## Evaluation of four-dimensional nonbinary LDPC-coded modulation for next-generation long-haul optical transport networks |

Optics Express, Vol. 20, Issue 8, pp. 9296-9301 (2012)

http://dx.doi.org/10.1364/OE.20.009296

Acrobat PDF (909 KB)

### Abstract

Leveraging the advanced coherent optical communication technologies, this paper explores the feasibility of using four-dimensional (4D) nonbinary LDPC-coded modulation (4D-NB-LDPC-CM) schemes for long-haul transmission in future optical transport networks. In contrast to our previous works on 4D-NB-LDPC-CM which considered amplified spontaneous emission (ASE) noise as the dominant impairment, this paper undertakes transmission in a more realistic optical fiber transmission environment, taking into account impairments due to dispersion effects, nonlinear phase noise, Kerr nonlinearities, and stimulated Raman scattering in addition to ASE noise. We first reveal the advantages of using 4D modulation formats in LDPC-coded modulation instead of conventional two-dimensional (2D) modulation formats used with polarization-division multiplexing (PDM). Then we demonstrate that 4D LDPC-coded modulation schemes with nonbinary LDPC component codes significantly outperform not only their conventional PDM-2D counterparts but also the corresponding 4D bit-interleaved LDPC-coded modulation (4D-BI-LDPC-CM) schemes, which employ binary LDPC codes as component codes. We also show that the transmission reach improvement offered by the 4D-NB-LDPC-CM over 4D-BI-LDPC-CM increases as the underlying constellation size and hence the spectral efficiency of transmission increases. Our results suggest that 4D-NB-LDPC-CM can be an excellent candidate for long-haul transmission in next-generation optical networks.

© 2012 OSA

## 1. Introduction

1. Y. Miyamoto and S. Suzuki, “Advanced optical modulation and multiplexing technologies for high-capacity OTN based on 100 Gb/s channel and beyond,” IEEE Commun. Mag. **48**(3), S65–S72 (2010). [CrossRef]

3. H. G. Batshon, I. B. Djordjevic, and T. Schmidt, “Ultra high speed optical transmission using subcarrier-multiplexed four-dimensional LDPC-coded modulation,” Opt. Express **18**(19), 20546–20551 (2010). [CrossRef] [PubMed]

5. M. Arabaci, I. B. Djordjevic, L. Xu, and T. Wang, “Four-dimensional nonbinary LDPC-coded modulation schemes for ultra high-speed optical fiber communication,” IEEE Photon. Technol. Lett. **23**(18), 1280–1282 (2011). [CrossRef]

6. I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Proposal for beyond 100 Gb/s optical transmission based on bit-interleaved LDPC-coded modulation,” IEEE Photon. Technol. Lett. **19**(12), 874–876 (2007). [CrossRef]

7. 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]

3. H. G. Batshon, I. B. Djordjevic, and T. Schmidt, “Ultra high speed optical transmission using subcarrier-multiplexed four-dimensional LDPC-coded modulation,” Opt. Express **18**(19), 20546–20551 (2010). [CrossRef] [PubMed]

5. M. Arabaci, I. B. Djordjevic, L. Xu, and T. Wang, “Four-dimensional nonbinary LDPC-coded modulation schemes for ultra high-speed optical fiber communication,” IEEE Photon. Technol. Lett. **23**(18), 1280–1282 (2011). [CrossRef]

## 2. Optical transmission setup

*R*and 0.75

_{s}*R*, respectively, where

_{s}*R*is the symbol rate which is defined as the information bit rate

_{s}*R*= 40 Gb/s divided by the FEC code rate

_{i}*R*, which is set to

*R*= 0.8, corresponding to 25% ( = 1/

*R*- 1) overhead. For efficient encoding and hardware-friendly decoding, we employ regular and quasi-cyclic (QC-) LDPC codes. More specifically, our binary QC-LDPC component code is the (3,15)-regular QC-LDPC(16935, 13550) code whose construction was described in detail in our previous work [8

