 40 Gbit/s optical 8-DPSK with NRZ and RZ impulse shaping,” |

19. | E. Desurvire, |

20. | J. G. Proakis, |

21. | R. A. Griffin and A. C. Carter, “Optical Differential Quadrature Phase-Shift Key (oDPSK) for High Capacity Optical Transmission,” |

22. | P. J. Winzer and A. Kalmár, “Sensitivity enhancement of optical receivers by impulsive coding,” J. Lightwave Technol. |

23. | M. Pauer and P. Winzer, “Impact of extinction ratio on return-to-zero coding gain in optical noise limited receivers,” IEEE Photonics Technol. Lett. |

24. | P. Humblet and M. Azioglou, “On the bit error rate of lightwave systems with optical amplifiers,” J. Lightwave Technol. , |

25. | W. A. Atia and R. S. Bondurant, “Demonstration of return-to-zero signaling in both OOK and DPSK formats to improve receiver sensitivity in an optically preamplified receiver,” |

26. | J. S. Sinsky, A. Adamiecki, A. Gnauck, C. Burrus, J. Leuthold, O. Wohlgemuth, and A. Umbach, “A 42.7- Gb/s integrated balanced optical front end with record sensitivity,” |

27. | A. Agata, K. Tanaka, and N. Edagawa, “Study on the optimum ReedĐSolomon-based FEC codes for 40-Gb/s-based ultralong-distance WDM transmission,” J. Lightwave Technol. , |

**OCIS Codes**

(060.4080) Fiber optics and optical communications : Modulation

(060.4510) Fiber optics and optical communications : Optical communications

**ToC Category:**

Fiber Optics and Optical Communications

**Citation**

Torsten Wuth, Erik Agrell, Magnus Karlsson, and Mats Sköld, "Fiber communications using convolutional coding and bandwidth-efficient modulation," Opt. Express **14**, 542-555 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-2-542

