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Statistical physics approach to evaluation of outage probability in optical communications

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PDF

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)

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

- Monomode
- Weak nonlinearity,
- slow in z

NLS in the envelope approximation

rescaling

averaging over amplifiers

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

two-component

order BIREFRINGENCE matrixes

(2*2, traceless, self-adjoint)

first

second

Polarization

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

Getting rid of fast polarization axis rotation

ordered exponential

Pauli matrixes

weak

isotropic

Disorder

PMD

Disorder in Birefringence

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

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

+sampling window function

Optical filter

``Setting the clock”

First order PMD

compensation

Filters and ``tricks”

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

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)

Bare case

Setting the clock

First order compensation (nonzero chirp)

Saddle-point

(optimal fluctuation)

calculations

First order compensation (zero chirp)

M. Karlsson, P.Andrekson,

``Polarization-Mode

Dispersion-Induced in soliton

Transmission systems”,

IEEE Photonics Techn. Lett.

Vol.13,Oct. 2001.

c3

c2

c1

c4

compensating fibers

The idea: to achieve higher (p) compensatingdegree

Higher-order compensation

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

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

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

BER Overlap Probability,

Extended (algebraic like) tail of the double statistics !!

No replicas!!!

Replicas+Numerics

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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