ch4_ofts

© Adolfo Cartaxo Chapter 4, Optical Fibre Telecommunication Systems, 2012 1

Chapter 4

Wavelength Division Multiplexed Systems

2011/2012


Objectives

• Introduce WDM systems

• Provide knowledge on the main types of WDM systems

• Provide knowledge on the main limitations and design of point-to-point WDM systems

• Provide knowledge on the architecture, elements and main

impairments of WDM networks

Bibliography

Chapters 5, 7 and 13 of “Optical Networks”


λλλλ1, λλλλ2, ... ,λλλλNλλλλ1, λλλλ2, ... ,λλλλN

1 optical fibre

AmplificationSection

Basic Elements and Requirements of a (point-to-point) WDM System

Tunable optical sources

with reduced linewidth

WavelengthWavelengthCombinerCombiner

WavelengthWavelengthSplitterSplitter

Challenge:Low insertion loss

Challenge:High selectivity

in the optical domain(to separate channels with low crosstalk)

Individual OpticalReceivers

(One per wavelength channel, color blind)

= PIN + electrical receiver


WDM Multiplexing / Demultiplexing

• Methods– Selective: uses AWG (loss independent of number of wavelengths)– Non-selective: uses combination of optical filters (loss dependent of

number of wavelengths)

• Multiplexers / Demultiplexers: passive (reciprocal) devices– Technologies:

• Gratings• Fibre Bragg gratings• Arrayed waveguide gratings (AWGs)

• Techniques for high count multiplexing– Multi-stage (per wavelength band)– Interleaving

These technologies and techniques have been addressed in chapter 2


Tunable Lasers• Why tunable? (... and not fixed-wavelength?)

– More expensive

– With fixed-wavelength lasers, a 100-channel WDM system needs 100 different laser types � inventory and sparing issues from manufacturers, system providers to network operators

– Tunable lasers are also one of the key enablers of reconfigurable

optical networks:

• they provide the flexibility to choose the transmit wavelength at the source of a lightpath; we need as many tunable lasers in a network node as the number of lighpaths

• The tuning time required for such applications is on the order of milliseconds because the wavelength selection happens only at the times where the lightpath is set up, or when it needs to be rerouted in the event of a failure

[ON] section 3.5.3


Tunable Lasers (2)

• Tuning mechanisms:

– Injection current into a semiconductor laser– Temperature tuning– Mechanical tuning

[ON] section 3.5.3

• Ideal tunable laser

– can tune rapidly over a wide continuous tuning range of over 100 nm.

– should be stable over its lifetime and easily controllable and manufacturable.


Optical Channel Density

• WDM provides a number of uniformly spaced frequency-slots for optical channels

– The system operator may not populate all of them with signals– The spacing of these frequency slots determines the potential optical

channel density

Any channel spacing can be chosen but in practice most WDM systems fall into two specific categories based on industry standards.

Adoption of standards is important to guarantee the “communication” between different manufacturers’ equipments and reduce manufacturing costs

ch ,maxch

ch

Maximum number of channels (channel capacity)in a given bandwidth, :

: channel spacing (assumed the same over the whole bandwidth)

WDM

WDM

BBN

νν

=∆

∆


Categories of WDM: CWDM and ...• CWDM (Coarse Wavelength Division Multiplexing)

– Based on channel spacing of 20 nm across a range from 1260 to 1620 nm set by ITU standard G.694.2 � 18 channels (centered at 1250 + i×20 nm) across the low-loss window of dry fibres (bands O, E, S, C and L)

– For use in metro networks where in many cases data rates to 2.5 Gbit/s are used and transmission distances are at most tens of km � optical amplifiers are not required.

– Avoids high costs associated with precise wavelength control (uncooled lasers and mux/demux with weaker selectivity can be used)

CWDM spacingis uniform in wavelength but not in

frequency units


Categories of WDM: ..... and DWDM

• DWDM (Dense Wavelength Division Multiplexing)

– Uses channel spacing of 200 GHz or less

– Normal center-frequency spacings are 200, 100, 50 or 25 GHz based on a standard grid developed by ITU developed for the EDFA band

– Most DWDM systems operate in the EDFA band (around 1550 nm): used for long-haul, high-capacity transmission

DWDM spacingis uniform in

frequency but not in wavelength

units

Difference in system capacity between CWDM and DWDM is dramatic !!!

