FEC IN OFC

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FORWARD CORRECTING CODES

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JANUARY 2012

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1.History of FEC2.Analysis of FEC

3.Principles of FEC and How they Work

4.Different Types of FEC

5.Three Generations of FEC

6.Positive impacts of FEC7.Applications

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HISTORY OF FECS

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The story of forward error correction (FEC) begins at end of 1940s.

Hamming invented the Hamming Code.

In 1950s Basic Concepts of several kinds of Codes were developed.

These are BCH , RS and Convolutional Codes.

In 1970s one of the first applications of the FEC was the Voyager

spacecraft.

HISTORY OF FECS

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Until the end of the 1980s FEC was ignored in OPTICAL FIBERCOMMUNICATIONS SYSTEMS

Because optical fiber communications system has very low BER (biterror rate ) at the order of10-9 to 10-15.But in typical radio and satellite

communication systems , BER is about 10-3 to 10-5

The first fully implimented application of FEC for optical transmission

was in submarine systems developed at the beginning of 1990s .B.C.Hand RS codes were used in submarine cable systems.

automatic routin throu h universal tele hone network

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HISTORY OF FECS

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ANALYSIS OF FORWARD ERROR

CORRECTING CODES

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In digital communication systems usually there are four manners for

applying error control coding shown below.

1-Automatic Repeat Request (ARQ)

2-Forward Error Correcting (FEC)

3-Hybrid Error Correcting (HEC)

4-Information Repeat Request (IRQ)

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All the codes but FEC need feedback channels.Because FEC by adding redundant data

which is used for correcting messages , provides the receiver to detect and correct

limited errors in the message without asking the sender to transmit other useful data

.So it can easily build a real time connection between one user and multiple users.This

makes FEC more practical.

ANALYSIS OF FORWARD ERROR

CORRECTING CODES

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In FEC , Communication systems needs a larger bandwidth than the original

message needs.Because transmitter adds some bits for receiver to correct and

detect the bit errors.These added bits are called redundant bits. FEC provides much

lower transmission delay compared to other error correction techniques.

It does not require original data to be retransmitted.

PRINCIPLES OF FEC AND HOW THEY WORK

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DIFFERENT TYPES OF FECS

The two major categories of FEC are Block Codes and Convolutional Codes

1-BLOCK CODES : Block codes work on fixed sized blocks of bits or symbols of

predetermined size.

a) GROUP LINEAR CODES

b) CYCLIC CODES

c) BCH CODE

d) REED-SOLOMON CODE

e) HAMMING CODE

2-CONVOLUTIONAL CODES: Convolutional codes work on arbitrary length bits or

symbol streams.Another difference against block code is convolutional code has

memory.

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BLOCK CODES

Generally, a block code is any code defined with a finite codeword length.

Systematic Block Code

Original message Control bits

Codeword

If the codeword is constructed by

Adding redundancy to the

Original message , it is called a

systematic code.

Examples of block codes: BCH, Hamming, Reed-Solomon, Turbo Codes,

Turbo Product Codes, LDPCs

RS ENCODER CHANNEL RS ENCODERInput Output

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BLOCK CODES

DATA OOO .0

DIVISOR

n zeros

n+1 bits

Remainder =CRC

Process at sender

n bits

DATA CRC

Process at Receiver

DIVISOR

Remainder

1- At th e sender a string of n zeros added to the data unit for error detection.

2- The new enlarged data unit is divided by thr predetermined divisor.The remainder is

called CRC

3- The n zeros that were added to data unit in step 1 are replaced by the n bit CRC4- The composite data is sent through the transmission channel.

5-The receiver divides this coming composite data with the same divisor which is used

at sender .

6-If there is no remainder after division , then there is no errors.A remainder indicates

that some bits corrupted during the transmission.The data unit is rejected.

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CONVOLUTIONAL CODES

Convolutional codes are generated using a shift register to apply a polynomial to a

stream of data.

Convolutional codes are typically decoded using the Viterbi algorithm, which increases in

complexity exponentially with the constraint length.

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THREE GENERATIONS OF FECS

REED AND SOLOMON CODES

-The first generation FEC systems was RS Code which has a net coding gain (NCG)

aproximately 6 dB .

-However , as transmission rates gradually increased to 10 Gbps other optical problems

gained in significance.

These are nonlinear effects but also ChromaticDispersion (CD) and polarization mode

dispersion (PMD).T hen first generation of FEC became invaluable.

