Turbo Codes

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1. 1. IN

INTR

TROD

ODUC

UCTIO

TION

N

TURBO CODES

TURBO CODES constitute major development in the field of Forward Error constitute major development in the field of Forward Error Correction (FEC).

Correction (FEC).

In electrical engineering and digital communications turbo codes are a class of In electrical engineering and digital communications turbo codes are a class of high performa

high performance error nce error correctcorrection code ion code develodeveloped in ped in 1993 which are 1993 which are findinfinding g use inuse in deep satellite communication and other applications where designers seek to achieve deep satellite communication and other applications where designers seek to achieve maximal information transfer over a limited bandwidth communication link in the maximal information transfer over a limited bandwidth communication link in the presence of data corrupting noise.

presence of data corrupting noise.

Exhibiting performance approaching the Shannon limit, Turbo Codes (TC) Exhibiting performance approaching the Shannon limit, Turbo Codes (TC) have the TC block set features efficient encoder and decoder designs seen rapid have the TC block set features efficient encoder and decoder designs seen rapid adoption in the

adoption in the design of design of digital communication sysdigital communication systems. Desirable and Designtems. Desirable and Designableable introduces the basics of turbo codes in their different flavors (more specifically, introduces the basics of turbo codes in their different flavors (more specifically, parallel concatenated convolutional turbo codes and block turbo codes). Through the parallel concatenated convolutional turbo codes and block turbo codes). Through the application of systemic design methodology that considers data transfer and storage as application of systemic design methodology that considers data transfer and storage as top priority candidates for optimization, the authors show how turbo codes can be top priority candidates for optimization, the authors show how turbo codes can be imp

implemlemenented ted anand d ththe e atattratractictive ve peperfrforormamancnce e reresusultlts s ththat at cacan n be be achachievieved ed inin throughput, latency .

throughput, latency .

The last ten years have seen the appearance of a new type of correction code

-the

the turturbo bo codcode. e. ThiThis s reprepresresentents s a a sigsignifinificancant t devdeveloelopmepment nt in in the the fiefield ld of of erroerror-

r-correcting codes. The principle of decoding is to be found in an iterative exchange of

correcting codes. The principle of decoding is to be found in an iterative exchange of

inform

information between elementary decodersation between elementary decoders, , called extrinsic informacalled extrinsic information, and tion, and it it is thisis this

principle from which the term turbo originates. The turbo concept is now applied to

block codes as well as other parts of a digital transmission system, such as detection,

demodulation. Applications that integrate turbo codes into their standards are mobile

communications,

communications, wireless wireless networks networks and and local local radio radio loops. loops. Future Future applications applications couldcould

include cable transmission, short-distance communication or data storage includes

cable transmission, short-distance communication or data storage.

Nehru College of Engineering And Research Centre Nehru College of Engineering And Research Centre

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2.

THE “TURBO PRINCIPLE”

Allows a single very complex operation (decoding a turbo code) to be split Allows a single very complex operation (decoding a turbo code) to be split into two much simpler operat

into two much simpler operations (decoding component codes).ions (decoding component codes).

Use “soft information” from output of one operation to assist with the other operation. Use “soft information” from output of one operation to assist with the other operation.

3. 3. ERRO

ERROR DET

R DETECTION

ECTION AND C

AND CORREC

ORRECTION

TION

•

•Errors can be categorized as follows:Errors can be categorized as follows:

a).

a). Single bit: oSingle bit: one bit error ne bit error per data unit.per data unit.

b). Burst: two or more bit bit errors per data unit. b). Burst: two or more bit bit errors per data unit.

•

•Redundancy is the concept of sending extra bits for use in error detection.Redundancy is the concept of sending extra bits for use in error detection. •

•For common methods For common methods of error detection of error detection are the following:are the following:

a). V

a). Vertical ertical redundancy check(VRC)redundancy check(VRC) b). Longitudinal redundancy check (LRC) b). Longitudinal redundancy check (LRC)

c). Cyclic redundancy check (CRC) c). Cyclic redundancy check (CRC) d). Checksum

d). Checksum

•

•In VRC an extra bit is added to the data unit.In VRC an extra bit is added to the data unit. •

•VRC can detect only an odd number of errors: it cannot detect an odd number of VRC can detect only an odd number of errors: it cannot detect an odd number of

errors. errors.

