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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 8 — Apr. 9, 2012
  • pp: 9296–9301
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Evaluation of four-dimensional nonbinary LDPC-coded modulation for next-generation long-haul optical transport networks

Yequn Zhang, Murat Arabaci, and Ivan B. Djordjevic  »View Author Affiliations


Optics Express, Vol. 20, Issue 8, pp. 9296-9301 (2012)
http://dx.doi.org/10.1364/OE.20.009296


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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

The rest of the paper is organized as follows. Section 2 explicates our optical transmission setup. In Section 3, we describe the transmitter and receiver configurations of the 4D nonbinary LDPC-coded modulation (4D-NB-LDPC-CM) and the prior-art 4D bit-interleaved LDPC-coded modulation (4D-BI-LDPC-CM) schemes. Similarities and differences between the two schemes are also highlighted. Section 4 presents our numerical results. It is shown that the 4D schemes significantly outperform their 2D counterparts employing polarization-division multiplexing (PDM). Furthermore, among the two 4D schemes, 4D-NB-LDPC-CM is shown to be superior to 4D-BI-LDPC-CM. Finally, Section 5 concludes our paper.

2. Optical transmission setup

Our 4D LDPC-coded modulation optical transmission system is depicted in Fig. 1
Fig. 1 Dispersion map of the 4D-LDPC-CM transmission system under test.
and is evaluated using VPI Transmission Maker v8.5. Our fiber model takes into account dispersion effects, ASE noise, and impairments due to nonlinear phase noise, Kerr nonlinearities and stimulated Raman scattering. Fiber parameters are listed in Table 1

Table 1. SMF and DCF parameters

table-icon
View This Table
. Our goal is to explore the fundamental limits on the transmission distances that could be achieved by the proposed 4D LDPC-coded modulation schemes (both binary and nonbinary) and compare them against those achievable by its counterpart polarization-division multiplexing 2D LDPC-coded modulation schemes. Thus, we assume perfect chromatic dispersion (CD) and polarization-mode dispersion (PMD) compensation. To achieve this in our simulations, we perform inline CD compensation via dispersion compensating fibers (DCFs) and adopt polarization tracking.

3. Four-dimensional nonbinary LDPC-coded modulation

In this section, we describe the transmitter (Tx) and receiver (Rx) configurations of 4D-NB-LDPC-CM scheme, and compare them against those of the prior-art 4D-BI-LDPC-CM scheme. The Tx/Rx structures of 4D-NB-LDPC-CM are depicted in Fig. 2
Fig. 2 (a) Transmitter and (b) receiver configurations of 4D-NB-LDPC-CM.
. The source signal entering the transmitter is indeed composed of m parallel binary information streams of length K bits each (see also Fig. 3
Fig. 3 (a) Transmitter and (b) receiver configurations of 4D-BI-LDPC-CM.
). We can consider these m parallel bit streams as a single nonbinary stream over an alphabet of q = 2m symbols. This 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 = (Ix, Qx, Iy, Qy), where Ix and Qx correspond to the in-phase and quadrature components in x-polarization, while Iy and Qy 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 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.

For comparison, we depicted 4D-BI-LDPC-CM Tx/Rx architectures in Fig. 3. The architectures in Fig. 2 and Fig. 3, although look quite similar, bear significant differences. Instead of a single 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 2m-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

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

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

,11

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]

]. (Note that although omitted in Fig. 3, the bit LLRs are combined to form symbol LLRs which are used by the BCJR equalizer as the a priori estimates on symbol LLRs). The underlying idea behind turbo equalization is to exploit the inherent dependence between bits of a transmitted symbol by combining the reliability estimates obtained by independently operating binary LDPC decoders on the bits of a transmitted symbol to form an initial reliability estimate on the transmitted symbol itself. In fact, such a feedback mechanism is of critical importance for bit-interleaved LDPC-coded modulation [6

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

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

,11

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]

]. The turbo-like decoder will stop when either convergence is achieved or a predefined number of feedback iterations is reached. In 4D-BI-LDPC-CM, we perform the maximum of 25 iterations in each binary LDPC decoder, and perform 3 outer iterations between the binary LDPC decoders and the BCJR equalizer. Thus, binary LDPC decoders are allowed to run for a maximum of 100 ( = 25 x 4) iterations in total. In 4D-NB-LDPC-CM, on the other hand, there is no need for outer iteration since both the equalizer and the nonbinary decoder operate on the 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

