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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 17 — Aug. 15, 2011
  • pp: 16708–16714
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Energy-efficient spatial-domain-based hybrid multidimensional coded-modulations enabling multi-Tb/s optical transport

Ivan B. Djordjevic  »View Author Affiliations


Optics Express, Vol. 19, Issue 17, pp. 16708-16714 (2011)
http://dx.doi.org/10.1364/OE.19.016708


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Abstract

In addition to capacity, the future high-speed optical transport networks will also be constrained by energy consumption. In order to solve the capacity and energy constraints simultaneously, in this paper we propose the use of energy-efficient hybrid D-dimensional signaling (D>4) by employing all available degrees of freedom for conveyance of the information over a single carrier including amplitude, phase, polarization and orbital angular momentum (OAM). Given the fact that the OAM eigenstates, associated with the azimuthal phase dependence of the complex electric field, are orthogonal, they can be used as basis functions for multidimensional signaling. Since the information capacity is a linear function of number of dimensions, through D-dimensional signal constellations we can significantly improve the overall optical channel capacity. The energy-efficiency problem is solved, in this paper, by properly designing the D-dimensional signal constellation such that the mutual information is maximized, while taking the energy constraint into account. We demonstrate high-potential of proposed energy-efficient hybrid D-dimensional coded-modulation scheme by Monte Carlo simulations.

© 2011 OSA

1. Introduction

The exponential internet traffic growth projections require considerable increase of transmission rates at every level of the underlying information infrastructure, from core to access and data center networks. Higher volumes of traffic also increase the energy consumption of transmission and switching equipment needed to route this traffic. Recent studies indicate that the energy consumed by the Internet equipment is roughly 8% of the total energy consumed in the US with predictions that it can grow up to 50%, with current trend, by the end of this decade [1

1. B. G. Bathula, M. Alresheedi, and J. M. H. Elmirghani, “Energy efficient architectures for optical networks,” in Proc. IEEE London Communications Symposium, London, Sept. 2009.

,2

2. N. Vasic, and D. Kostic, “Energy-aware traffic engineering” in EPFL Technical Report, (2008).

]. Therefore, the Internet is becoming constrained not only by capacity, but also by its energy consumption.

In order to solve high-bandwidth demands and energy-efficiency problems simultaneously, in this paper, we propose an energy-efficient spatial-domain-based hybrid coded-modulation scheme. The proposed scheme is based on hybrid D-dimensional (D>4) signal constellations, and exploits all available degrees of freedom for conveyance of the information over a single carrier including amplitude, phase, polarization and OAM. From Shannon’s theory we know that the channel capacity is a logarithmic function of signal-to-noise ratio, but linear function in number of dimensions. Therefore, by increasing the number of dimensions we can dramatically improve the overall channel capacity. On the other hand, the energy-efficiency problem can be solved by properly designing the D-dimensional signal constellation such that the mutual information is maximized, while taking the energy constraint into account. We demonstrate high-potential of proposed energy-efficient hybrid D-dimensional coded-modulation scheme by Monte Carlo simulations. The proposed coded-modulation scheme is very flexible, it can be used for various applications ranging from short-haul to long-haul, and can be used in both single-mode fiber (SMF) and MMF links.

The remainder of the paper is organized as follows. In Section 2, we describe the energy-efficient signal constellation design. In Section 3, we describe the proposed energy-efficient spatial-domain-based hybrid low-density parity-check (LDPC)-coded modulation scheme. We present our numerical results and discuss their significance in Section 4. Finally, some important concluding remarks are given in Section 5.