•

•In LRC, a redundant data unit is follows n data units.In LRC, a redundant data unit is follows n data units. •

•CRC, the most powerfull of the redundancy checking techniques, is based on binaryCRC, the most powerfull of the redundancy checking techniques, is based on binary

division. division.

•

•CheckChecksum isum is uss used by ed by the hthe higher igher layer layer protoprotocols cols (( TCP/TCP/IP) foIP) for error error detectr detection.ion.

a). T

a). To divides the data o divides the data into sections .into sections .

b). Add the sections together using one's complement arithmetic. b). Add the sections together using one's complement arithmetic.

c). T

c). Take the complement of ake the complement of the final sum; this the final sum; this is the checksum.is the checksum.

•

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4. 4. TY

TYPE

PES OF

S OF ER

ERRO

RORS

RS

Wherev

Wherever an electromager an electromagnetic signnetic signal flow al flow one poinone point to another ,it is subjet to another ,it is subject toct to unp

unpredredictaictable ble infinferenerence ce frofrom m heatheat,ma,magnegnetism tism and and othother er formforms s of of elecelectrictricityity.Th.Thisis inference can change the shape or timing of the signal.There are two types of errors inference can change the shape or timing of the signal.There are two types of errors :sing

:single bit error and burst errorle bit error and burst error.In singl.In single bit error e bit error a ‘0’ is chana ‘0’ is changed to ‘1’ or a ‘1’ iged to ‘1’ or a ‘1’ iss changed to ‘0’.In burst error ,multiple bits are changed.

changed to ‘0’.In burst error ,multiple bits are changed.

Fig(1) : Types of errors Fig(1) : Types of errors

4. 4. A)

A) SINGLE

SINGLE BIT

BIT ERROR

ERROR

The term single bit error means that only one bit of given data unit is The term single bit error means that only one bit of given data unit is changed from 1 to 0 or from

changed from 1 to 0 or from 0 to 1. 0 to 1. In single bit error only one In single bit error only one bit in the data unit hasbit in the data unit has changed. changed. ↑ ↑ 0 changed to 1 0 changed to 1 ↑ ↑ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0

Fig (2): Single Bit Error Fig (2): Single Bit Error

errors errors

Single bit

Single bit _Burst_Burst

0 0 0 0 1 0 1 0

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Figure shows the

Figure shows the effect of a single beffect of a single bit error it error as a data unit.For as a data unit.For aa single bit error to occur ,the noise mu

single bit error to occur ,the noise must have a duration of ‘1’ st have a duration of ‘1’ microsecond.A microsecond.A singlesingle bit error can happen if we are sending data using parallel transmission.

bit error can happen if we are sending data using parallel transmission.

Example: Example:

If 8 wires are used

If 8 wires are used to send all of to send all of the 8 the 8 bits of a bybits of a byte at the sametime te at the sametime and one of and one of the wires is noisy one bit can be corrupted in each time.

the wires is noisy one bit can be corrupted in each time.

BURST ERROR BURST ERROR

A burst error means that two or more bits in the data unit have changed. A burst error means that two or more bits in the data unit have changed.

0 0 00 00 11 11 00 11 00 ↓ ↓ ↓↓ 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0

Fig (3): Burst Error Fig (3): Burst Error

Figure shows the ef

Figure shows the effect of burst error on a data fect of burst error on a data unit.In this caseunit.In this case ‘0001

‘00011010 1010 ‘ ‘ was was send send but but ‘001‘001111111110’ 0’ was was receivereceived.The d.The length length of of the the burst burst isis measu

measured red from the first corfrom the first corrupted birupted bit to the last corruptet to the last corrupted bit.Bud bit.Burst error is mostrst error is most likely to happen in a serial communication.the number of bits affected depends on the likely to happen in a serial communication.the number of bits affected depends on the data rate and duration of noise.

data rate and duration of noise.

5.

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Detection: Detection: W

We can de e can de detect many errors during tdetect many errors during transmissionransmission

Redundancy: Redundancy:

One error detection mechanism allows to send every data unit twice. the One error detection mechanism allows to send every data unit twice. the receiving device would them be able to do a bit for bit comparison between the two receiving device would them be able to do a bit for bit comparison between the two versions of the data, instead of repeating the entire data stream ,a shorter groups of versions of the data, instead of repeating the entire data stream ,a shorter groups of bits may be appended to the end of each unit. This technique is called redundancy. bits may be appended to the end of each unit. This technique is called redundancy.

