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Statistical physics approach to evaluation of outage probability in optical communications

Statistical physics approach to evaluation of outage probability in optical communications. Misha Chertkov (Theoretical Division, LANL). In collaboration with Vladimir Chernyak (Corning) Ildar Gabitov (LANL + Tucson) Igor Kolokolov (Landau Inst.) Vladimir Lebedev (Landau Inst.)

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Statistical physics approach to evaluation of outage probability in optical communications

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  1. Statistical physics approach to evaluation of outage probability in optical communications Misha Chertkov (Theoretical Division, LANL) In collaboration with Vladimir Chernyak(Corning) Ildar Gabitov(LANL + Tucson) Igor Kolokolov(Landau Inst.) Vladimir Lebedev(Landau Inst.) Avner Peleg(LANL)

  2. What is the idea:Fiber Optics+Statistics. • Introduction: Material. Fiber Electro-dynamics. Noise.Disorder. • ImpairmentConsequence • Amplifier Noise jitter, degradation • Birefringent disorderPolarization Mode Dispersion • broadening, pulse splitting, jitter Bit-error-rate.Does it fluctuate? How to evaluate/calculate BER (<<1) ? Joint effect of noise and birefringent disorder Theoretical interest e.g. analogy with spin-glasses Practical consequences for optical communications

  3. Fiber Electrodynamics • Monomode • Weak nonlinearity, • slow in z NLS in the envelope approximation rescaling averaging over amplifiers

  4. Linear vsNonlinear Soliton solution Dispersion balances nonlinearity Dispersion Management Integrability (Zakharov & Shabat ‘72) Information Coding Return-to-Zero (RZ)Non-Return-to-Zero (NRZ)Differential Phase Coding RZ 1 1 0 1 0

  5. complex two-component order BIREFRINGENCE matrixes (2*2, traceless, self-adjoint) first second Polarization

  6. It causes: (1) pulsejitter (walk away from the slot) (2) pulsedegradation 3 for successful fiber performance Additive (amplifier) noise short correlated ! i.e. different for different pulses Linear: jitter and amplitude degradation are equally important Soliton: jitter essentially more important than amplitude degradation Elgin (1985) Gordon-Haus

  7. Getting rid of fast polarization axis rotation ordered exponential Pauli matrixes weak isotropic Disorder PMD Disorder in Birefringence

  8. Polarization Mode Dispersion(PMD) Linear 0 Poole, Wagner ‘86 Poole ’90;’91 Polarization (PMD) vector (of first order) Statistics of PMD vector is Gaussian. Differential group delay (DGD) pulse splitting broadening jitter

  9. 1 1 0 1 0 Eye diagram PDF ``intensity” input output 1 1 1 0 0

  10. Electrical filter+sampling window function 1) Measure intensity in each slot ! • Linear operator for • Optical filter • ``Compensation” tricks 2) Build histogram (PDF) of pulse Intensity collecting statistics over many slots (separately for initially empty and filled slots) 3) BER decision level Bit-Error-Rate

  11. Electrical filter +sampling window function Optical filter ``Setting the clock” First order PMD compensation Filters and ``tricks”

  12. Calculate BER for given realization of disorder (averaging over noise) Does BER (as a functional of disorder) fluctuate ? Noise and disorder.Order of averaging. Linear model

  13. C. Xie, H. Sunnerud, M. Karlsson, P.Andrekson, ``Polarization-Mode Dispersion-Induced in soliton Transmission systems”, IEEE Photonics Techn. Lett. Vol.13,Oct. 2001. Monte-Carlo numerics with 10 000 fiber realizations (artificial rescaling of decision level)

  14. Noise average in the interesting range one has to keep in only the leading in term!!

  15. ``Setting the clock”(no chirp) Bare case First order PMD compensation Optical filter always applies

  16. PDF of Bit-Error-Rate Bare case Setting the clock First order compensation (nonzero chirp) Saddle-point (optimal fluctuation) calculations First order compensation (zero chirp)

  17. Grossly underestimated Gaussian expectation Long (algebraic!) tail

  18. C. Xie, H. Sunnerud, M. Karlsson, P.Andrekson, ``Polarization-Mode Dispersion-Induced in soliton Transmission systems”, IEEE Photonics Techn. Lett. Vol.13,Oct. 2001.

  19. No compensation Timing jitter First order with chirp First order no chirp Example:

  20. main fiber c3 c2 c1 c4 compensating fibers The idea: to achieve higher (p) compensatingdegree Higher-order compensation

  21. main fiber c3 c2 c1 c4 ``Standard” compensating fibers c1 c2 c3 c4 1 2 3 4 Periodic 1 2 3 4 c4 c3 c2 c1 Quasi-periodic For Q-periodic --- Need !!!!! anti-stokes refraction measurement of birefringence (Hunter,Gisin,Gisin ’99) Q-periodic guarantees much stronger p-dependence of compensation than the ``standard” one

  22. Linear V.Chernyak,MC,I.Kolokolov,V.Lebedev Phys.RevE to appear; Optics. Lett. 28, (2003); Optics. Express. 11, 1607 (2003); JETP Lett. 78, 198-201 (2003) VC,MC,I. Gabitov,IK,VL, to appear in special issue of Journal of Lightware Technology (invited) Nonlinear( soliton transmission) VC,MC,IK, Avner Peleg submitted to Euro.Phys.Lett Soliton jitter (due to noise) is the dominant destructive factor Bare case

  23. Analogy with Functional Order Parameter approach for glassy states in infinite-range exchange spin systems Double (super) statistics Amplifier Noise Thermal Birefringent Disorder Exchange, J Pulse intensityGlassy states overlap, q PDF BER Overlap Probability, Extended (algebraic like) tail of the double statistics !! No replicas!!! Replicas+Numerics

  24. Conclusions Noise and disorder CAN NOT be considered separately ! Probability Distribution Function of BER is the proper method/tool of extreme outages (for PMD) and their compensation analysis No other alternative to the theory in evaluation of the extremely low valued BER

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