Abstract

In this paper, we first describe an optimal signal constellation design algorithm suitable for the coherent optical channels dominated by the linear phase noise. Then, we modify this algorithm to be suitable for the nonlinear phase noise dominated channels. In optimization procedure, the proposed algorithm uses the cumulative log-likelihood function instead of the Euclidian distance. Further, an LDPC coded modulation scheme is proposed to be used in combination with signal constellations obtained by proposed algorithm. Monte Carlo simulations indicate that the LDPC-coded modulation schemes employing the new constellation sets, obtained by our new signal constellation design algorithm, outperform corresponding QAM constellations significantly in terms of transmission distance and have better nonlinearity tolerance.

© 2014 Optical Society of America

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References

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  1. K. P. Ho, Phase modulated Optical Communication System (Springer, 2005).
  2. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2006).
  3. I. Hanzo, W. Webb, and T. Keller, Single- and Multi-carrier Quadrature Amplitude Modulation: Principles and Applications for Personal Communications, WLANs and Broadcasting (Wiley, 2000).
  4. A. P. T. Lau and J. M. Kahn, “Signal design and detection in presence of nonlinear phase noise,” J. Lightwave Technol. 25(3), 779–783 (2004).
  5. L. Beygi, E. Agrell, and M. Karlsson, “Optimization of 16-point ring constellations in the presence of nonlinear phase noise,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThO4.
    [Crossref]
  6. C. Hager, A. Grell, A. Alvarado, and E. Agrell, “Design of APSK constellations for coherent optical channels with nonlinear phase noise,” IEEE Trans. Commun. 61(8), 3362–3373 (2013).
  7. I. Djordjevic, T. Liu, L. Xu, and T. Wang, “Optimum signal constellation design for high-speed optical transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OW3H.2.
    [Crossref]
  8. T. Cover and J. Thomas, Elements of Information Theory (Wiley, 1991).
  9. I. B. Djordjevic and T. Wang, “On the LDPC-coded modulation for ultra-high-speed optical transport in the presence of phase noise,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper OM2B.1.
    [Crossref]
  10. Z. Tao, W. Yan, L. Liu, L. Li, S. Oda, T. Hoshida, and J. C. Rasmussen, “Simple fiber model for determination of XPM effects,” J. Lightwave Technol. 29(7), 974–986 (2011).
    [Crossref]
  11. M. Magarini, A. Spalvieri, F. Vacondio, M. Bertolini, M. Pepe, and G. Gavioli, “Empirical modeling and simulation of phase noise in long-haul coherent optical transmission systems,” Opt. Express 19(23), 22455–22461 (2011).
    [Crossref] [PubMed]
  12. G. Colavolpe, A. Barbieri, and G Caire, “Algorithms for iterative decoding in the presence of strong phase noise,” IEEE J. Sel. Area Commun.  23(9) 1748–1757 (2005).
    [Crossref] [PubMed]
  13. M. Magarini, L. Barletta, A. Spalvieri, A. Leven, M. Pepe, and G. Gavioli, “Impact of nonideal phase reference on soft decoding of differentially encoded modulation,” IEEE Photon. Technol. Lett. 24(23), 2179–2182 (2012).
    [Crossref]
  14. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010).
    [Crossref]

2013 (1)

C. Hager, A. Grell, A. Alvarado, and E. Agrell, “Design of APSK constellations for coherent optical channels with nonlinear phase noise,” IEEE Trans. Commun. 61(8), 3362–3373 (2013).

2012 (1)

M. Magarini, L. Barletta, A. Spalvieri, A. Leven, M. Pepe, and G. Gavioli, “Impact of nonideal phase reference on soft decoding of differentially encoded modulation,” IEEE Photon. Technol. Lett. 24(23), 2179–2182 (2012).
[Crossref]

2011 (2)

2010 (1)

2005 (1)

G. Colavolpe, A. Barbieri, and G Caire, “Algorithms for iterative decoding in the presence of strong phase noise,” IEEE J. Sel. Area Commun.  23(9) 1748–1757 (2005).
[Crossref] [PubMed]

2004 (1)

Agrell, E.

C. Hager, A. Grell, A. Alvarado, and E. Agrell, “Design of APSK constellations for coherent optical channels with nonlinear phase noise,” IEEE Trans. Commun. 61(8), 3362–3373 (2013).

Alvarado, A.

C. Hager, A. Grell, A. Alvarado, and E. Agrell, “Design of APSK constellations for coherent optical channels with nonlinear phase noise,” IEEE Trans. Commun. 61(8), 3362–3373 (2013).

Barbieri, A.

G. Colavolpe, A. Barbieri, and G Caire, “Algorithms for iterative decoding in the presence of strong phase noise,” IEEE J. Sel. Area Commun.  23(9) 1748–1757 (2005).
[Crossref] [PubMed]

Barletta, L.

