Abstract

We present the Almouti-type polarization-time (PT) coding scheme suitable for use in multilevel (M≥2) block-coded modulation schemes with coherent detection. The PT-decoder is found it to be similar to the Alamouti combiner. We also describe how to determine the symbols log-likelihood ratios in the presence of laser phase noise. We show that the proposed scheme is able to compensate even 800 ps of differential group delay, for the system operating at 10 Gb/s, with negligible penalty. The proposed scheme outperforms equal-gain combining polarization diversity OFDM scheme. However, the polarization diversity coded-OFDM and PT-coding based coded-OFDM schemes perform comparable. The proposed scheme has the potential of doubling the spectral efficiency compared to polarization diversity schemes.

© 2008 Optical Society of America

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References

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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. Y. Han and G. Li, "Polarization diversity transmitter and optical nonlinearity mitigation using polarization-time coding," in Proc. COTA 2006, Paper no. CThC7, Whistler, Canada, 2006.
  7. 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]
  8. D. Penninckx and V. Morenás, "Jones matrix of polarization mode dispersion," Opt. Lett. 24, 875-877 (1999).
    [CrossRef]
  9. 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.
  10. E. Biglieri, R. Calderbank, A. Constantinides, A. Goldsmith, A. Paulraj, and H. V. Poor, MIMO Wireless Communications, Cambridge University Press, Cambridge 2007.
  11. W. Shieh, X. Yi, Y. Ma, and Q. Yang, "Coherent optical OFDM: has its time come? [Invited]," J. Opt. Netw. 7, 234-255 (2008).
    [CrossRef]
  12. I. B. Djordjevic, L. Xu, and T. Wang, "Simultaneous chromatic dispersion and PMD compensation by using coded-OFDM and girth-10 LDPC codes," Opt. Express 16, 10269-10278 (2008).
    [CrossRef] [PubMed]
  13. J. G. Proakis, Digital Communications (McGraw-Hill, Boston, 2001).
  14. M. Cvijetic, Coherent and Nonlinear Lightwave Communications (Artech House, Boston, 1996). I. B. Djordjevic, L. L. Minkov, and H. G. Batshon, "Mitigation of linear and nonlinear impairments in high-speed optical networks by using LDPC-coded turbo equalization," IEEE J. Sel. Areas Comm., accepted for publication.

2008 (4)

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]

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.

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.

I. B. Djordjevic, L. Xu, and T. Wang, "Simultaneous chromatic dispersion and PMD compensation by using coded-OFDM and girth-10 LDPC codes," Opt. Express 16, 10269-10278 (2008).
[CrossRef] [PubMed]

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, L. Xu, and T. Wang, "Simultaneous chromatic dispersion and PMD compensation by using coded-OFDM and girth-10 LDPC codes," Opt. Express 16, 10269-10278 (2008).
[CrossRef] [PubMed]

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]

Yang, Q.

Yi, X.

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)

J. Opt. Netw. (1)

Opt. Express (3)

Opt. Lett. (1)

Other (5)

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.

Y. Han and G. Li, "Polarization diversity transmitter and optical nonlinearity mitigation using polarization-time coding," in Proc. COTA 2006, Paper no. CThC7, Whistler, Canada, 2006.

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

M. Cvijetic, Coherent and Nonlinear Lightwave Communications (Artech House, Boston, 1996). I. B. Djordjevic, L. L. Minkov, and H. G. Batshon, "Mitigation of linear and nonlinear impairments in high-speed optical networks by using LDPC-coded turbo equalization," IEEE J. Sel. Areas Comm., accepted for publication.

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Figures (4)

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 PT coding scheme based on OFDM concatenated with LDPC coding: (a) transmitter architecture, (b) OFDM transmitter architecture (x- or y-polarization), (c) receiver architecture, and (d) balanced coherent detector 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.

Equivalent OFDM channel model. ϕCD(k) denotes the phase distortion of kth subcarrier due to chromatic dispersion.

Fig. 4.
Fig. 4.

BER performance of Alamouti-type polarization-time coding scheme: (a) uncoded case, and (b) LDPC-coded case. B2B: back-to-back.

Equations (12)

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H ( ω ) = [ h xx h xy h yx h yy ] = R 1 P ( ω ) R , P ( ω ) = [ e jωτ / 2 0 0 e jωτ / 2 ] ,
r i , k = H ( k ) s i , k e j ( ϕ T ϕ L O ) + n i , k ,
r i , k ( m ) = H ( k ) s i , k ( m ) e j ( ϕ T ϕ L O ) + n i , k ( m ) , m = 1 , 2
[ r ( 1 ) x , i , k r * ( 2 ) x , i , k ] = [ h x x e j ϕ P N h xy e j ϕ PN h xy * e j ϕ PN h xx * e j ϕ PN ] [ S x , i , k S y , i , k ] + [ n x , i , k ( 1 ) n x , i , k * ( 2 ) ] ,
[ r y , i , k ( 1 ) r y , i , k * ( 2 ) ] = [ h yx e j ϕ PN h xy e j ϕ PN h xy * e j ϕ PN h yx * e j ϕ PN ] [ S x , i , k S y , i , k ] + [ n y , i , k ( 1 ) n y , i , k * ( 2 ) ] .
S ˜ x , i , k = h xx * r x , i , k ( 1 ) e j ϕ PN + h xy r x , i , k * ( 2 ) e j ϕ PN + h yx * r y , i , k ( 1 ) e j ϕ PN + h yy r y , i , k * ( 2 ) e j ϕ PN ,
S ˜ y , i = h xy * r x , i , k ( 1 ) e j ϕ PN h xx r x , i , k * ( 2 ) e j ϕ PN + h yy * r y , i , k ( 1 ) e j ϕ PN h yx r y , i , k * ( 2 ) e j ϕ PN ,
S ˜ i , k = r x , i , k h xx * + r y , i , k h xy * ( h xx 2 + h xy 2 ) e j ϕ PN ,
λ x ( y ) ( s ϕ T ) = ( Re [ s ˜ i , k , x ( y ) ( ϕ T ) ] Re [ QAM ( map ( s ) ) ] ) 2 2 σ 2
( Im [ s ˜ i , k , x ( y ) ( ϕ T ) ] Im [ QAM ( map ( s ) ) ] ) 2 2 σ 2 ; s = 0 , 1 , , 2 n b 1
λ x ( y ) ( s ) = log { exp [ λ x ( y ) ( s | ϕ T ) 1 σ PN 2 π exp ( ϕ T 2 2 σ PN 2 ) ] d ϕ T } .
L ( b ̂ j , x ( y ) ) = log s : b j = 0 exp [ λ x ( y ) ( s ) ] s : b j = 1 exp [ λ x ( y ) ( s ) ] .

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