Abstract

We present two PMD compensation schemes suitable for use in multilevel (M≥2) block-coded modulation schemes with coherent detection. The first scheme is based on a BLAST-type polarization-interference cancellation scheme, and the second scheme is based on iterative polarization cancellation. Both schemes use the LDPC codes as channel codes. The proposed PMD compensations schemes are evaluated by employing coded-OFDM and coherent detection. When used in combination with girth-10 LDPC codes those schemes outperform polarization-time coding based OFDM by 1 dB at BER of 10-9, and provide two times higher spectral efficiency. The proposed schemes perform comparable and are able to compensate even 1200 ps of differential group delay with negligible penalty.

© 2008 Optical Society of America

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  1. I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, "Using LDPC-coded modulation and coherent detection for ultra high-speed optical transmission," J. Lightwave Technol. 25, 3619-3625 (2007).
    [CrossRef]
  2. L. L. Minkov, I. B. Djordjevic, H. G. Batshon, L. Xu, T. Wang, M. Cvijetic, and F. Kueppers, "Demonstration of PMD compensation by LDPC-coded turbo equalization and channel capacity loss characterization due to PMD and quantization," IEEE Photon. Technol. Lett. 19, 1852-1854 (2007).
    [CrossRef]
  3. W. Shieh, X. Yi, Y. Ma, and Y. Tang, "Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems," Opt. Express 15, 9936-9947 (2007).
    [CrossRef] [PubMed]
  4. H. Sun, K. -T. Wu, and K. Roberts, "Real-time measurements of a 40 Gb/s coherent system," Opt. Express 16, 873-879 (2008).
    [CrossRef] [PubMed]
  5. S. Alamouti, "A simple transmit diversity technique for wireless communications," IEEE J. Sel. Areas Commun. 16, 1451-1458 (1998).
    [CrossRef]
  6. I. B. Djordjevic, L. Xu, and T. Wang, "PMD compensation in multilevel coded-modulation schemes with coherent detection using Alamouti-type polarization-time coding," in Proc. IEEE LEOS Summer Topicals 2008, pp. 103-104, July 2008.
    [CrossRef]
  7. G. J. Foschini, "Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas," Bell Labs Tech. J. 1, 41-59 (1996).
    [CrossRef]
  8. E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. Paulraj, and H. V. Poor, MIMO Wireless Communications (Cambridge University Press, Cambridge 2007).
    [CrossRef]
  9. I. B. Djordjevic, S. Denic, J. Anguita, B. Vasic, and M. A. Neifeld, "LDPC-coded MIMO optical communication over the atmospheric turbulence channel," J. Lightwave Technol. 26, 478-487 (2008).
    [CrossRef]
  10. D. Penninckx, and V. Morenás, "Jones matrix of polarization mode dispersion," Opt. Lett. 24, 875-877 (1999).
    [CrossRef]
  11. I. B. Djordjevic, L. Xu, T. Wang, and M. Cvijetic, "Large girth low-density parity-check codes for long-haul high-speed optical communications," in Proc. OFC/NFOEC 2008, Paper no. JWA53.

2008 (2)

2007 (3)

1999 (1)

1998 (1)

S. Alamouti, "A simple transmit diversity technique for wireless communications," IEEE J. Sel. Areas Commun. 16, 1451-1458 (1998).
[CrossRef]

1996 (1)

G. J. Foschini, "Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas," Bell Labs Tech. J. 1, 41-59 (1996).
[CrossRef]

Alamouti, S.

S. Alamouti, "A simple transmit diversity technique for wireless communications," IEEE J. Sel. Areas Commun. 16, 1451-1458 (1998).
[CrossRef]

Anguita, J.

Batshon, H. G.