M. Magarini, L. Barletta, A. Spalvieri, A. Leven, M. Pepe, and G. Gavioli, “Impact of nonideal phase reference on soft decoding of differentially encoded modulation,” IEEE Photon. Technol. Lett. 24(23), 2179–2182 (2012).
[Crossref]

Bertolini, M.

Caire, G

G. Colavolpe, A. Barbieri, and G Caire, “Algorithms for iterative decoding in the presence of strong phase noise,” IEEE J. Sel. Area Commun.  23(9) 1748–1757 (2005).
[Crossref] [PubMed]

Colavolpe, G.

G. Colavolpe, A. Barbieri, and G Caire, “Algorithms for iterative decoding in the presence of strong phase noise,” IEEE J. Sel. Area Commun.  23(9) 1748–1757 (2005).
[Crossref] [PubMed]

Essiambre, R.-J.

Foschini, G. J.

Gavioli, G.

M. Magarini, L. Barletta, A. Spalvieri, A. Leven, M. Pepe, and G. Gavioli, “Impact of nonideal phase reference on soft decoding of differentially encoded modulation,” IEEE Photon. Technol. Lett. 24(23), 2179–2182 (2012).
[Crossref]

M. Magarini, A. Spalvieri, F. Vacondio, M. Bertolini, M. Pepe, and G. Gavioli, “Empirical modeling and simulation of phase noise in long-haul coherent optical transmission systems,” Opt. Express 19(23), 22455–22461 (2011).
[Crossref] [PubMed]

Goebel, B.

Grell, A.

C. Hager, A. Grell, A. Alvarado, and E. Agrell, “Design of APSK constellations for coherent optical channels with nonlinear phase noise,” IEEE Trans. Commun. 61(8), 3362–3373 (2013).

Hager, C.

C. Hager, A. Grell, A. Alvarado, and E. Agrell, “Design of APSK constellations for coherent optical channels with nonlinear phase noise,” IEEE Trans. Commun. 61(8), 3362–3373 (2013).

Hoshida, T.

Kahn, J. M.

Kramer, G.

Lau, A. P. T.

Leven, A.

M. Magarini, L. Barletta, A. Spalvieri, A. Leven, M. Pepe, and G. Gavioli, “Impact of nonideal phase reference on soft decoding of differentially encoded modulation,” IEEE Photon. Technol. Lett. 24(23), 2179–2182 (2012).
[Crossref]

Li, L.

Liu, L.

Magarini, M.

M. Magarini, L. Barletta, A. Spalvieri, A. Leven, M. Pepe, and G. Gavioli, “Impact of nonideal phase reference on soft decoding of differentially encoded modulation,” IEEE Photon. Technol. Lett. 24(23), 2179–2182 (2012).
[Crossref]

M. Magarini, A. Spalvieri, F. Vacondio, M. Bertolini, M. Pepe, and G. Gavioli, “Empirical modeling and simulation of phase noise in long-haul coherent optical transmission systems,” Opt. Express 19(23), 22455–22461 (2011).
[Crossref] [PubMed]

Oda, S.

Pepe, M.

M. Magarini, L. Barletta, A. Spalvieri, A. Leven, M. Pepe, and G. Gavioli, “Impact of nonideal phase reference on soft decoding of differentially encoded modulation,” IEEE Photon. Technol. Lett. 24(23), 2179–2182 (2012).
[Crossref]

M. Magarini, A. Spalvieri, F. Vacondio, M. Bertolini, M. Pepe, and G. Gavioli, “Empirical modeling and simulation of phase noise in long-haul coherent optical transmission systems,” Opt. Express 19(23), 22455–22461 (2011).
[Crossref] [PubMed]

Rasmussen, J. C.

Spalvieri, A.

M. Magarini, L. Barletta, A. Spalvieri, A. Leven, M. Pepe, and G. Gavioli, “Impact of nonideal phase reference on soft decoding of differentially encoded modulation,” IEEE Photon. Technol. Lett. 24(23), 2179–2182 (2012).
[Crossref]

M. Magarini, A. Spalvieri, F. Vacondio, M. Bertolini, M. Pepe, and G. Gavioli, “Empirical modeling and simulation of phase noise in long-haul coherent optical transmission systems,” Opt. Express 19(23), 22455–22461 (2011).
[Crossref] [PubMed]

Tao, Z.

Vacondio, F.

Winzer, P. J.

Yan, W.