... while 40 100-GHz DWDM channelsfit into the EDFA C-band (1530-1565 nm),

two CWDM channels do not quite fit into the same band


DWDM Frequency Grid by ITU

Wavelength, nm

Fibr

e lo

ss p

aram

eter

,a, d

B/k

m

ITU-T G.692: different frequency spacingsbetween adjacent channels; grid anchored

at 193.1 THz (1552.52 nm); only C and L bands

Secondwindow

~1270-1350nm

Thirdwindow

~1480-1600nm

Alternativechannel spacings

• 25 GHz (~0.2 nm)• 50 GHz (~0.4 nm)• 100 GHz (~0.4 nm)• 200 GHz (~1.6 nm)


Wavelength, nm

EDFA

Gai

n,dB

Third Window Bands

C Band(Conventional)

~ 1530-1565nmBandwidth ~35nm

L Band(Long λλλλ)

~ 1565-1625nmBandwith: ~60nm

Total available bandwidth~ 90 nm

⇓⇓⇓⇓

~ 112 channels(spaced by 100 GHz,

about 0.8 nm)

Signals are split between a pair of parallel amplifiers (one for each band) with a 5 nm gap between

C and L bands. L band EDFA amplification can be achieved with longer (100 m or more) doped fibre.


Top-capacity Commercial (P2P) DWDM Systems

160 λλλλs × 10 Gb/s


1.6 Tb/s

3.2 Tb/sTransXpress

InfinityNokia Siemens

Networks

160 λλλλs × 40 Gb/s6.4 Tb/sOPTera Long Haul 5000Nortel



2.56 Tb/s

1.28 Tb/sLambdaXtremeLucent


640 λλλλs × 2.5 Gb/s1.6 Tb/sCoreStreamCiena

Number of wavelengthsCapacityEquipment

DesignationSystem Vendor


Channel Spacing Requirements• What is the required channel spacing?

– Ideally, the WDM demultiplexer should transmit all light (no loss) at the center wavelength of the optical channel, and block adjacent channels completely.

– In practice, the demux has some attenuation at the center of the channel (typically, 3 to 5 dB), and adjacent channels are attenuated by 20 to 40 dB.

– Actual transmission of the demux depends on the technology used and spreads out more than over the adjacent channels � origin of crosstalk (XTalk) between optical channels.

εi =pc,i/p0

Signal

Interchannel Crosstalk

p0

pc,i

ν

Dem

ux tr

ansm

ittan

ce (d

B)

ν1 ν2 νS νNch

pc,2

pc,1

νi ...... ......

( )( )

dem

20 dem S

Demux with transfer function,

Signal power at demux output: : input power per channel (same for all channels)

H

p H pp

ν

ν≈

( ) 2, dem

, 0

10 0 ,

Power from XTalk channel : Normalised XTalk power from channel :

Difference in dB between signal and XTalk levels(channel suppression, dB): 10log

c i i

i c i

i c i

i p H pi p p

P P

νε

ε

≈

=

− = −


Demux Bandwidth Requirements• The crosstalk can be reduced by using demuxes with bandwidth narrower

than the optical channel bandwidth (channel spacing) � reduces the amount of leakage power of other optical channels detected by the PIN

• ... but the bandwidth should be wide enough to transmit the signal and cope with drift of source wavelength

� required bandwidth is due to signal bandwidth (2Rb,ch) and

drift of nominal emission wavelength (2∆νch/5)

Rule of thumb for minimum -3 dB Mux and Demux bandwidths:

B-3 dB = 2Rb,ch + 2∆νch/5

Rb,ch = channel bit rate∆νch = channel spacing

� ITU-T specifies a maximum drift of ±∆νch/5 for a channel spacing ≥ 200 GHz(higher drift causes increase of crosstalk and signal loss)