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

*q*-ary LDPC codes were obtained by randomly assigning nonzero elements from the finite field of

*q*elements to the 1s in that of the QC-LDPC(16935, 13550) binary code, while ensuring that the QC property is preserved. For more details on how

*q*-ary QC-LDPC codes can be obtained from binary QC-LDPC codes, we refer the interested readers to our previous works [8

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

9. M. Arabaci, I. B. Djordjevic, R. Saunders, and R. M. Marcoccia, “Polarization-multiplexed rate-adaptive non-binary-quasi-cyclic-LDPC-coded multilevel modulation with coherent detection for optical transport networks,” Opt. Express **18**(3), 1820–1832 (2010). [CrossRef] [PubMed]

3. H. G. Batshon, I. B. Djordjevic, and T. Schmidt, “Ultra high speed optical transmission using subcarrier-multiplexed four-dimensional LDPC-coded modulation,” Opt. Express **18**(19), 20546–20551 (2010). [CrossRef] [PubMed]

## 3. Four-dimensional nonbinary LDPC-coded modulation

*m*parallel binary information streams of length

*K*bits each (see also Fig. 3 ). We can consider these

*m*parallel bit streams as a single nonbinary stream over an alphabet of

*q*= 2

*symbols. This*

^{m}*q*-ary information stream of length

*K*is encapsulated into a codeword of length

*N*symbols by a

*q*-ary LDPC encoder of code rate

*R*=

*K*/

*N*. The mapper maps each

*q*-ary codeword symbol to a

*q*-ary 4D constellation point

**= (**

*s**I*

_{x},

*Q*

_{x},

*I*

_{y},

*Q*

_{y}), where

*I*and

_{x}*Q*correspond to the in-phase and quadrature components in x-polarization, while

_{x}*I*and

_{y}*Q*correspond to those in y-polarization. The output of the mapper is used to drive the 4D modulator, composed of a distributed feedback (DFB) laser, a polarization beam splitter (PBS), two I/Q modulators and a polarization beam combiner (PBC). At the Rx side, the received optical signal is first split into two polarizations using the PBS and the resulting signals are fed to two balanced coherent detectors. Outputs of the coherent detectors are sampled at the symbol rate to obtain the estimates on the coordinates corresponding to the transmitted symbols and then passed to the equalizer employing Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm [10, and references therein]. Compared to the conventional 2D schemes where each polarization branch is equipped with a separate BCJR equalizer block, the proposed 4D scheme uses a single BCJR equalizer which handles both polarizations simultaneously, and hence, it can compensate for the nonlinear crosstalk between polarizations, whereas the conventional 2D schemes lack such capability. The BCJR equalizer is initialized by the probability distribution functions estimated with the help of histograms. The symbol LLRs at the output of the BCJR equalizer are finally forwarded to a

_{y}*q*-ary LDPC decoder matched to the encoder at the transmitter side. The estimates of the

*m*information sequences sent by the transmitter are then passed to the sink.

*q*-ary LDPC encoder, the Tx of 4D-BI-LDPC-CM features

*m*parallel binary LDPC encoders each processing its corresponding information bit stream. To make a fair comparison between the two schemes, in 4D-BI-LDPC-CM, we also consider LDPC codes with code rates

*R = K*/

*N*in each parallel branch. The codewords are then placed in an

*m*×

*N*block-interleaver row-wise. The mapper reads the data out of the interleaver column-wise and maps the

*m*-bit tuple to a 2

*-ary constellation symbol. The rest of the operations are the same as those performed by the Tx of 4D-NB-LDPC-CM. At the Rx side, as the binary LDPC decoders require bit LLRs to initialize the decoding process, the symbol LLRs produced by the BCJR equalizer are converted to bit LLRs. Upon decoding, the extrinsic information (bit LLRs after decoding minus those before decoding) from the LDPC decoders are fed back to the BCJR equalizer. This is the infamous turbo equalization operation [6*