L. L. Minkov, I. B. Djordjevic, H. G. Batshon, L. Xu, T. Wang, M. Cvijetic, and F. Kueppers, "Demonstration of PMD compensation by LDPC-coded turbo equalization and channel capacity loss characterization due to PMD and quantization," IEEE Photon. Technol. Lett. 19, 1852-1854 (2007).
[CrossRef]

Cvijetic, M.

I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, "Using LDPC-coded modulation and coherent detection for ultra high-speed optical transmission," J. Lightwave Technol. 25, 3619-3625 (2007).
[CrossRef]

L. L. Minkov, I. B. Djordjevic, H. G. Batshon, L. Xu, T. Wang, M. Cvijetic, and F. Kueppers, "Demonstration of PMD compensation by LDPC-coded turbo equalization and channel capacity loss characterization due to PMD and quantization," IEEE Photon. Technol. Lett. 19, 1852-1854 (2007).
[CrossRef]

Denic, S.

Djordjevic, I. B.

I. B. Djordjevic, S. Denic, J. Anguita, B. Vasic, and M. A. Neifeld, "LDPC-coded MIMO optical communication over the atmospheric turbulence channel," J. Lightwave Technol. 26, 478-487 (2008).
[CrossRef]

I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, "Using LDPC-coded modulation and coherent detection for ultra high-speed optical transmission," J. Lightwave Technol. 25, 3619-3625 (2007).
[CrossRef]

L. L. Minkov, I. B. Djordjevic, H. G. Batshon, L. Xu, T. Wang, M. Cvijetic, and F. Kueppers, "Demonstration of PMD compensation by LDPC-coded turbo equalization and channel capacity loss characterization due to PMD and quantization," IEEE Photon. Technol. Lett. 19, 1852-1854 (2007).
[CrossRef]

Foschini, G. J.

G. J. Foschini, "Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas," Bell Labs Tech. J. 1, 41-59 (1996).
[CrossRef]

Kueppers, F.

L. L. Minkov, I. B. Djordjevic, H. G. Batshon, L. Xu, T. Wang, M. Cvijetic, and F. Kueppers, "Demonstration of PMD compensation by LDPC-coded turbo equalization and channel capacity loss characterization due to PMD and quantization," IEEE Photon. Technol. Lett. 19, 1852-1854 (2007).
[CrossRef]

Ma, Y.

Minkov, L. L.

L. L. Minkov, I. B. Djordjevic, H. G. Batshon, L. Xu, T. Wang, M. Cvijetic, and F. Kueppers, "Demonstration of PMD compensation by LDPC-coded turbo equalization and channel capacity loss characterization due to PMD and quantization," IEEE Photon. Technol. Lett. 19, 1852-1854 (2007).
[CrossRef]

Morenás, V.

Neifeld, M. A.

Penninckx, D.

Roberts, K.

Shieh, W.

Sun, H.

Tang, Y.

Vasic, B.

Wang, T.

L. L. Minkov, I. B. Djordjevic, H. G. Batshon, L. Xu, T. Wang, M. Cvijetic, and F. Kueppers, "Demonstration of PMD compensation by LDPC-coded turbo equalization and channel capacity loss characterization due to PMD and quantization," IEEE Photon. Technol. Lett. 19, 1852-1854 (2007).
[CrossRef]

I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, "Using LDPC-coded modulation and coherent detection for ultra high-speed optical transmission," J. Lightwave Technol. 25, 3619-3625 (2007).
[CrossRef]

Wu, K. -T.

Xu, L.

I. B. Djordjevic, M. Cvijetic, L. Xu, and T. Wang, "Using LDPC-coded modulation and coherent detection for ultra high-speed optical transmission," J. Lightwave Technol. 25, 3619-3625 (2007).
[CrossRef]

L. L. Minkov, I. B. Djordjevic, H. G. Batshon, L. Xu, T. Wang, M. Cvijetic, and F. Kueppers, "Demonstration of PMD compensation by LDPC-coded turbo equalization and channel capacity loss characterization due to PMD and quantization," IEEE Photon. Technol. Lett. 19, 1852-1854 (2007).
[CrossRef]

Yi, X.