This means

B-3 dB < ∆νch


Crosstalk (XTalk) Modeling

( ) ( ) ( )[ ] ( ) ( )[ ]

( )( )

0 S S S 0

S

Electric field at the PIN input (just one channel interferer):

= 2 cos 2 2 cos 2

={0, 1}, depending on whether a 0 or 1 is being sent in the desired channel; = {0, 1},

i i i i

i

E t p d t t t p d t t t

d td t

πν φ ε πν φ⋅ + + ⋅ +

( ) ( )S

S

depending on whether a 0 or 1 is being sent in the XTalk channel; and is the optical frequency of the signal and XTalk carriers; and are the random phases of the signal and XTalk channels

(

i

it tν ν

φ φit is assumed that all channels have an infinite extinction ratio)

( ) ( )

( ) ( )

S ,1 0

S ,0 0

Worst case XTalk (lower power level for 1 and higher power level for 0)

For bit 1, 1, and 0 (worst case):


i i

i i i

d t d t p p

d t d t p pε

= = =

= = =

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )0 S 0 0 S S S

Power incident on PIN within the receiver bandwidth (proportional to the squared electric field)

= 2 cos 2i i i i i i ip t p d t p d t p d t d t t t tε ε π ν ν φ φ+ + ⋅ − + −

( ) ( ) ( )

S

0 S 0

For interchannel XTalk, , and the electrical receiver cuts-off the last term:

=

i

i i ip t p d t p d t

ν ν

ε

≠

+


Power Penalty due to Interchannel Crosstalk

Ideal situation (no interchannel XTalk)

,1 0 ,0

0

2

no XT

, 0

2

12

i i

i

i

p p p

Q k p k p

Qpk

= = ⇒

= = ⇒

=

Real situation (with interchannel XTalk):

( ) ( )

( )

,1 0 ,0 0

0 0

2

2w/ XT

,

2 1

1 12 1

i i i

i i i

i

i

p p p p

Q k p p k p

Qpk

ε

ε ε

ε

= = ⇒

= − = − ⇒

= −

Interchannel XTalk power penalty, in dB

( )w/ XTinterXT 10 10

no XT

10log 20log 1ii

i

pP

pε

∆ = = − −

Q factor dependence on power levels of bits 1 and 0 (for dominance of signal-ASE beat noise)

( ) ( ),1 ,0,1 ,0

,1 ,0

n i ii i

r i r i

k p pQ k p p

k p k p−

= = −+

Definition of power penalty, in dB

real w/ XTinterXT 10 10

ideal no XT

10log 10logi i

i i

p pP

p p

∆ = =

Exercise: derive expression for the

power penalty in case of an unamplified system


Example of Application

( ) ( )1 2

220 20interXT interXT10

When the two channels have the same suppression,

1 10 2 Channel suppression (dB)= 20log 1 10 3P P

ε ε ε

ε −∆ −∆

= =

= − ⇒ − − +

interXT 1 dB 0.0118 Channel suppression 19.27 dBiP ε⇓

∆ ≤ ⇒ ≤ ⇒ ≥

Calculation of the required adjacent channel suppression (dB) for an interchannel XTalk penalty not exceeding 1 dB.

1. Assuming just one adjacent channel

( ) ( )220 20interXT interXT101 10 Channel suppression (dB)= 20log 1 10P P

iε −∆ −∆= − ⇒ − −

( )1

1interXT 10

In case of interfering channels, should be replaced by :

20log 1

Nii i

Ni i

N

P

ε ε

ε=

=

∑

∆ = − − ∑

interXT 1 dB 0.0059 Channel suppression 22.27 dBP ε⇓

∆ ≤ ⇒ ≤ ⇒ ≥

2. Assuming the main XTalk comes from the two adjacent channels (neglecting XTalk coming from the other channels)

Required suppression

increases with the number of

interfering channels


Capacity Limitations in DWDM systems

Maximum count of channels:

Nch,max = pmax / pch

pmax = maximum power imposed by,e. g., EDFAs

pch = average power per channel(necessary to fulfil the required

system margin)