Er

Erroror r dedetectectiotion n ususes es ththe e coconcncepept t of of redredududunundadancyncy, , memeanans s adaddiding ng exextra tra bitbits s toto detecting errors at the destination.

detecting errors at the destination.

Dete

Detectio

ction M

n M eth

ethods

ods

A.VRC A.VRC B.LRC B.LRC C.CRC C.CRC D.CHECKSUM D.CHECKSUM

5. A) V

5. A) Vertical redundancy

ertical redundancy check:

check:

In a vertical redundancy check the parity bit is added to every data unit. So that the In a vertical redundancy check the parity bit is added to every data unit. So that the total number of 1’s becomes even. It

total number of 1’s becomes even. It is most common and least expensive mechanism.is most common and least expensive mechanism.

Performance: Performance:

VRC cannot detect errors where the total number of bits changed is even. If

VRC cannot detect errors where the total number of bits changed is even. If any twoany two bits

bits change in transmission ,the change in transmission ,the changes cancel each other and the data unit will pchanges cancel each other and the data unit will passass a parity check even though the data unit is damaged.T

a parity check even though the data unit is damaged.The same holds he same holds true for any eventrue for any even number of errors.VRC can detect all single-bit errors.It can detect burst errors only if number of errors.VRC can detect all single-bit errors.It can detect burst errors only if the

the total number total number of errors of errors in each in each data unit data unit is is odd.odd.

5. B) Longitudinal redundancy check:

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A block of bits organized in a table. a block of bits divided into rows and a A block of bits organized in a table. a block of bits divided into rows and a redundant row of bits is added to the whole block. These two are based on addition. redundant row of bits is added to the whole block. These two are based on addition.

Performance: Performance:

LRC detecting burst errors .If two bits in one unit are damaged and two bits in LRC detecting burst errors .If two bits in one unit are damaged and two bits in exactly the same positions in another data unit are also damaged, the LRC checker exactly the same positions in another data unit are also damaged, the LRC checker will not detect an error.

will not detect an error.

5. C) Cyclic redundancy check:

CR

CRC C is is babasesed d on on bibinanary ry didivivisisionon. . In In CRCRC C a a nono: : of of redredunundadant nt bibitsts, , calcalled CRCled CRC remainder is appended to the end of data units so that the redundancy data unit remainder is appended to the end of data units so that the redundancy data unit b

becoecomemes s exexactactly ly didivivisisiblble e by by a a sesecocondnd, , prprededeteetermirminened d bibinanary ry nunumbmberer. . As As itsits destination the incoming data units is divided by the same number. If at this step there destination the incoming data units is divided by the same number. If at this step there is no remainder, the data unit is accepted. The remainder indicates that the data units is no remainder, the data unit is accepted. The remainder indicates that the data units have been damaged in transmit and must be rejected.

have been damaged in transmit and must be rejected.

Performance Performance

CRC is

CRC is very effective error detection methodvery effective error detection method.CRC can detect .CRC can detect all burst errorsall burst errors that affect an odd number of bits.

that affect an odd number of bits.

5. D) Checksum

Th

The e errerror or dedetectectition on memeththod od usused ed by by ththe e hihighgher er laylayer er prprototococolols s is is calcalledled checksum. In the sender the checksum generator subdivides the data units in to equal checksum. In the sender the checksum generator subdivides the data units in to equal se

segmgmenents ts of of n n bibitsts. . ThThesese e sesegmgmenents ts are are adaddeded d totogegethther er ususining g 1’1’s s comcomplplememenentt arithmetic. The total is then complemented and appended to the end of the original arithmetic. The total is then complemented and appended to the end of the original data units is redundancy bits, called the checksum failed.The extended data unit is data units is redundancy bits, called the checksum failed.The extended data unit is transmitted across the network. So if the sum of the data segment T, The checksum transmitted across the network. So if the sum of the data segment T, The checksum will be –T.

will be –T.

6.

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This can be handled in two ways. In one when an error is discovered the This can be handled in two ways. In one when an error is discovered the receiver can have the sender retransmit the entire data units. In other, a receiver can receiver can have the sender retransmit the entire data units. In other, a receiver can use an error correcting code, which automatically corrects certain errors.It requires use an error correcting code, which automatically corrects certain errors.It requires more redundancy bits than detection codes.

more redundancy bits than detection codes.