In order to attest the advantages of using 4D modulation formats, 4D LDPC-coded modulation schemes (both binary and nonbinary) are compared to their conventional counterparts employing PDM and 2D signal constellations, whose Tx and Rx configurations can be found in [6

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]

] for binary and in [7

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]

] for nonbinary LDPC-coded modulation. Effectively, 4D schemes use the state of polarization to define a larger signal constellation whereas PDM-2D schemes use it for multiplexing. For a fair comparison between the two schemes, we need to compare them when they both attain the same information bit rate. Regardless of being binary or nonbinary LDPC-coded modulation, if we assume that both the 4D scheme and the corresponding PDM-2D scheme operate at the same symbol rate of Rs symbols/s and that they both employ component LDPC codes of code rate R, the information bit rate of the 4D scheme is given by RRslog2(M4D) and that of the PDM-2D scheme is given by 2RRslog2(M2D), both in information-bits/s, where M4D and M2D 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 M4D = (M2D)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.

In order to further manifest the superiority of 4D-NB-LDPC-CM over 4D-BI-LDPC-CM, we performed comparisons between the two for three different 4D modulation formats, i.e., 16-, 32- and 64-4D. Our results are presented in Fig. 5
Fig. 5 BER vs. transmission distance comparison of 4D-NB-LDPC-CM and 4D-BI-LDPC-CM.
. Note that, in addition to 16-4D and 64-4D constellations, we also included simulations with 32-4D constellation into Fig. 5 in order to obtain a better insight into how the performances of 4D-BI-LDPC-CM and 4D-NB-LDPC-CM change as the underlying 4D constellation size changes. Concurring with the results obtained under ASE noise dominated transmission scenario presented in [7

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]

], 4D-NB-LDPC-CM significantly outperforms 4D-BI-LDPC-CM especially as the underlying constellation size, and hence the spectral efficiency, and hence the aggregate bit rates increase. For example, for transmission at 240 Gb/s, 4D-NB-LDPC-CM can provide more than 1500 km additional reach compared to 4D-BI-LDPC-CM. In addition to improving transmission reach compared to 4D-BI-LDPC-CM, 4D-NB-LDPC-CM can also improve the latency at the receiving ends since it avoids costly turbo equalization steps which passes through the inherently complex BCJR equalization block about 3 to 5 times for acceptable performance in BI-LDPC-CM schemes [3

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]

,6

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]

,11

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

We have evaluated the performance of four-dimensional nonbinary LDPC-coded modulation scheme suitable for next-generation optical transport networks (OTNs). We first revealed the advantages of utilizing a higher-dimensional modulation format in LDPC-coded modulation by comparing 4D schemes with the corresponding PDM-2D schemes. Further, we demonstrated that 4D-NB-LDPC-CM is much more advantageous to use compared to 4D-BI-LDPC-CM as it provides longer transmission reaches. We also noted than the improvement in transmission reach offered by 4D-NB-LDPC-CM over 4D-BI-LDPC-CM increases with increasing constellation size and hence increasing spectral efficiency, which is the direction that optical fiber communication is going toward. Given their superior performances, we strongly advocate adopting 4D-NB-LDPC-CM schemes over both 4D-BI-LDPC-CM and PDM-2D schemes for next-generation OTNs.

Acknowledgments

This work was supported in part by NSF under Grant CCF-0952711.

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. 48(3), S65–S72 (2010). [CrossRef]

2.

L.-S. Yan, X. Liu, and W. Shieh, “Toward the Shannon limit of spectral efficiency,” IEEE Photon. J. 3, 325–328 (2011).

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]

4.

E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightwave Technol. 27(22), 5115–5126 (2009). [CrossRef]

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]

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]

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]

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

  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]
  2. L.-S. Yan, X. Liu, and W. Shieh, “Toward the Shannon limit of spectral efficiency,” IEEE Photon. J.3, 325–328 (2011).
  3. 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]
  4. E. Agrell and M. Karlsson, “Power-efficient modulation formats in coherent transmission systems,” J. Lightwave Technol.27(22), 5115–5126 (2009). [CrossRef]
  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]
  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. Express18(3), 1820–1832 (2010). [CrossRef] [PubMed]
  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]

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