… imposed by the maximumpower of the WDM signal

… imposed by the maximumbandwidth of the WDM signal

BWDM,max = maximum bandwidth imposed

by, e. g., the EDFAs’ gain

∆νch = channel spacing


Nch,max = BWDM,max / ∆νch

Rb,ch = channel bit rateMaximum bit rate of the WDM signal

Rb,WDM,max = Nch,max · Rb,ch




Nch,max = pmax / pch = 100 / 10–6/10 = 398.1

Calculation of the maximum bit rate of a WDM signal in a 25 GHz channel spacing and 2.5 Gbit/s per channel link

... that uses EDFAs with uniform gain in the 1530-1560 nm band and maximum output power of 20 dBm

… assuming that the average signal power per channel required at the PIN input to guarantee the target system margin is -6 dBm

EDFAs’ bandwidth, in Hz:

BWDM,max = c / (λ0)2 (∆λ)max = 3768 GHz

(λ0 = 1545 nm ; (∆λ)max = 30 nm)

Maximum bit rate of the WDM signal

Rb,WDM,max = Nch,max · Rb,ch = 150 × 2.5 = 375 Gbit/s


Nch,max = BWDM,max / ∆νch = 3768 / 25 = 150.7


Gain Equalization in EDFA Chains

• The preferred solution today is to add an optical filter within the amplifier with a carefully designed passband to compensate for the gain spectrum of the amplifier so as to obtain a flat spectrum at its output.

• Both dielectric thin-film filters and long-period fiber gratings are good candidates for this purpose.

No equalisation

Pre-emphasis

Equalizing filter within each amplifier


Dependence of Q-factor on Launch Power Level

• Q-factor variations with launched power in long-haul systems.

• Q factor increases initially with launched power, reaches a peak value, and then decreases with a further increase in power because of the onset of the nonlinear effects.

• The reduction in multi-channel systems is more pronounced than in single channel systems due to the contribution of interchannel nonlinear fibre effects.

• XPM is usually the most important multi-channel nonlinear impairment at 10 Gbit/s per channel: just a few (~6) channels contribute to this limitation.

Q fa

ctor

Section input power

Single-channel

Multi-channel

Reduction of maximum input power �Reduction of maximum nonlinear phase shift

due to interchannel nonlinear fibre effects(XPM, FWM and SRS)


Design of WDM Links

The similar steps to single channel systems design are followed but with a reduction of the maximum input power per section

Remarks

1) Transmission penalties due to multi-channel fibre nonlinear effects (XPM, FWM and SRS) should be taken into account.

2) FEC has no impact on the penalty due to each multi-channel fibre nonlinear effect.

System margin of the link

, ,FEC ,SPM,max ,XPM,max ,FWM,maxdBs R R i i i iM OSNR OSNR P P P= − − ∆ − − ∆ − ∆ −… …


WDM Networks

• These networks provide circuit-switched end-to-end optical channels, or lightpaths, between network nodes to their users, or clients.

• A lightpath consists of an optical channel, or wavelength, between two network nodes that is routed through multiple intermediate nodes. Intermediate nodes may switch and convert wavelengths.

• These networks may thus be thought of as wavelength-routing networks.

• Lightpaths are set up and taken down as dictated by the users of the network.

• Noteworthy features of these networks:

– Wavelength reuse– Wavelength conversion – Transparency– Circuit switching – Survivability


Architecture of WDM NetworksWDM Network Elements

• Optical Line Terminals (OLTs)

• Optical Add-Drop Multiplexers (OADMs),

• Optical Crossconnects (OXCs)

• Optical line amplifiers -deployed along the fibre link at periodic locations to amplify the light signal

• OLTs, OADMs, and OXCs may themselves incorporate optical amplifiers

• OLTs are widely deployed, and OADMs are deployed to a lesser extent. OXCs are just beginning to be deployed

• The architecture supports a variety of topologies, including ring and mesh topologies.• The users (or clients) of this network are connected to the OLTs, OADMs, or OXCs.• The network supports a variety of client types, such as IP routers, ATM switches, and SONET terminals and ADMs.