2. Energy-efficient signal constellation design

The basic energy-efficient optical communication problem can be formulated as follows. The set of symbols X = {x 1, x 2,…,xM} that occur with a priori probabilities p 1,…,pM [pi = Pr(xi)]; with corresponding energies E 1,…,EM; are to be transmitted over the optical channel of interest. The symbols from the set X satisfy the following two constraints: (1) ∑i pi = 1 (probability constraint) and (2) ∑i piEiE (energy constraint). In the presence of amplified spontaneous emission (ASE) noise and various channel impairments (fiber nonlinearities, PMD, PDL and filtering effects), we can use the Lagranagian method in maximizing the mutual information I(X,Y), defined as I(X,Y) = H(X)-H(X|Y), where H(X) is the entropy of the channel input X and H(X|Y) is the conditional entropy of channel input X given the channel output Y. The corresponding Lagranagian, by taking energy and probability constraints into account, can be formulated as follows:
L=ipilogpiH(X)(ipijPijlogQjiH(X|Y))+λ(ipi1)+μ(ipiEiE),
(1)
where with Pij we denoted the transition probabilities Pij = Pr(yj|xi), which can be determined by channel estimation or for ASE noise dominated scenario we can use Gaussian approximation. In Eq. (1), with Qji we denoted Pr(xi|yj), which can be determined by Bayes’ rule as Qji = Pr(xi|yj) = Pr(xi,yj)/Pr(yj) = Pijpi/∑kPkjpk. The optimum signal constellation coordinates cannot be found in analytical form, however, we can use Arimoto-Blahut-like algorithm, but now taking the energy constraint into account. The energy-efficient Arimoto-Blahut algorithm (EE-ABA) can be formulated as follows:
  • 0) Initialization: Choose arbitrary input distribution, say uniform pi = 1/M.
  • 1) Qji update-rule: Qji(t)=Pijpi(t)/kPkjpk(t),   Pij=Pr(yj|xi).
  • 2) pi update-rule: pi(t+1)=exp(μEiH(t)(xi|Y))kexp(μEkH(t)(xk|Y)),
where H(xi|Y)=kPiklogQki and the parameter μ is determined from energy constraint. Repeat the steps 1)-2) until convergence. (The superscript (t) denotes the iteration index.).

The step 1) is derived based on Bayes’ rule: Qji = Pr(xi|yj) = Pr(xi,yj)/Pr(yj) = Pijpi/∑kPkjpk. In the absence of noise and channel impairments we set the conditional entropy term in step 2) to zero and obtain the Gibbs distribution pi = exp(-βEi)/[∑k exp(-βEk)]. Notice that original Arimoto-Blahut algorithm [15

15. R. E. Blahut, “Computation of channel capacity and rate distortion functions,” IEEE Trans. Inf. Theory 18(4), 460–473 (1972). [CrossRef]

] does not impose the energy constraint. By EE-ABA, we obtain the optimum source distribution, while taking the energy constraint into account. Unfortunately, it is not practical to use the signal constellation points with non-uniform distribution. To solve this problem, we propose to apply this algorithm for an auxiliary signal constellation with significantly larger number of constellation points M’ than desired signal constellation size M, such that M’>>M, and then determine the desired constellation points as a center of mass of closest M’/M constellation points in this auxiliary signal constellation.

As an illustration, in Fig. 1
Fig. 1 Information capacities per dimension for different normalized energy cost values and different number of amplitude levels per dimension L: (a) coherent detection case, and (b) direct detection case.
we report the information capacities for different normalized energy cost functions for number of amplitude levels per dimension L. In Fig. 1(a), we provide the results corresponding to coherent detection, while in Fig. 1(b) we provide the results corresponding to direct detection. It is clear from the Figure, that when the normalized energy cost function is lower than one, we are facing certain information capacity degradation. For channel model we use I-ary input J-ary output (J>I) channel model, which is a valid model for reasonably high signal-to-noise ratios (SNRs).

3. Energy-efficient hybrid coded-modulations schemes enabling multi-Tb/s optical transport

The spectral efficiency of the proposed hybrid D-dimensional scheme, where D = 2MN, is
SED-dim.constellationSEPDM-QAM=log2LD2log2MQAM=Dlog2L2log2MQAM
(4)
times better than that of polarization-division-multiplexed (PDM) quadrature amplitude modulation (QAM) scheme. In (4), with M QAM we denoted the QAM signal constellation size. Therefore, for the same number of amplitude levels per dimension (M QAM = L 2), the spectral efficiency of the proposed scheme is (D/4)-times better than that of PDM-QAM. The aggregate data rate (per single wavelength) is determined by
log2(L2MN) ch . bitsch . sym .×Rs ch . sym .s×r info . bitsch . bits,
(5)
where r is the code rate, which is assumed to be equal for LDPC codes at each level, and R s is the symbol rate.