Bell Labs Tech. J. (1)

G. J. Foschini, "Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas," Bell Labs Tech. J. 1, 41-59 (1996).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

S. Alamouti, "A simple transmit diversity technique for wireless communications," IEEE J. Sel. Areas Commun. 16, 1451-1458 (1998).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

L. L. Minkov, I. B. Djordjevic, H. G. Batshon, L. Xu, T. Wang, M. Cvijetic, and F. Kueppers, "Demonstration of PMD compensation by LDPC-coded turbo equalization and channel capacity loss characterization due to PMD and quantization," IEEE Photon. Technol. Lett. 19, 1852-1854 (2007).
[CrossRef]

J. Lightwave Technol. (2)

Opt. Express (2)

Opt. Lett. (1)

Other (3)

I. B. Djordjevic, L. Xu, T. Wang, and M. Cvijetic, "Large girth low-density parity-check codes for long-haul high-speed optical communications," in Proc. OFC/NFOEC 2008, Paper no. JWA53.

E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. Paulraj, and H. V. Poor, MIMO Wireless Communications (Cambridge University Press, Cambridge 2007).
[CrossRef]

I. B. Djordjevic, L. Xu, and T. Wang, "PMD compensation in multilevel coded-modulation schemes with coherent detection using Alamouti-type polarization-time coding," in Proc. IEEE LEOS Summer Topicals 2008, pp. 103-104, July 2008.
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Magnitude response of h xx and h xy Jones matrix coefficients against the normalized frequency for: (a) θ = π/2 and ε = 0, and (b) θ = π/3 and ε = 0.

Fig. 2.
Fig. 2.

The architecture of polarization interference cancelation scheme in combination with LDPC-coded OFDM: (a) transmitter architecture, (b) OFDM transmitter configuration, (c) receiver architecture, (d) coherent detector configuration, and (e) OFDM receiver configuration. DFB: distributed feedback laser, PBS(C): polarization beam splitter (combiner), MZM: dual-drive Mach-Zehnder modulator, APP: a posteriory probability, LLRs: log-likelihood ratios.

Fig. 3.
Fig. 3.

The configurations of polarization interference cancelation schemes: (a) BLAST-type polarization interference cancelation scheme, and (b) iterative polarization cancelation scheme.

Fig. 4.
Fig. 4.

BER performance of proposed schemes against polarization diversity OFDM, and PTcoding based OFDM. B2B: back-to-back.

Fig. 5.
Fig. 5.

BER performance of proposed polarization interference cancelation schemes for LDPC-coded OFDM.

Equations (8)

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H = [ h xx h xy h yx h yy ] = RP ( ω ) R 1 , P ( ω ) = [ e j ω τ 2 0 0 e j ω τ 2 ] ,
r i , k = H k s i , k e j [ ϕ CD ( k ) + ϕ T ϕ LO ] + n i , k ,
C k = diag 1 ( R k ) Q k , D k = diag 1 ( R k ) R k I ,
C k = diag 1 ( S k ) ( S k ) H k , D k = diag 1 ( S k ) S k I ,
r ˜ i , k ( l + 1 ) = r ˜ i , k ( l ) [ C k H k diag ( C k H k ) ] s ˜ i , k ( l ) ,
λ x ( y ) ( q ) = ( Re [ s ˜ i , k , x ( y ) ] Re [ QAM ( map ( q ) ) ] ) 2 2 σ 2
( Im [ s ˜ i , k , x ( y ) ] Im [ QAM ( map ( q ) ) ] ) 2 2 σ 2 ; q = 0 , 1 , , 2 b 1
L ( v ̂ j , x ( y ) ) = log Σ q : v j = 0 exp [ λ x ( y ) ( q ) ] Σ q : v j = 1 exp [ λ x ( y ) ( q ) ] .

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