^{m}6. I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Proposal for beyond 100 Gb/s optical transmission based on bit-interleaved LDPC-coded modulation,” IEEE Photon. Technol. Lett. **19**(12), 874–876 (2007). [CrossRef]

10. M. Tüchler, R. Koetter, and A. Singer, “Turbo equalization: Principles and new results,” IEEE Trans. Commun. **50**(5), 754–767 (2002). [CrossRef]

11. I. B. Djordjevic, L. L. Minkov, L. Xu, and T. Wang, “Suppression of fiber nonlinearities and PMD in coded-modulation schemes with coherent detection by using turbo equalization,” J. Opt. Commun. Netw. **1**(6), 555–564 (2009). [CrossRef]

6. I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Proposal for beyond 100 Gb/s optical transmission based on bit-interleaved LDPC-coded modulation,” IEEE Photon. Technol. Lett. **19**(12), 874–876 (2007). [CrossRef]

10. M. Tüchler, R. Koetter, and A. Singer, “Turbo equalization: Principles and new results,” IEEE Trans. Commun. **50**(5), 754–767 (2002). [CrossRef]

11. I. B. Djordjevic, L. L. Minkov, L. Xu, and T. Wang, “Suppression of fiber nonlinearities and PMD in coded-modulation schemes with coherent detection by using turbo equalization,” J. Opt. Commun. Netw. **1**(6), 555–564 (2009). [CrossRef]

*q*-ary state space. In order to provide 4D-NB-LDPC-CM with a comparable number of iterations, we set the number of decoding iterations in

*q*-ary LDPC decoder to the maximum of 50 iterations. Although this gives an advantage to the BI-LDPC-CM in terms of the total number of decoding iterations, we observed that running more than 50 iterations in nonbinary LDPC decoders does not enhance error correction performance.

## 4. Numerical results and analysis

**19**(12), 874–876 (2007). [CrossRef]

7. 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]

*R*symbols/s and that they both employ component LDPC codes of code rate

_{s}*R*, the information bit rate of the 4D scheme is given by

*RR*log

_{s}_{2}(

*M*

_{4D}) and that of the PDM-2D scheme is given by 2

*RR*log

_{s}_{2}(

*M*

_{2D}), both in information-bits/s, where

*M*

_{4D}and

*M*

_{2D}are the constellation sizes used in the 4D scheme and the PDM-2D scheme, respectively. Thus, the proposed 4D scheme is comparable to a PDM-2D scheme, in aggregate data rate, when

*M*

_{4D}= (

*M*

_{2D})

^{2}. For example, the 4D scheme with a signal constellation of size 16, which will be called as the 16-4D scheme, is comparable to PDM-QPSK. Similarly, 64-4D scheme is comparable to PDM-8QAM. The aggregate bit rates then become (i) 4 × 50 × 0.8 = 160 Gb/s for 16-4D and PDM-QPSK, and (ii) 6 × 50 × 0.8 = 240 Gb/s for 64-4D and PDM-8QAM.

7. 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]

**18**(19), 20546–20551 (2010). [CrossRef] [PubMed]

**19**(12), 874–876 (2007). [CrossRef]

11. I. B. Djordjevic, L. L. Minkov, L. Xu, and T. Wang, “Suppression of fiber nonlinearities and PMD in coded-modulation schemes with coherent detection by using turbo equalization,” J. Opt. Commun. Netw. **1**(6), 555–564 (2009). [CrossRef]

## 5. Conclusion

## Acknowledgments

## References and links

1. | Y. Miyamoto and S. Suzuki, “Advanced optical modulation and multiplexing technologies for high-capacity OTN based on 100 Gb/s channel and beyond,” IEEE Commun. Mag. |

2. | L.-S. Yan, X. Liu, and W. Shieh, “Toward the Shannon limit of spectral efficiency,” IEEE Photon. J. |

3. | H. G. Batshon, I. B. Djordjevic, and T. Schmidt, “Ultra high speed optical transmission using subcarrier-multiplexed four-dimensional LDPC-coded modulation,” Opt. Express |