4. Performance analysis

We evaluate the bit-error rate (BER) performance of the proposed energy-efficient spatial-domain-based hybrid D-dimensional LDPC-coded modulation and compare it against the performance of the corresponding coded PDM-QAM. We performed Monte Carlo simulations for ASE noise scenario for three APP demapper-LDPC decoder iterations and 25 LDPC decoder inner iterations. The results of simulations are shown in Fig. 3
Fig. 3 Energy-efficient hybrid LDPC-coded modulation.
, where we compare BER performance of energy-efficient polarization-division multiplexed (EE-PDM) (column-weight-3, girth-10) (16935,13550) LDPC coded modulation (CM) against that of PDM-QAM (for the same LDPC code). It is clear that for fixed L, the increase in the number of dimensions leads to small performance degradation as long as orthogonality of basis functions is preserved. The aggregate data rate of EE PDM coded-modulation scheme, per single OAM mode, is determined by 2 × Rs × log2(LM) × r / OAM mode, where Rs is the symbol rate and r is the code rate. By setting R s = 31.25 Giga symbols/s (GS/s)/OAM mode, r = 0.8, L = 4, and M = 4 the aggregate data rate is 400 Gb/s, which is compatible with 400 Gb/s Ethernet when one OAM mode is used. As another example, by setting L = 4, M = 8, R s = 50 GS/s, and r = 0.8, the aggregate data rate is 1.28 Tb/s/OAM mode, which is compatible with Tb/s Ethernet when one OAM mode is used. On the other hand, the aggregate data rate of PDM 256-QAM, for R s = 50 GS/s and r = 0.8, is 2 × Rs × log2(256) × r = 640 Gb/s, which is not sufficient for Tb/s Ethernet. Let us now compare the performance of EE PDM L = 4, M = 4 coded-modulation with PDM 256-QAM, having the same number of constellation points. At BER of 2.5 × 10−7, the L = 4, M = 4 EE-PDM coded modulation scheme outperforms corresponding PDM 256-QAM by even 9.98 dB! In the same Figure, we provide the curve for three-dimensional signal-constellation with 64 points, obtained by sphere packing method due to Sloane [16

16. N. J. A. Sloane, R. H. Hardin, T. S. Duff, and J. H. Conway, “Minimal-energy clusters of hard spheres,” Discrete Comput. Geom. 14(1), 237–259 (1995). [CrossRef]

]. The EE-PDM scheme with L = 4, M = 4 outperforms the sphere packing scheme by 0.98 dB at BER of 5.7 × 10−7. Notice that aggregate data rate of EE-PDM scheme for L = M = 4 with Rs = 31.25 GS/s is 400 Gb/s, while the aggregate data rate of PDM sphere packing constellation is only 300 Gb/s. The proposed EE spatial-domain-based hybrid coded-modulation scheme is, therefore, a promising candidate for both 400 Gb/s and Tb/s Ethernet technologies, while significantly outperforming the conventional PDM-QAM. By using several OAM modes (two modes are used in EE CM schemes shown in Fig. 3), we can clearly achieve multi-Tb/s serial optical transport.

5. Concluding remarks

Inspired by high potential of multidimensional signal constellations and recent demonstrations in which OAM modes are successfully excited in MMFs, we proposed the use of energy-efficient spatial-domain-based hybrid coded D-dimensional modulation as an enabling technology for multi-Tb/s serial optical transport. We demonstrated by simulations that proposed energy-efficient coded modulation scheme significantly outperforms conventional PDM-QAM scheme. As an example, the L = 4, M = 4 EE-PDM coded modulation scheme outperforms corresponding PDM 256-QAM by even 9.98 dB at BER of 2.5 × 10−7. We also have presented an energy-efficient Arimoto-Blahut algorithm and described how it can be used in energy-efficient signal constellation design. Finally, we demonstrated that proposed energy-efficient signal constellations can be used to enable 400 Gb/s Ethernet, Tb/s Ethernet, and multi-Tb/s serial optical transport.