6. A) Single bit error correction:

A bit has two states 0 and 1.an errors occurs when receiver reads a 1 bit 0 or a A bit has two states 0 and 1.an errors occurs when receiver reads a 1 bit 0 or a 0 bit as a 1.to correct the error the receiver simply reverse the value of the altered bit. 0 bit as a 1.to correct the error the receiver simply reverse the value of the altered bit.

6. B) Hamming code:

It can be applied to data units of any length and uses the relationships between It can be applied to data units of any length and uses the relationships between da

data ta anand d redredunundadancyncy. . ThThe e nunumbmber er of of redredunundadancy ncy bibits ts reqrequiuired red to to mamake ke ththesesee corrections, in dramatically higher than that required for single bit correction.

corrections, in dramatically higher than that required for single bit correction.

7. 7. BTC

BTC: BLO

: BLOCK T

CK TURB

URBO CO

O CODE

DE

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Block Turbo Code (BTC) is a type of turbo codes. . Block Turbo-codes (BTC) are Block Turbo Code (BTC) is a type of turbo codes. . Block Turbo-codes (BTC) are promising forward error correction (FEC) codes providing close-to-optimal coding promising forward error correction (FEC) codes providing close-to-optimal coding

gai

gain for rather hign for rather high codih coding rate (R > ng rate (R > 0.70.7) and less sub) and less subject to an ject to an erroerror floor thar floor thann Convolution Turbo Codes (CTC).

Convolution Turbo Codes (CTC).

8. 8. CO

CONV

NVOLU

OLUTIO

TIONAL

NAL COD

CODE

E

In telecommunication, a

In telecommunication, a convolutional codeconvolutional code is a type of error-correcting code inis a type of error-correcting code in wh

whicich h (a(a) ) eaceachh m-bim-bit t infinformormatiation on sysymbombol l (eac(eachh mm-b-bit it ststrinring) g) to to be be enencocodeded d isis transformed into an

transformed into an nn-bit symbol, where-bit symbol, where mm//nn is the codeis the code raterate ((nn ≥≥ mm) and (b) the) and (b) the transformation is a function of the last information symbols, where

transformation is a function of the last information symbols, where k k is the constraintis the constraint length of the code.

length of the code.

FIG(4) : Convolutional Code FIG(4) : Convolutional Code

The

The orioriginginal al TuTurbo rbo codcode e useused d a a parparallallel el conconcatecatenatnation ion of of two two relrelativatively ely simsimpleple recursive systematic covolutional (RSC) codes with large interleaving. Although the recursive systematic covolutional (RSC) codes with large interleaving. Although the component codes are weak, the output turbo code word is very powerful due to the component codes are weak, the output turbo code word is very powerful due to the “In

“Interterleavleaver er gaigain” n” whiwhich ch proproducduces es a a ranrandomdom-lik-like e oveoverall rall codcodewoeword rd or or flofloor or thathann Convolution Turbo Codes (CTC).

Convolution Turbo Codes (CTC).

9. 9. TU

TURB

RBO DE

O DECO

CODI

DING

NG

d

RSC1

RSC2

Interleaver

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•• DecoDecoderders ars are ase assosociatciated wed with ith each each comcomponponent ent encencodeoderr..

•• DeDecocodeders rs tatake ke tuturnrns s esestimtimatiating ng anand d exexchchanangiging ng didiststribribututioion n on on ininfoformrmatiationon bits.

bits.

Information about the decoded input bits is passed iteratively between the two Information about the decoded input bits is passed iteratively between the two decoders.

decoders.

Fig(5) : Turbo Decoding Fig(5) : Turbo Decoding

Interleaver Interleaver



 The interleaverThe interleaver’s function is to permute low weight code words in one encoder ’s function is to permute low weight code words in one encoder into high weight code words for

into high weight code words for the other encoder.the other encoder.



 Most input sequences are associated with parity sequences that are not self-Most input sequences are associated with parity sequences that are not

self-terminating. terminating.

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Input sequences with self-terminating parity sequences form

Input sequences with self-terminating parity sequences form terminatinterminating g code code wordwords.s. The

The orioriginginal al TuTurbo rbo codcode e useused d a a parparallallel el conconcatecatenatnation ion of of two two relrelativatively ely simsimpleple recursive systematic convolutional (RSC) codes with large interleaving.

recursive systematic convolutional (RSC) codes with large interleaving.

