Abstract

Because Shannon’s entropy can be obtained by Stirling’s approximation of thermodynamics entropy, the statistical physics energy minimization methods are directly applicable to the signal constellation design. We demonstrate that statistical physics inspired energy-efficient (EE) signal constellation designs, in combination with large-girth low-density parity-check (LDPC) codes, significantly outperform conventional LDPC-coded polarization-division multiplexed quadrature amplitude modulation schemes. We also describe an EE signal constellation design algorithm. Finally, we propose the discrete-time implementation of D-dimensional transceiver and corresponding EE polarization-division multiplexed system.

© 2012 Optical Society of America

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References

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  1. B. G. Bathula, M. Alresheedi, and J. M. H. Elmirghani, in Proc. IEEE London Commun. Symp. (IEEE, 2009).
  2. G. Wannier, Statistical Physics (Dover, 1987).
  3. T. Cover and J. Thomas, Elements of Information Theory (Wiley, 1991).
  4. G. Foschini, R. Gitlin, and S. Weinstein, IEEE Trans. Commun. Electron. 22, 28 (1974).
    [CrossRef]
  5. I. Djordjevic, Opt. Express 19, 16708 (2011).
    [CrossRef]
  6. H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, IEEE Photon. J. 2, 593 (2010).
    [CrossRef]

2011 (1)

2010 (1)

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, IEEE Photon. J. 2, 593 (2010).
[CrossRef]

1974 (1)

G. Foschini, R. Gitlin, and S. Weinstein, IEEE Trans. Commun. Electron. 22, 28 (1974).
[CrossRef]

Alresheedi, M.

B. G. Bathula, M. Alresheedi, and J. M. H. Elmirghani, in Proc. IEEE London Commun. Symp. (IEEE, 2009).

Bathula, B. G.

B. G. Bathula, M. Alresheedi, and J. M. H. Elmirghani, in Proc. IEEE London Commun. Symp. (IEEE, 2009).

Batshon, H. G.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, IEEE Photon. J. 2, 593 (2010).
[CrossRef]

Cover, T.

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

Djordjevic, I.

Djordjevic, I. B.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, IEEE Photon. J. 2, 593 (2010).
[CrossRef]

Elmirghani, J. M. H.

B. G. Bathula, M. Alresheedi, and J. M. H. Elmirghani, in Proc. IEEE London Commun. Symp. (IEEE, 2009).

Foschini, G.

G. Foschini, R. Gitlin, and S. Weinstein, IEEE Trans. Commun. Electron. 22, 28 (1974).
[CrossRef]

Gitlin, R.

G. Foschini, R. Gitlin, and S. Weinstein, IEEE Trans. Commun. Electron. 22, 28 (1974).
[CrossRef]

Thomas, J.

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

Wang, T.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, IEEE Photon. J. 2, 593 (2010).
[CrossRef]

Wannier, G.

G. Wannier, Statistical Physics (Dover, 1987).

Weinstein, S.

G. Foschini, R. Gitlin, and S. Weinstein, IEEE Trans. Commun. Electron. 22, 28 (1974).
[CrossRef]

Xu, L.

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, IEEE Photon. J. 2, 593 (2010).
[CrossRef]

IEEE Photon. J. (1)

H. G. Batshon, I. B. Djordjevic, L. Xu, and T. Wang, IEEE Photon. J. 2, 593 (2010).
[CrossRef]

IEEE Trans. Commun. Electron. (1)

G. Foschini, R. Gitlin, and S. Weinstein, IEEE Trans. Commun. Electron. 22, 28 (1974).
[CrossRef]

Opt. Express (1)

Other (3)

B. G. Bathula, M. Alresheedi, and J. M. H. Elmirghani, in Proc. IEEE London Commun. Symp. (IEEE, 2009).

G. Wannier, Statistical Physics (Dover, 1987).

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

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Figures (3)

Fig. 1.
Fig. 1.

Information capacities per dimension. For channel model, we useI-ary input J-ary output (J>I) channel model, which is a valid model for reasonably high signal-to-noise ratios. The inset figure shows optimum constellation for L=4 and D=1.

Fig. 2.
Fig. 2.

D-dimensional EE coded modulation (CM) scheme: (a) DT D-dim. modulator, (b) DT D-dim. demodulator, (c) Tx configuration, and (d) Rx configuration. PBS(C), polarization-beam splitter (combiner); Ts, symbol duration; T, sampling interval, related to Ts by T=Ts/U, where U is the oversampling factor; DFB, distributed feedback laser.

Fig. 3.
Fig. 3.

BER performance of EE-PDM LDPC-coded modulation. A given CIPQ signal constellation is obtained by placing one point in the origin and then running the IPQ procedure. Inset, optimum 8-ary constellation for D=2.

Equations (5)

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St=klogC({Ni}i=1M)=klog[N!/(N1!NM!)],
S(X)(NlogNi=1MNilogNi)/N=i=1M(Ni/N)log(Ni/N)=i=1Mpilogpi=H(X).
Lm=S(X)S(X|Y)+α(1ipi)+β(EipiEi)
H(X)H(X|Y)+α(1ipi)+β(EipiEi),
si=CDm=1DϕimΦm,

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