Abstract

We propose a coded N-dimensional modulation scheme suitable for ultra-high-speed serial optical transport. The proposed scheme can be considered as a generalization of OFDM, and hence, we call it as generalized OFDM (GOFDM). In this scheme, the orthogonal subcarriers are used as basis functions and the signal constellation points are defined over this N-dimensional linear space. To facilitate implementation, we propose using N-dimensional pulse-amplitude modulation (ND-PAM) as the signal constellation diagram, which is obtained as the N-ary Cartesian product of one-dimensional PAM. In conventional OFDM, QAM/PSK signal constellation points are transmitted over orthogonal subcarriers and then they are multiplexed together in an OFDM stream. Individual subcarriers, therefore, carry N parallel QAM/PSK streams. In the proposed GOFDM scheme instead, an N-dimensional signal constellation point is transmitted over all N subcarriers simultaneously. When some of the subcarriers are severely affected by channel impairments, the constellation points carried by those subcarriers may be lost in the conventional OFDM. In comparison, under such conditions, the overall signal constellation point will face only small distortion in GOFDM and it can be recovered successfully using the information on the other high fidelity subcarriers. Furthermore, because the channel capacity is a logarithmic function of signal-to-noise ratio but a linear function of the number of dimensions, the spectral efficiency of optical transmission systems can be improved with GOFDM.

© 2011 OSA

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References

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  1. J. Hong, T. Schmidt, M. Traverso, and E. Yoshikazu, “40G and 100G modules enable next generation networks,” Proc. SPIE 7631, 763115, 763115-7 (2009).
    [CrossRef]
  2. W. Shieh, and I. Djordjevic, OFDM for Optical Communications (Elsevier/Academic Press, 2009).
  3. Y. Ma, Q. Yang, Y. Tang, S. Chen, and W. Shieh, “1-Tb/s single-channel coherent optical OFDM transmission over 600-km SSMF fiber with subwavelength bandwidth access,” Opt. Express 17(11), 9421–9427 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  6. I. B. Djordjevic, M. Arabaci, and L. Minkov, “Next generation FEC for high-capacity communication in optical transport networks,” J. Lightwave Technol. 27(16), 3518–3530 (2009).
    [CrossRef]
  7. H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Modified hybrid subcarrier/amplitude/ phase/polarization LDPC-coded modulation for 400 Gb/s optical transmission and beyond,” Opt. Express 18(13), 14108–14113 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  14. M. C. Davey, Error-Correction using Low-Density Parity-Check Codes, Ph.D. dissertation, (University of Cambridge, 1999).
  15. T. M. Cover, and J. A. Thomas, Elements of Information Theory (Wiley, 1991).
  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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    [CrossRef] [PubMed]
  19. J. G. Proakis, Digital Communications (McGraw-Hill, 2001).

2010 (4)

2009 (7)

2007 (1)

J. McDonough, “Moving standards to 100 GbE and beyond,” IEEE Commun. Mag. 45(11), 6–9 (2007).
[CrossRef]

2004 (1)

M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory 50(8), 1788–1793 (2004).
[CrossRef]

1995 (1)

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]

Agrell, E.

Arabaci, M.

Batshon, H. G.

Chen, S.

Conway, J. H.

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]

Djordjevic, I. B.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Modified hybrid subcarrier/amplitude/ phase/polarization LDPC-coded modulation for 400 Gb/s optical transmission and beyond,” Opt. Express 18(13), 14108–14113 (2010).
[CrossRef] [PubMed]

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]

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]

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]

M. Arabaci, I. B. Djordjevic, R. Saunders, and R. M. Marcoccia, “High-rate non-binary regular quasi-cyclic LDPC codes for optical communications,” J. Lightwave Technol. 27(23), 5261–5267 (2009).
[CrossRef]

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
[CrossRef]

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

Duff, T. S.

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]

Fossorier, M. P. C.

M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory 50(8), 1788–1793 (2004).
[CrossRef]

Hardin, R. H.

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]

Hong, J.

J. Hong, T. Schmidt, M. Traverso, and E. Yoshikazu, “40G and 100G modules enable next generation networks,” Proc. SPIE 7631, 763115, 763115-7 (2009).
[CrossRef]

Karlsson, M.

Ma, Y.

Marcoccia, R. M.

McDonough, J.

J. McDonough, “Moving standards to 100 GbE and beyond,” IEEE Commun. Mag. 45(11), 6–9 (2007).
[CrossRef]

Minkov, L.

Saunders, R.

Schmidt, T.

Shieh, W.

Sloane, N. J. A.

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]

Tang, Y.

Traverso, M.

J. Hong, T. Schmidt, M. Traverso, and E. Yoshikazu, “40G and 100G modules enable next generation networks,” Proc. SPIE 7631, 763115, 763115-7 (2009).
[CrossRef]

Wang, T.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Modified hybrid subcarrier/amplitude/ phase/polarization LDPC-coded modulation for 400 Gb/s optical transmission and beyond,” Opt. Express 18(13), 14108–14113 (2010).
[CrossRef] [PubMed]

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
[CrossRef]

Xu, L.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Modified hybrid subcarrier/amplitude/ phase/polarization LDPC-coded modulation for 400 Gb/s optical transmission and beyond,” Opt. Express 18(13), 14108–14113 (2010).
[CrossRef] [PubMed]

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
[CrossRef]

Yang, Q.