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### References

- O. Vassilieva, T. Hoshida, S. Choudhary, G. Castanon, H. Kuwahara, T. Terahara, H. Onaka, "Numerical comparison of NRZ, CS-RZ and IM-DPSK formats in 43 Gbit/s WDM transmission", 14th Annual Meeting of the IEEE Lasers and Electro-Optics Society (LEOS), 673-674, Nov. 12-13, 2001.
- W. Kaiser, G. Mohs, T. Wuth, R. Neuhauser, W. Rosenkranz, C. Glingener, "225 km repeaterless 10 Gb/s transmission over uncompensated SSMF using duobinary modulation and Raman amplification," 14th Annual Meeting of the IEEE Lasers and Electro-Optics Society (LEOS), 155-156, Nov. 12-13, 2001.
- T. Mizuochi, K. Kubo, H. Yoshida, H. Fujita, H.Tagami, M. Akita, K. Motoshima, "Next generation FEC for optical networks," Proc. of Optical Fiber Communication Conference, OFC 2003, paper ThN1, 2003.
- I. B. Djordjevic, S. Sankaranarayanan, and B. Vasic, "Irregular Low-Density Parity-Check Codes for Long-Haul Optical Communications," IEEE Photonics Technol. Lett., vol. 16, pp. 338-340, 2004. [CrossRef]
- E. Forestieri, R. Gangopadhyay and G. Prati, "Performance of convolutional codes in a direct-detection PPM channel," IEEE Transactions on Communications, 37, 1303-1317, 1989. [CrossRef]
- K. Seki, "Single-chip FEC codec LSI using iterative CSOC decoder for 10 Gb/s long-haul optical transmission systems," IEEE Custom Integrated Circuits Conference, Orlando, USA, 155-158, May 12-15, 2002.
- S. Lin and D. J. Costello, Jr., Error Control Coding, 2nd ed., Prentice Hall, Inc., 2004.
- H. Bülow, G. Thielecke, and F. Buchali, "Optical Trellis-Coded Modulation," Proc. of Optical Fiber Communication Conference, OFC 2004, paper WM5, 2004.
- P. Faraj, S. Schöllmann, J. Leibrich,W. Rosenkranz, "8.4 dB net coding gain achieved with a serially concatenated coding scheme for differential quadrature phase shift keyed optical systems," Proc. of European Conference of Optical Communication, ECOC 2005, paper Tu 3.2.4, 2005.
- G. Kramer, A. Ashikhmin, A. J. van Wijngaarden and X. Wei, "Spectral efficiency of coded phase-shift keying for fiber-optic communication," J. Lightwave Technol. 21, 2438-2445, 2003. [CrossRef]
- G. Ungerboeck, "Channel coding with mulitlevel/phase signals," IEEE Transactions of Information Theory IT- 28, 55-67, 1982. [CrossRef]
- M. Ohm and J. Speidel, "Quarternary optical ASK-DPSK and receivers with direct detection," IEEE Photonics Technol. Lett. 15, 159-161, 2003. [CrossRef]
- X. Liu, X. Wei, Y.-H. Kao, J. Leuthold, C. R. Doerr, and L. F. Mollenauer, "Quartenary differential-phase amplitude-shift-keying for DWDM transmission," Proc. of European Conference on Optical Communication, ECOC 2003, paper Th2.6.5, 2003.
- X. Liu, X. Wei, Y.-H. Kao, J. Leuthold, C. R. Doerr, Y. Su, and L. F. Mollenauer, "Return-to-zero quaternary differential-phase amplitude-shift-keying for long-haul transmission," Proc. of Optical Fiber Communication Conference, OFC 2004, paper FN2, 2004.
- J. Hansryd, J. van Howe, and C. Xu, "Nonlinear crosstalk and compensation in QDPASK optical communication systems," IEEE Photonics Technol. Lett. 17, 232-234, 2005. [CrossRef]
- C. Wree, J. Leibrich and W. Rosenkranz, "RZ-DQPSK Format with High Spectral Efficiency and High Robustness Towards Fiber Nonlinearities," Proc. of European Conference on Optical Communication, ECOC 2002, paper 9.6.6, 2002.
- J.-X. Cai, C. R. Davidson, D. G. Foursa, L. Liu, Y. Cai, B. Bakhshi, G. Mohs, W. W. Patterson, P. C. Corbett, A. J. Lucero, W. Anderson, H. Li, M. Nissov, A. N. Pilipetski, and N. S. Bergano, "Experimental comparison of the RZ-DPSK and NRZ-DPSK modulation formats," Proc. of Optical Fiber Communication Conference, OFC 2005, paper OThO1, 2005.
- M. Ohm and J. Speidel, "Optimal receiver bandwidths, bit error probabilities and chromatic dispersion tolerance of 40 Gbit/s optical 8-DPSK with NRZ and RZ impulse shaping," Proc. of Optical Fiber Communication Conference, OFC 2005, paper OFG5, 2005.
- E. Desurvire, Erbium Doped Fiber Amplifiers, Principles and Applications, John Wiley and Sons, Inc., New York, 1994.
- J. G. Proakis, Digital Communications, 4th ed., McGraw-Hill, NewYork, 2001.
- R. A. Griffin and A. C. Carter,"Optical Differential Quadrature Phase-Shift Key (oDPSK) for High Capacity Optical Transmission," Proc. of Optical Fiber Communication Conference, OFC 2002, paper WX6, 2002.
- P. J. Winzer and A. Kalmár, "Sensitivity enhancement of optical receivers by impulsive coding," J. Lightwave Technol. 17, 171-177, 1999. [CrossRef]
- M. Pauer and P. Winzer, "Impact of extinction ratio on return-to-zero coding gain in optical noise limited receivers," IEEE Photonics Technol. Lett. 15, 879-881, 2004. [CrossRef]
- P. Humblet and M. Azioglou, "On the bit error rate of lightwave systems with optical amplifiers," J. Lightwave Technol., 9, 1576-1582, 1991. [CrossRef]
- W. A. Atia and R. S. Bondurant, "Demonstration of return-to-zero signaling in both OOK and DPSK formats to improve receiver sensitivity in an optically preamplified receiver," Proc. LEOS 12th Annual meeting, 226-227, 1999.
- J. S. Sinsky, A. Adamiecki, A. Gnauck, C. Burrus, J. Leuthold, O. Wohlgemuth and A. Umbach,"A 42.7- Gb/s integrated balanced optical front end with record sensitivity," Proc. Conf. on Optical Fiber Communications, OFC'03, paper PD39, 2003.
- A. Agata, K. Tanaka, and N. Edagawa, "Study on the optimum ReedÐSolomon-based FEC codes for 40-Gb/sbased ultralong-distance WDM transmission," J. Lightwave Technol., 20, 2189-2195, 2002. [CrossRef]

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