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CONCETENATED CODES

-Then system designers started to seek more powerfull FEC codes.T

-These are Concetenated Codes.

They have approximately 8 dB net coding gain.They were classified as the second generation

of FEC codes around 2004.

Various kinds of code are listed in ITU_T.975.1


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Linear 1:N protection

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OUTER CODE INNER CODE CHANNEL INNER CODEOUTER

CODE

Simple (classical single level ) concetenated code

-Generally outer code is a RS code.-Generally inner code is a Convolutional code.

-RS code is used for error detection and correction.

-RS code has very good burst error performance , but has very bad noisy channel

performance

-Convolutional codes has very good noisy channel performance

-input data in encoded first as RS coded after that encoded as convolutional code.Then transmitted.At the receiver side Convolutional decodes the transmitted data .Then

RS decoder decodes and and corrects the data if needed.

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TURBO CODES

-Block Turbo Codes belongs to third generation FEC codes has net coding gain of 10 dB.

-These are classified into two categories

-First , Turbo Convolutional Codes (TCC)

-Second Block Turbo Codes (BTC) FEC .

-Both codes are superior over the concatenated codes.

-Generally TCC shows greater correction capability than BTC at low code rates .

-Conversely , BTC shows better performance at high code rates.

-This means lower power consumption and cost.BTC has a large minimum distance of 16.

-All these advantages seem to make it suitable for optical communication systems.

-The basic idea of turbo codes is to use two convolutional codes in parallel with some kind of

interleaving in between

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Turbo encoder

DECODER 1 INTERLEAVER DECODER 2 DE-INTERLEAVER

Input 1

nput 2

output

Turbo decoder

INTERLEAVER

ENCODER 2

ENCODER 1

Output 2

Output 1

Input

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INTERLEAVINGIf burst errors occur , it is very difficult to correct all errors .Especially in the

second and the third generation of FECs for avoiding from burst errors, a method

which is called as interleaving is applied.

X0 X3 X6 X9 X12X1 X4 X7 X10 X13X2 X5 X8 X11 X14

write

read

Input Sequence:X0 , X1, X2 , X3, X4 , X5, X6 , X7, X8 , X9, X10 , X11 , X12, X13 , X14,Output Sequence:X0 , X3, X6,X9 ,X12X1 X4, X7, X10 , X13, X2 , X5 , X8 ,X11, ,X14,

Interleaving depth 5

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LIGHT DENSITY PARITY CHECK CODE (LDPC)- Another potential solution to realize 10 dB net coding gain is LDPC.

-LDPC coding is catogorized as a third generation FEC .

-This coded was invented by Gallager in 1960s .-But it could not be implemented because of technological problems.

-In 1990s it was rediscovered by Mackay.-In 2002 LDPC codes were applied to optical Fiber Communications by Vasic and Djordjevic.

-They claimed the implementation cost should be lower than for BTC for 40 Gb/s systems.

-They showed that at a BER of 10 -13 net coding gain 10.9 dB which was demonstrated in

simulation.The calculation showed that The LDPC has potential to be improved further

more.-A precise comparison between BTC and LDPC , in terms of attainable net coding gain with

lower redundancy, reduced circuit size , lower latency , fewer iterations,has not been

completed.

-

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POSITIVE IMPACTS ON TRANSMISSION

SYSTEMS

Achieving the maximum transmission capacity

Reducing the numbers of repeaters.

Utilizing lower grade fibers.

Improving the sensitivity of optical receivers (ORs)

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APPLICATIONS

-With the development of digital technology .FEC codes has become to be used very intensively

in digital storage systems, deep-space and satellite communication systems, terestial radio andspecial in fiber optic systems.

In the internet transmission delay is an untolerant problem for real time application . Therefore

FEC is a potential error corecting code.To solve the problem of packet loss, FEC uses an adaptive

error control scheme for packet video based on Reed Solomon coding which encodes a block of

packets into npacket codeword .

In wireless communication system , the most common problem is multipath fading , multipath

propagation refraction .Therefore wireless system needs error correcting codes to ensure

reliability .We can see FEC codes are widely used in wireless communication table.

Wireless CommunicationTechnology FEC methods

Third generation Wireless Technology (3G) Convolutional Coding : Turbo Coding

Fourth generation Wireless Technology (4G) Concatenated Coding

Bluetooth

Convolutional Coding : Turbo Coding , LDPS,

RS

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FEC IN OFC