Acknowledgments

This work was supported in part by the National Science Foundation (NSF) under Grant CCF-0952711, through NSF CIAN ERC under grant EEC-0812072, and in part by NEC Labs.

References and links

1.

B. G. Bathula, M. Alresheedi, and J. M. H. Elmirghani, “Energy efficient architectures for optical networks,” in Proc. IEEE London Communications Symposium, London, Sept. 2009.

2.

N. Vasic, and D. Kostic, “Energy-aware traffic engineering” in EPFL Technical Report, (2008).

3.

I. Djordjevic, H. G. Batshon, L. Xu, and T. Wang, “Four-dimensional optical multiband-OFDM for beyond 1.4 Tb/s serial optical transmission,” Opt. Express 19(2), 876–882 (2011). [CrossRef] [PubMed]

4.

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.

I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010). [CrossRef] [PubMed]

6.

I. B. Djordjevic, M. Arabaci, L. Xu, and T. Wang, “Spatial-domain-based multidimensional modulation for multi-Tb/s serial optical transmission,” Opt. Express 19(7), 6845–6857 (2011). [CrossRef] [PubMed]

7.

S. Murshid and A. Chakravarty, “Tapered optical fiber quadruples bandwidth of multimode silica fibers using same wavelength,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper FWI2.

8.

S. H. Murshid and J. Iqbal, “Spatial combination of optical channels in a multimode waveguide,” in Laser Science, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JWA32.

9.

I. B. Djordjevic, “Heterogeneous transparent optical networking based on coded OAM modulation,” IEEE Photon. J. 3(3), 531–537 (2011). [CrossRef]

10.

A. Li, A. Al Amin, X. Chen, and W. Shieh, “Reception of mode and polarization multiplexed 107-Gb/s CO-OFDM signal over a two-mode fiber,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC), Postdeadlines Papers (Optical Society of America, 2011), Paper PDPB8.

11.

M. Salsi, C. Koebele, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Bigot-Astruc, L. Provost, F. Cerou, and G. Charlet, “Transmission at 2x100Gb/s, over two modes of 40km-long prototype few-mode fiber, using LCOS-based mode multiplexer and demultiplexer,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC), Postdeadlines Papers (Optical Society of America, 2011), Paper PDPB9.

12.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, R.-J. Essiambre, P. Winzer, D. W. Peckham, A. McCurdy, and R. Lingle, “Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC), Postdeadlines Papers (Optical Society of America, 2011), Paper PDPB10.

13.

J. Sakaguchi, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, T. Hayashi, T. Taru, T. Kobayashi, and M. Watanabe, “109-Tb/s (7×97×172-Gb/s SDM/WDM/PDM) QPSK transmission though 16.8-km homogeneous multi-core fiber,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC), Postdeadlines Papers (Optical Society of America, 2011), paper PDPB6.

14.

B. Zhu, T. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. Yan, J. Fini, E. Monberg, F. Dimarcello, K. Abedin, P. Wisk, D. Peckham, and P. Dziedzic, “Space-, wavelength-, polarization-division multiplexed transmission of 56-Tb/s over a 76.8-km seven-core fiber,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC), Postdeadlines Papers (Optical Society of America, 2011), Paper PDPB7.

15.

R. E. Blahut, “Computation of channel capacity and rate distortion functions,” IEEE Trans. Inf. Theory 18(4), 460–473 (1972). [CrossRef]

16.