Lightpaths


OLT

• Transponder adaptation functions:– Modification of the signal wavelength

(in order to get an ITU wavelength)– Addition of overhead for control and

management functions– Addition of FEC– BER monitoring

O/E/O

O/E/O

Non ITU λ

Non ITU λ

Router IP

ADM SDH

ADM SDH

Laser

λOSC

ITU λ1

MUX EDFAITU λ2

ITU λ3

Adaptation functions

Optical Line Terminal

Transponder

λ1, λ2, λ3, λOSC

Only the multiplexing function is illustrated. The demultiplexing is also performed in the OLT (for

the opposite direction of communication)

• OLTs multiplex multiple wavelengths into a single fiber and also demultiplex a composite WDM signal into individual wavelengths.

• OLTs are used at either end of a point-to-point link.

Addition of optical supervisory channel, λOSC

= 1510 or 1620 nm

• Transponder aspects:– Can be fixed-wavelength or tunable.– typically are the bulk of the cost, footprint,

and power consumption in an OLT. – reducing the number of transponders helps

minimize both the cost and the size of the equipment deployed.


OADMs• OADMs are used at locations where some fraction of the wavelengths need to

be terminated locally and others need to be routed to other destinations.

• They are typically deployed in linear or ring topologies.

• Several architectures (parallel, series) using different technologies (AWG, FBG) have been proposed

• Static and reconfigurable OADMs are available– In reconfigurable OADMs, the wavelengths that are dropped and added in the

OADM can be changed– Reconfigurable OADMs allow the lightpaths can be set and removed as needed– Reconfigurable OADMs can be implemented using optical switches or tuned FBGs.

λNch

MUXDMUXλ1, λ2, ..., λNch

Optical switch (electrically controled by the network management)

Transponders

λ2

λ1

Example of a reconfigurable OADM using a

parallel architecture


OXCs• OXCs features

– Functions are similar to OADMs but on a much larger scale in terms of number of ports and wavelengths involved,

– are deployed in mesh topologies or in order to interconnect multiple rings– allow a fast reconfiguration of the network lightpaths

• OXC architectures– Opaque (O/E and E/O conversions are used inside the OXC)

• Signal regeneration is possible • Wavelength conversion is possible• Limited capacity and just one bit rate is used

– Transparent (all-optical)• Several architectures have been proposed with and without wavelength conversion

Remark

• OADM and OXC performances are mainly degraded by intrachannel XTalk• Signals of same optical frequency are combined in OADMs and OXCs

due to the imperfect isolation between ports of the optical switches


All-optical OXC Architectures

Remark: OLTs of OXC do not use transponders

Optical Switch

λ1λ2λ3

λ1λ2λ3

λ1λ2λ3

λ1λ2λ3

λ1λ2λ3

λ1λ2λ3

OLT

OLT

OLTOLT

OLT

OLTλ1, λ2, λ3

λ1, λ2, λ3

λ1, λ2, λ3

λ1, λ2, λ3

λ1, λ2, λ3

λ1, λ2, λ3

X

Without wavelength conversion

Optical Switch

λ1λ2λ3

λ1λ2λ3

λ1λ2λ3

OLT

OLT

OLTOLT

OLT

OLTλ1, λ2, λ3

λ1, λ2, λ3

λ1, λ2, λ3

λ1, λ2, λ3

λ1, λ2, λ3

λ1, λ2, λ3

λ1λ2λ3

λ1λ2λ3

λ1λ2λ3

Wavelength Converters

With wavelength conversion


Intrachannel XTalk Modeling

( ) ( ) ( )[ ] ( ) ( )[ ]

( )( )

0 S S S 0

S

Electric field at the PIN input (just one channel interferer):

= 2 cos 2 2 cos 2

={0, 1}, depending on whether a 0 or 1 is being sent in the desired channel; = {0, 1},

i i i i

i

E t p d t t t p d t t t

d td t

πν φ ε πν φ⋅ + + ⋅ +

( ) ( )S

S

depending on whether a 0 or 1 is being sent in the XTalk channel; and is the optical frequency of the signal and XTalk carriers; and are the random phases of the signal and XTalk channels