Although the component codes are weak, the output turbo code word is very Although the component codes are weak, the output turbo code word is very p

powowerferful ul dudue e to to ththe e “I“Intnterlerleaveaver er gagainin” ” whwhich ich prprododucuces es a a rarandndomom-l-likike e ovovererallall codeword.

codeword.

Fig(6) : Concatenated encoder and decoder Fig(6) : Concatenated encoder and decoder

The encoder is formed by the parallel concatenation of two convolutional The encoder is formed by the parallel concatenation of two convolutional codes separated by an interleaver or permuter. An iterative process through the two codes separated by an interleaver or permuter. An iterative process through the two corresponding decoders is used to decode the data received from the channel. Each corresponding decoders is used to decode the data received from the channel. Each elementary decoder passes to the other soft (probabilistic) information about each bit elementary decoder passes to the other soft (probabilistic) information about each bit of the sequence to decode. This soft information, called extrinsic information, is of the sequence to decode. This soft information, called extrinsic information, is updated at each iteration.

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10.THE MINIMUM DISTANCE OF TURBO-LIKE

CODE

We derive worst-case upper bounds on the minimum distance of parallel We derive worst-case upper bounds on the minimum distance of parallel concate

concatenated Turbo nated Turbo codescodes, , seriallserially y concatconcatenated Turbo enated Turbo codescodes, , repeat-repeat-accumuaccumulatelate cod

codes, es, reprepeat-eat-conconvolvolute ute codcodes, es, and and gengeneraleralizatizationions s of of thethese se codcodes es obtobtainained ed byby allo

allowinwing g nonnon-li-lineanear r and and larlarge-mge-memoemory ry conconstitstituenuent t codcodes. es. WWe e shoshow w thathat t parparalleallel- l-concatenated

concatenated

T

Tururbo bo cocodedes s anand d reprepeateat-co-convnvololutute e cocodedes s wiwith th susub-b-lilinenear ar memmemorory y areare asymptotically bad. We also show that depth-two serially concatenated codes with asymptotically bad. We also show that depth-two serially concatenated codes with constant-memory outer codes and sub-linear-memory inner codes are asymptotically constant-memory outer codes and sub-linear-memory inner codes are asymptotically bad. In contrast, we prove that depth-three serially concatenated codes obtained by bad. In contrast, we prove that depth-three serially concatenated codes obtained by

co

concancatetenanatinting g a a reprepetietitition on cocode de wiwith th twtwo o accaccumumululatoator r cocodedes s ththrorougugh h ranrandodomm permutations can be asymptotically good.

permutations can be asymptotically good.

11.TURBO CODES IN IEEE

The goal is to describe the main ideas behind the new class of codes called The goal is to describe the main ideas behind the new class of codes called turbo codes, whose performance in terms of bit

turbo codes, whose performance in terms of bit error probability has been shown to beerror probability has been shown to be very close to the Shannon limit. A numerical example, using a simple concatenated very close to the Shannon limit. A numerical example, using a simple concatenated coding scheme, provides a vehicle for illustrating how error performance can be coding scheme, provides a vehicle for illustrating how error performance can be improved when soft outputs from the decoders are used in an iterative decoding improved when soft outputs from the decoders are used in an iterative decoding process.

process.

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12.

ADVANTAGES & DISADVANTAGES

ADVANTAGES

Of all practical error correction methods known to date, turbo

Of all practical error correction methods known to date, turbo codescodes and low-and low-density parity-check codes (LDPCs) come closest to approaching the Shannon limit, density parity-check codes (LDPCs) come closest to approaching the Shannon limit, the theoretical limit of maximum information transfer rate over a noisy channel.

the theoretical limit of maximum information transfer rate over a noisy channel.

Turbo codes make it possible to increase data rate without increasing the Turbo codes make it possible to increase data rate without increasing the power of a transmission, or they can be used to decrease the amount of power used to power of a transmission, or they can be used to decrease the amount of power used to transmit at a certain data rate. Their main drawbacks are the relatively high decoding transmit at a certain data rate. Their main drawbacks are the relatively high decoding comp

complexlexity ity and and relarelativtively ely highigh h latelatencyncy, , whiwhich ch makmake e thethem m unsunsuituitable able for for somsomee applications. For satellite use, this is not of great concern, since the transmission applications. For satellite use, this is not of great concern, since the transmission distance itself introduces latency due to the finite propagation speed.

distance itself introduces latency due to the finite propagation speed.