IEEE J. Sel. Area Commun (1)

G. Colavolpe, A. Barbieri, and G Caire, “Algorithms for iterative decoding in the presence of strong phase noise,” IEEE J. Sel. Area Commun.  23(9) 1748–1757 (2005).
[Crossref] [PubMed]

IEEE Photon. Technol. Lett. (1)

M. Magarini, L. Barletta, A. Spalvieri, A. Leven, M. Pepe, and G. Gavioli, “Impact of nonideal phase reference on soft decoding of differentially encoded modulation,” IEEE Photon. Technol. Lett. 24(23), 2179–2182 (2012).
[Crossref]

IEEE Trans. Commun. (1)

C. Hager, A. Grell, A. Alvarado, and E. Agrell, “Design of APSK constellations for coherent optical channels with nonlinear phase noise,” IEEE Trans. Commun. 61(8), 3362–3373 (2013).

J. Lightwave Technol. (3)

Opt. Express (1)

Other (7)

L. Beygi, E. Agrell, and M. Karlsson, “Optimization of 16-point ring constellations in the presence of nonlinear phase noise,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2011, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OThO4.
[Crossref]

K. P. Ho, Phase modulated Optical Communication System (Springer, 2005).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2006).

I. Hanzo, W. Webb, and T. Keller, Single- and Multi-carrier Quadrature Amplitude Modulation: Principles and Applications for Personal Communications, WLANs and Broadcasting (Wiley, 2000).

I. Djordjevic, T. Liu, L. Xu, and T. Wang, “Optimum signal constellation design for high-speed optical transmission,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OW3H.2.
[Crossref]

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

I. B. Djordjevic and T. Wang, “On the LDPC-coded modulation for ultra-high-speed optical transport in the presence of phase noise,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper OM2B.1.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 Constellation diagrams of received signal with 16-QAM constellation, L = 2000km, for different launch powers.
Fig. 2
Fig. 2 The optimized 2D 16-ary signal constellations for: (a) linear phase noise model, (b) nonlinear phase noise model (after 2000 km of SMF and launch power of – 6dBm).
Fig. 3
Fig. 3 The LDPC coded modulation scheme with Monte Carlo integration to evaluate LLRs. PBS/C: polarization beam splitter/combiner, LPF: low-pass filter, ADC: analog-to-digital converter, APP: a posteriori probability.
Fig. 4
Fig. 4 BER performance for proposed LLR-OSCDs for 16-ary 2D constellation.
Fig. 5
Fig. 5 BER vs. launch power for uncoded 8-ary NL-OSCD and 8-QAM.
Fig. 6
Fig. 6 BER vs transmission length plot for LDPC-coded 8-ary NL-OSCD and 8-star-QAM.
Fig. 7
Fig. 7 BER vs. launch power for uncoded 16-ary NL-OSCD and 16-QAM.
Fig. 8
Fig. 8 BER vs transmission length plot for LDPC-coded 16-ary NL-OSCD and 16-QAM.
Fig. 9
Fig. 9 BER vs. transmission length plots for LDPC-coded 16-ary NL-OSCD and 16-QAM when span length is 100 km.

Tables (1)

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Table 1 Parameters of the System under Study

Equations (17)

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r k =s( a k , θ k )+ z k ,     r k = [ r k ( 1 ) r k ( i ) r k ( N ) ] T
s( a k , θ k )= e j θ k [ a k ( 1 ) a k ( i ) a k (N) ] T ,   z k = [ z k ( 1 ) z k ( i ) z k ( N ) ] T
θ k =( θ k1 +Δ θ k ) mod 2π
p ΔΘ ( Δ θ k )= n= p(0, δ Δθ 2 ,Δ θ k n2π)
p R ( r| a k , θ k )= e | | r k s( a k , θ k ) | | 2 N 0 /(π N 0 ) 
Y=( X+Z ) e j Φ NL
Φ NL = 0 L γP( z )dz=γ L eff P 
L eff = 1 e αL α
Φ NL = γ L eff { | E 0 + n 1 | 2 + | E 0 + n 1 + n 2 | 2 ++ | E 0 + n 1 ++ n N A | 2 }
δ 2 =2 n sp hναΔν N A  L 
L L m =LL( { A ^ m ,P( A ^ m ) } )= n 1 k=0 n1 max y A ^ m LL( x k ,y )
LL( x k ,y )= 1 NS i=1 NS { x k1 Re[ ( y 1 + y 2 j ) e j×P N i ] } 2 + { x k2 Im[ ( y 1 + y 2 j ) e j×P N i ] } 2 2 δ 2
L( a k , θ k )= p R ( r| a k , θ k ) p R ( r| a k =0 )  
l( a,θ )= l=1 L L( a k , θ k )
l( a,θ )=logL(a,θ)
l( a )=log{ exp[ l( a,θ ) ] p Θ ( θ )dθ}
l( a )=log E θ { exp[ l( a,θ ) ] }

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