(

i

it tν ν

φ φit is assumed that all channels have an infinite extinction ratio)

( ) ( ) [ ]( )

( ) ( )

S

,1 0

S ,0 0

Worst case XTalk (lower power level for 1 and higher power level for 0)

For bit 1, 1, and 1, cos =-1 (worst case), :

1 2


i i i

i i

i i i

d t d t

p p

d t d t p p

ε ε

ε

ε

= = ⋅

= −

= = =

�

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )0 S 0 0 S S S

Power incident on PIN within the receiver bandwidth (proportional to the squared electric field)

= 2 cos 2i i i i i i ip t p d t p d t p d t d t t t tε ε π ν ν φ φ+ + ⋅ − + −

( ) ( ) ( )( ) ( ) ( ) ( )[ ]

S

0 S 0

0 S S

For intrachannel XTalk, :

=

2 cos

i

i i i

i i i

p t p d t p d t

p d t d t t t

ν ν

ε

ε φ φ

=

+ ⋅ +

⋅ −


Power Penalty due to Intrachannel XTalk

Ideal situation (no intrachannel XTalk)

,1 0 ,0

0

2

no XT

, 0

2

12

i i

i

i

p p p

Q k p k p

Qpk

= = ⇒

= = ⇒

=

Real situation (with intrachannel XTalk): ( )

( )( ) ( )

( )

,1 0 ,0 0

0 0

2

2w/ intra

1 2 ,

1 2 2 1 2

1 12 1 2

i i i i

i i i i i

i

i i

p p p p

Q k p p k p

Qpk

ε ε

ε ε ε ε

ε ε

= − = ⇒

= − − = − −

⇒ =

− −

Intrachannel XTalk power penalty, in dB

( ) ( )1

w/ intraintra 10 10 10

no intra

10log 20log 1 2 20log 1 2ii

i i ii

pP

p

εε ε ε

∆ = = − − − ≈ − −

�

Q factor dependence on power levels of bits 1 and 0 (for dominance of signal-ASE beat noise)

( ) ( ),1 ,0,1 ,0

,1 ,0

n i ii i

r i r i

k p pQ k p p

k p k p−

= = −+

Definition of power penalty, in dB

real w/ intraintraXT 10 10

ideal no intra

10log 10logi i

i i

p pP

p p

∆ = =

Exercise: derive expression for the intrachannel Xtalk power penalty in case of an unamplified system



( ) ( )1 2

220 20intra intra10

When the two interferers result from the same isolation,

1 10 16 Switch isolation (dB)= 20log 1 10 12P P

ε ε ε

ε −∆ −∆

= =

= − ⇒ − − +

intra 1 dB 0.0118 4 Switch isolation 25.27 dBiP ε⇓

∆ ≤ ⇒ ≤ ⇒ ≥

Calculation of the switch required isolation (dB) for an intrachannel XTalk penalty not exceeding 1 dB.

1. Assuming just one interferer

( ) ( )220 20intra intra101 10 4 Switch isolation (dB)= 20log 1 10 6P P

iε −∆ −∆= − ⇒ − − +

( )1

1intra 10

In case of interferers, should be replaced by :

20log 1 2

Nii i

Ni i

N

P

ε ε

ε=

=

∑

∆ = − − ∑

intra 1 dB 0.0118 16 Switch isolation 31.27 dBiP ε⇓

∆ ≤ ⇒ ≤ ⇒ ≥

2. Assuming the intrachannel XTalk comes from two interferersresulting from the same switch isolation level

Required isolation

increases with the square of the

number of interferers


OTN – Optical Transport Network• OTN is a recent ITU-T standardisation (G.709)

– designed to transport data packet traffic such as IP and Ethernet over fibre optics, as well as legacy traffic (SDH).

