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Statistical physics approach to evaluation of outage probability in optical communications

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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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slide1

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)

slide2

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

slide3

Fiber Electrodynamics

  • Monomode
  • Weak nonlinearity,
  • slow in z

NLS in the envelope approximation

rescaling

averaging over amplifiers

slide4

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

slide5

complex

two-component

order BIREFRINGENCE matrixes

(2*2, traceless, self-adjoint)

first

second

Polarization

slide6

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

slide7

Getting rid of fast polarization axis rotation

ordered exponential

Pauli matrixes

weak

isotropic

Disorder

PMD

Disorder in Birefringence

slide8

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

slide9

1 1 0 1 0

Eye diagram

PDF

``intensity”

input

output

1 1 1 0 0

slide10

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

slide11

Electrical filter

+sampling window function

Optical filter

``Setting the clock”

First order PMD

compensation

Filters and ``tricks”

slide12

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

slide13

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)

slide14

Noise average

in the interesting range one

has to keep in

only the leading in term!!

slide15

``Setting the clock”(no chirp)

Bare case

First order PMD

compensation

Optical filter always applies

slide16

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)

slide17

Grossly underestimated

Gaussian expectation

Long (algebraic!) tail

slide18

C. Xie, H. Sunnerud,

M. Karlsson, P.Andrekson,

``Polarization-Mode

Dispersion-Induced in soliton

Transmission systems”,

IEEE Photonics Techn. Lett.

Vol.13,Oct. 2001.

slide19

No compensation

Timing jitter

First order with chirp

First order no chirp

Example:

slide20

main fiber

c3

c2

c1

c4

compensating fibers

The idea: to achieve higher (p) compensatingdegree

Higher-order compensation

slide21

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

slide22

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

slide23

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

slide24

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

ad