Yoshikazu, E.

J. Hong, T. Schmidt, M. Traverso, and E. Yoshikazu, “40G and 100G modules enable next generation networks,” Proc. SPIE 7631, 763115, 763115-7 (2009).
[CrossRef]

Discrete Comput. Geom. (1)

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]

IEEE Commun. Mag. (1)

J. McDonough, “Moving standards to 100 GbE and beyond,” IEEE Commun. Mag. 45(11), 6–9 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, “Multidimensional LDPC-coded modulation for beyond 400 Gb/s per wavelength transmission,” IEEE Photon. Technol. Lett. 21(16), 1139–1141 (2009).
[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]

IEEE Trans. Inf. Theory (1)

M. P. C. Fossorier, “Quasi-cyclic low-density parity-check codes from circulant permutation matrices,” IEEE Trans. Inf. Theory 50(8), 1788–1793 (2004).
[CrossRef]

J. Lightwave Technol. (3)

Opt. Express (5)

Proc. SPIE (1)

J. Hong, T. Schmidt, M. Traverso, and E. Yoshikazu, “40G and 100G modules enable next generation networks,” Proc. SPIE 7631, 763115, 763115-7 (2009).
[CrossRef]

Other (5)

W. Shieh, and I. Djordjevic, OFDM for Optical Communications (Elsevier/Academic Press, 2009).

I. B. Djordjevic, L. Xu, and T. Wang, “Coded multidimensional pulse amplitude modulation for ultra-high-speed optical transmission,” in Proc. OFC/NFOEC 2011, Paper No. JThA041, Los Angeles Convention Center, Los Angeles, CA, USA, March 6–10, 2011.

M. C. Davey, Error-Correction using Low-Density Parity-Check Codes, Ph.D. dissertation, (University of Cambridge, 1999).

T. M. Cover, and J. A. Thomas, Elements of Information Theory (Wiley, 1991).

J. G. Proakis, Digital Communications (McGraw-Hill, 2001).

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Figures (3)

Fig. 1
Fig. 1

Proposed polarization-multiplexed LDPC-coded GOFDM scheme (only x-polarization branch is shown with all details): (a) Tx configuration and (b) Rx configuration. PBS/C: polarization beam splitter/combiner, 3 dB: 3 dB coupler, DAC: digital-to-analog conversion, ADC: analog-to-digital conversion, P/S: parallel-to-serial conversion, S/P: serial-to-parallel conversion, APP: a posteriori probability, LLRs: log-likelihood ratios.

Fig. 2
Fig. 2

GOFDM system performance: (a) uncoded symbol error-rates for symbol rate of 25 GS/s, and (b) binary-LDPC-coded GOFDM BER performance at symbol rate of 31.25 GS/s.

Fig. 3
Fig. 3

Nonbinary-LDPC-coded GOFDM BER performance.

Tables (1)

Tables Icon

Table 1 Mapping Rule Look-up Table for 43-3D-PAM Signal Constellation Used in OFDM

Equations (12)

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X N = X × X × × X N     t i m e s = { ( x 1 , x 2 , , x N ) | x i X ,       1 i N } .
λ ( s ( a ) ) = log [ P ( s ( a ) | r ) / P ( s ( 0 ) | r ) ] ,
P ( s ( a ) | r ) = P ( r | s ( a ) ) P ( s ( a ) ) / a P ( r | s ( a ) ) P ( s ( a ) ) .
λ ( s ( a ) ) = log [ ( P ( r | s ( a ) ) P ( s ( a ) ) ) / ( P ( r | s ( 0 ) ) P ( s ( 0 ) ) ) ] ,
L ( v ( a j ) ) = log [ s ( a ) :   a j = 1 exp ( λ ( s ( a ) ) ) / s ( a ) :   a j = 0 exp ( λ ( s ( a ) ) ) ] ,
H = [ I I I I I P S [ 1 ] P S [ 2 ] P S [ c 1 ] I P 2 S [ 1 ] P 2 S [ 2 ] P 2 S [ c 1 ] I P ( r 1 ) S [ 1 ] P ( r 1 ) S [ 2 ] P ( r 1 ) S [ c 1 ] ] ,
P c = ( 1 P s ( L PAM) ) N ,
P s ( L P A M ) = ( 1 1 L ) e r f c ( d 2 N 0 ) ,
P s = 1 ( 1 P s ( L P A M ) ) N = 1 [ 1 ( 1 1 L ) e r f c ( d 2 N 0 ) ] N .
E a v e = N 1 L i = 1 L A i 2 = N 1 L 1 3 L ( L 2 1 ) d N 2 = N 1 3 ( L 2 1 ) d N 2 ,
d N 2 = M = L N 2 ( L N 1 ) N ( L 2 1 ) d 2 2 .
P s = 1 ( 1 P s ( L P A M ) ) N = 1 [ 1 ( 1 1 L ) e r f c ( 3 N ( L 2 1 ) E a v N 0 ) ] N .

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