4. | E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightwave Technol. |

5. | M. Arabaci, I. B. Djordjevic, L. Xu, and T. Wang, “Four-dimensional nonbinary LDPC-coded modulation schemes for ultra high-speed optical fiber communication,” IEEE Photon. Technol. Lett. |

6. | I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Proposal for beyond 100 Gb/s optical transmission based on bit-interleaved LDPC-coded modulation,” IEEE Photon. Technol. Lett. |

7. | 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. |

8. | I. B. Djordjevic, M. Arabaci, and L. L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightwave Technol. |

9. | M. Arabaci, I. B. Djordjevic, R. Saunders, and R. M. Marcoccia, “Polarization-multiplexed rate-adaptive non-binary-quasi-cyclic-LDPC-coded multilevel modulation with coherent detection for optical transport networks,” Opt. Express |

10. | M. Tüchler, R. Koetter, and A. Singer, “Turbo equalization: Principles and new results,” IEEE Trans. Commun. |

11. | I. B. Djordjevic, L. L. Minkov, L. Xu, and T. Wang, “Suppression of fiber nonlinearities and PMD in coded-modulation schemes with coherent detection by using turbo equalization,” J. Opt. Commun. Netw. |

**OCIS Codes**

(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

(060.4080) Fiber optics and optical communications : Modulation

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: February 14, 2012

Revised Manuscript: March 30, 2012

Manuscript Accepted: April 1, 2012

Published: April 6, 2012

**Citation**

Yequn Zhang, Murat Arabaci, and Ivan B. Djordjevic, "Evaluation of four-dimensional nonbinary LDPC-coded modulation for next-generation long-haul optical transport networks," Opt. Express **20**, 9296-9301 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-8-9296

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### References

- Y. Miyamoto and S. Suzuki, “Advanced optical modulation and multiplexing technologies for high-capacity OTN based on 100 Gb/s channel and beyond,” IEEE Commun. Mag.48(3), S65–S72 (2010). [CrossRef]
- L.-S. Yan, X. Liu, and W. Shieh, “Toward the Shannon limit of spectral efficiency,” IEEE Photon. J.3, 325–328 (2011).
- H. G. Batshon, I. B. Djordjevic, and T. Schmidt, “Ultra high speed optical transmission using subcarrier-multiplexed four-dimensional LDPC-coded modulation,” Opt. Express18(19), 20546–20551 (2010). [CrossRef] [PubMed]
- E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightwave Technol.27(22), 5115–5126 (2009). [CrossRef]
- M. Arabaci, I. B. Djordjevic, L. Xu, and T. Wang, “Four-dimensional nonbinary LDPC-coded modulation schemes for ultra high-speed optical fiber communication,” IEEE Photon. Technol. Lett.23(18), 1280–1282 (2011). [CrossRef]
- I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, “Proposal for beyond 100 Gb/s optical transmission based on bit-interleaved LDPC-coded modulation,” IEEE Photon. Technol. Lett.19(12), 874–876 (2007). [CrossRef]
- 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]
- I. B. Djordjevic, M. Arabaci, and L. L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightwave Technol.27(16), 3518–3530 (2009). [CrossRef]
- M. Arabaci, I. B. Djordjevic, R. Saunders, and R. M. Marcoccia, “Polarization-multiplexed rate-adaptive non-binary-quasi-cyclic-LDPC-coded multilevel modulation with coherent detection for optical transport networks,” Opt. Express18(3), 1820–1832 (2010). [CrossRef] [PubMed]
- M. Tüchler, R. Koetter, and A. Singer, “Turbo equalization: Principles and new results,” IEEE Trans. Commun.50(5), 754–767 (2002). [CrossRef]
- I. B. Djordjevic, L. L. Minkov, L. Xu, and T. Wang, “Suppression of fiber nonlinearities and PMD in coded-modulation schemes with coherent detection by using turbo equalization,” J. Opt. Commun. Netw.1(6), 555–564 (2009). [CrossRef]

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