N. J. A. Sloane, R. H. Hardin, T. S. Duff, and J. H. Conway, “Minimal-energy clusters of hard spheres,” Discrete Comput. Geom. 14(1), 237–259 (1995). [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:
Capacity Limits

History
Original Manuscript: June 20, 2011
Revised Manuscript: July 20, 2011
Manuscript Accepted: July 26, 2011
Published: August 15, 2011

Virtual Issues
Space Multiplexed Optical Transmission (2011) Optics Express

Citation
Ivan B. Djordjevic, "Energy-efficient spatial-domain-based hybrid multidimensional coded-modulations enabling multi-Tb/s optical transport," Opt. Express 19, 16708-16714 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-17-16708


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References

  1. B. G. Bathula, M. Alresheedi, and J. M. H. Elmirghani, “Energy efficient architectures for optical networks,” in Proc. IEEE London Communications Symposium, London, Sept. 2009.
  2. N. Vasic, and D. Kostic, “Energy-aware traffic engineering” in EPFL Technical Report, (2008).
  3. I. Djordjevic, H. G. Batshon, L. Xu, and T. Wang, “Four-dimensional optical multiband-OFDM for beyond 1.4 Tb/s serial optical transmission,” Opt. Express 19(2), 876–882 (2011). [CrossRef] [PubMed]
  4. 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. I. B. Djordjevic and M. Arabaci, “LDPC-coded orbital angular momentum (OAM) modulation for free-space optical communication,” Opt. Express 18(24), 24722–24728 (2010). [CrossRef] [PubMed]
  6. I. B. Djordjevic, M. Arabaci, L. Xu, and T. Wang, “Spatial-domain-based multidimensional modulation for multi-Tb/s serial optical transmission,” Opt. Express 19(7), 6845–6857 (2011). [CrossRef] [PubMed]
  7. S. Murshid and A. Chakravarty, “Tapered optical fiber quadruples bandwidth of multimode silica fibers using same wavelength,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper FWI2.
  8. S. H. Murshid and J. Iqbal, “Spatial combination of optical channels in a multimode waveguide,” in Laser Science, OSA Technical Digest (CD) (Optical Society of America, 2010), paper JWA32.
  9. I. B. Djordjevic, “Heterogeneous transparent optical networking based on coded OAM modulation,” IEEE Photon. J. 3(3), 531–537 (2011). [CrossRef]
  10. A. Li, A. Al Amin, X. Chen, and W. Shieh, “Reception of mode and polarization multiplexed 107-Gb/s CO-OFDM signal over a two-mode fiber,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC), Postdeadlines Papers (Optical Society of America, 2011), Paper PDPB8.
  11. M. Salsi, C. Koebele, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Bigot-Astruc, L. Provost, F. Cerou, and G. Charlet, “Transmission at 2x100Gb/s, over two modes of 40km-long prototype few-mode fiber, using LCOS-based mode multiplexer and demultiplexer,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC), Postdeadlines Papers (Optical Society of America, 2011), Paper PDPB9.
  12. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, R.-J. Essiambre, P. Winzer, D. W. Peckham, A. McCurdy, and R. Lingle, “Space-division multiplexing over 10 km of three-mode fiber using coherent 6 × 6 MIMO processing,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC), Postdeadlines Papers (Optical Society of America, 2011), Paper PDPB10.
  13. J. Sakaguchi, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, T. Hayashi, T. Taru, T. Kobayashi, and M. Watanabe, “109-Tb/s (7×97×172-Gb/s SDM/WDM/PDM) QPSK transmission though 16.8-km homogeneous multi-core fiber,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC), Postdeadlines Papers (Optical Society of America, 2011), paper PDPB6.
  14. B. Zhu, T. Taunay, M. Fishteyn, X. Liu, S. Chandrasekhar, M. Yan, J. Fini, E. Monberg, F. Dimarcello, K. Abedin, P. Wisk, D. Peckham, and P. Dziedzic, “Space-, wavelength-, polarization-division multiplexed transmission of 56-Tb/s over a 76.8-km seven-core fiber,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC), Postdeadlines Papers (Optical Society of America, 2011), Paper PDPB7.
  15. R. E. Blahut, “Computation of channel capacity and rate distortion functions,” IEEE Trans. Inf. Theory 18(4), 460–473 (1972). [CrossRef]
  16. N. J. A. Sloane, R. H. Hardin, T. S. Duff, and J. H. Conway, “Minimal-energy clusters of hard spheres,” Discrete Comput. Geom. 14(1), 237–259 (1995). [CrossRef]

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