– the target is long distance transmission with data bit rates from 2.5 Gbit/s up to 40 Gbit/s

– defines an Optical Transport Hierarchy (OTH) similar to SDH with two stages: first is electrical (mapping of tributary signals and overhead insertion) and second is optics (creation of optical channels and WDM structure)

– Capabilities: FEC - RS(255,239) -, management, protocol transparency and asynchronous timing

39.813 Gbit/sSTM-25643.018 Gbit/sOTU39.953 Gbit/sSTM-6410.709 Gbit/sOTU22.488 Gbit/sSTM-162.666 Gbit/sOTU1Line ratesSDHLine ratesOTN (G.709)


Forward Error Correction (FEC) for OFTS


Why Forward Error Correction?

• It is entirely possible that a specified BER cannot be achieved.

• Only viable alternative � use an error-correction scheme.

• In one approach, errors are detected but not corrected.

– Suitable when packet switching is used (Internet protocol).

• In FEC, errors are detected and corrected at the receiver without any retransmission of bits.

• This scheme is best suited for lightwave systems operating with SONET or SDH protocol (synchronous transmission).

• Historically, lightwave systems did not employ FEC until the useof in-line optical amplifiers became common.


Basics of Error-Correcting Codes

• Basic idea: add extra bits at transmitter using a suitable code.

• At the receiver end, a decoder uses these control bits to detect and correct errors.

• How many errors can be corrected depends on the coding scheme employed.

• In general, more errors can be corrected by adding more control bits to the signal.

• There is a limit to this process since line bit rate of the system increases after the FEC coder.


FEC Code Overhead and Redundancy

• Code redundancy: ρFEC= Rb,l / Rb,i −1

• Code ratio: rFEC = Rb,i / Rb,l

FEC coder FEC decoderTransmissionpathRb,lRb,i Rb,l Rb,i

Tx Rx

Effective (line) bit rateInformation

(data) bit rateOptical

transmitterOpticalreceiver

Optical channel


Types of Error-Correcting Codes

• Classified under names such as:

– linear,

– cyclic,

– Hamming,

– Reed–Solomon,

– convolutional,

– product, and

– turbo codes.

• Among these, Reed–Solomon (RS) codes have attracted most attention for lightwave systems.


Characterisation of RS Codes

• Reed-Solomon (RS) codes do not operate on bits but on groups of bits �symbols

• RS code considers blocks of k data symbols and calculates r additional symbols with redundant information (FEC overhead), based on the code.

• The transmitter sends the blocks of n = k + r symbols to the receiver � RS(n,k).

• k + r coded symbols have to be transmitted in the same duration as k information symbols, each coded symbol has k/(k+r) the duration of uncoded symbol � line bit rate increases by n/k � rFEC = k / n

• RS(n,k) codes have the restriction that if a symbol consists of b bits � length of the code: n = 2b-1.– code length of n = 255 if (8-bit) bytes are used as symbols.

• The number of redundant bits r can take any even value.

RS(n,k)coder

RS(n,k)decoder

Transmissionpath

Tx RxBlocks ofk symbols

Blocks of n=k+r

symbols

Blocks of n=k+r

symbolsBlocks ofk symbols


Performance of RS Codes

• The receiver considers a block of n symbols, and knowing the code used by the transmitter, it can correctly decode the k data symbols even if up to r/2 of the n symbols are in error.

( ), , , ,

, ,

Coded (line) symbol error probability

1 1

: line bit error probability

be s l e b l

e b l

P P

P

= − −

( ), , , , , ,2 1

, ,

Information symbol error probability

1

: line symbol error probability

: number of -combinations from elements: greater integer contained in

n n in ie s i i e s l e s l

i r

e s lni

iP C P Pn

P

C i nx x

−

= +

= ⋅ ⋅ −∑

( ) ( )1, , , , , , , ,

, ,

Information bit error probability

1 1 1 1

: information symbol error probability

b be b i e s i e s i e b i

e s i

P P P P

P

= − − ⇔ = − −


Useful Approximation to Calculate the Data Bit Error Probability

( ) 2 12 1, , , , , ,2 1 , ,

Approximation for information symbol error probability2 1

1 for <<1n rrn

e s i e s l e s lr e s lr

P C P P nPn

− − + +

+ = ⋅ ⋅ −


RS Codes for OFTS

G.709 ITU (OTN) recommendation

• RS(255, 239) with b = 8: FEC overhead of 6.7%.

• RS(255, 223) with b = 8: FEC overhead of 14.4%

Improvement in BER

due to FEC is quantified

through the coding gain

Single RS

codes

RSproduct

codes

Conca-tenated

RScodes


Coding Gain (1)

• Coding gain: a measure of improvement in bit error probability through FEC.

– It is expressed in terms of the equivalent value of Q (for a given bit error probability) as

• Factor of 20 is used in place of 10 because performance is often quantified through Q2.

• If FEC decoder improves BER from 10−3 to 10−9, Q increases from 3 to 6, resulting in a coding gain of 6 dB.

• Magnitude of coding gain increases with the FEC overhead.

min10 min 10 FEC,min 10

FEC,min

FEC,min

min

Coding gain

20 log 20 log 20 log

: minimum factor required at receiver input

with FEC to achieve the required data bit error probability: minimum fa

cQG Q Q

Q

Q Q

Q Q

= − =

ctor required at receiver input without FEC to achieve the required data bit error probability


Coding Gain (2)

10-9

Coding gain of RS(255,239)

Coding gain of RS(255,223)


Coding Gain of RS codes

• For single RS codes, coding gain is 5.5 dB for 10% overhead and increases sublinearly, reaching 8 dB for 50% overhead.

• It can be improved by concatenating two or more RS codes or by employing the RS product codes.

@ bit error probability

of 10-9


Compromise on FEC Implementation

• While implementing FEC, one faces a dilemma.

– As the overhead is increased to realize more coding gain, line bit rate increases.

– Since Q factor realized at the receiver depends on the bit rate, its value is reduced, and BER actually worsens.

– Decoder improves it but it first has to overcome the degradation caused by the increased bit rate.

• If an aggressive FEC scheme is employed, BER may degrade so muchthat the system is not operable even with the FEC coder.

• An optimum range of coding overhead exists for every system designed to operate at a specific bit rate over a certain distance.


Gross vs. Net Coding Gain

( )2

,2

, 10 min 10 FEC,min

Gross coding

Using the approximation for the required OSNR

1

1

and, for the same extinction ratio and optical filter with and without FEC, we can write

20log 20log

e nR

o

c N

Q B rosnrB r

G Q Q

+= ⋅−

= −

,

, ,FEC10

, gain,

10log

c G

e n

e nG

BB

−

��

, min FEC,min

FEC,min

min

Net coding gain

: minimum OSNR required at receiver input

with FEC to achieve the required data bit error probability: minimum OSNR required at receiver input

c NG OSNR OSNROSNR

OSNR

= −

without FEC to achieve the required data bit error probability

What really matters from the viewpoint of system design

(achievable distance)!

, ,FEC, , 10

,10log e n

c N c Ge n

BG G

B

= −

, , , ,FEC ,

,, , 10

,

For and

(in the same proportionality)

10 log

e n b i e n b l

b lc N c G

b i

B R B R

RG G

R

∝ ∝

= −


Symbol Interleaving

• Without interleaving, the symbols would be transmitted in row order � symbols in row 1 are transmitted, followed by the symbols in row 2, and so on.

• The idea of interleaving is to transmit the first d symbols in column 1, followed by the first d symbols in column 2, and so on. Thus, symbol 1 would be followed by symbol k + 1.

• When d symbols have been transmitted from all n columns, we transmit the next d symbols in column 1 - from rows (d + 1) to 2d -, followed by the next d symbols in column 2, and so on. The parameter d is called the interleaving depth.

• Suppose there is a burst of b symbol errors. Only ceil(b/d) of these symbols will occur in the same row due to interleaving � a (255,223) Reed-Solomon code will be able to correct any burst of b errors when interleaving to depth d is used, provided ceil(b/d) < 16.

n-k redundant symbolsdk...(d-1)k+3(d-1)k+2(d-1)k+1d

n-k redundant symbols...............

n-k redundant symbols3k...2k+32k+22k+13

n-k redundant symbols2k...k+2k+2k+12

n-k redundant symbolsk...3211

n...k...321Indexes

Information symbols Redundancy symbols

RS(n,k)

ch4_ofts

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