Prior to Turbo codes, because practical implementations of LDPCs had not Prior to Turbo codes, because practical implementations of LDPCs had not been developed, the most widespread technique that approached the Shannon limit been developed, the most widespread technique that approached the Shannon limit

combined Reed-Solomon error correction block codes. combined Reed-Solomon error correction block codes.

DISADVANTAGES DISADVANTAGES



 ThTheir eir mamain in drdrawawbabackcks s are are ththe e rerelatlativively ely hihigh gh dedecocodiding ng comcomplplexexity ity anandd relatively high latenc

relatively high latencyy, which make them , which make them unsuitable for some applications. For unsuitable for some applications. For satellite use, this is not of great concern, since the transmission distance itself satellite use, this is not of great concern, since the transmission distance itself introduces latency due to the finite propagation speed.

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13.

TURBO CODES :

TURBO CODES : PRINCIPLES A

PRINCIPLES AND

ND

APPLICATIONS

This is intended for use by advanced level students and professional engineers This is intended for use by advanced level students and professional engineers involved in coding and telecommunication research. The material is organized into a involved in coding and telecommunication research. The material is organized into a coherent framework, starting with basic concepts of block and Convolutional coding, coherent framework, starting with basic concepts of block and Convolutional coding, and

and gragraduadually lly incincreasreasing ing in in a a loglogical ical and and proprogregressssive ive manmanner ner to to mormore e advadvancanceded material, including applications

material, including applications

The application of turbo-codes in digital communication systems, mainly in The application of turbo-codes in digital communication systems, mainly in three parts. The first

three parts. The first part considers systems of combined turbo-code apart considers systems of combined turbo-code and modulation.nd modulation.

It is shown that by optimizing the labeling method and/or modifying the It is shown that by optimizing the labeling method and/or modifying the puncturing pattern, improvements of more than 0. 5 dB in signal to noise ratio

puncturing pattern, improvements of more than 0. 5 dB in signal to noise ratio (SNR)(SNR) are achieved at no extra cost of energy, complexity, or delay. Conventional are achieved at no extra cost of energy, complexity, or delay. Conventional codes with binary signaling divide the bit energy equally among the transmitted codes with binary signaling divide the bit energy equally among the transmitted turbo-encoder output bits. The second proposes a turbo-code scheme with unequal power encoder output bits. The second proposes a turbo-code scheme with unequal power allocation to the encoder output bits. 5 dB can be achieved over the conventional allocation to the encoder output bits. 5 dB can be achieved over the conventional turbo-coding scheme. The third part of this tackles the question of ``the sensitivity of turbo-coding scheme. The third part of this tackles the question of ``the sensitivity of the turbo-code performance towards the choice of the interleaver'', which was brought the turbo-code performance towards the choice of the interleaver'', which was brought up since the early studies of these codes. This is the first theoretical approach taken up since the early studies of these codes. This is the first theoretical approach taken towards this subject. The variance of the bound is evaluated. It is proven that the ratio towards this subject. The variance of the bound is evaluated. It is proven that the ratio of the standard deviation over the mean of the bound is asymptotically constant (for of the standard deviation over the mean of the bound is asymptotically constant (for lar

large ge ininteterlerleavaver er lenlengtgth, h, N)N), , dedecrecreasases es wiwith th N, N, anand d inincrecreasases es wiwith th SNSNR. R. ThThee distribution of the bound is also

distribution of the bound is also computationally developed.computationally developed.

It is shown that as SNR increases, a very low percentage of the interleavers It is shown that as SNR increases, a very low percentage of the interleavers deviate quite significantly from the average bound but the majority of the random deviate quite significantly from the average bound but the majority of the random interleavers result performances very close to the average. The contributions of input interleavers result performances very close to the average. The contributions of input words of different weights in the variance of performance bound are also evaluated. words of different weights in the variance of performance bound are also evaluated. Results show that these contributions vary significantly with SNR and N. New turbo Results show that these contributions vary significantly with SNR and N. New turbo codes based on the (8, 4, 3, 8) UM Hamming code are developed and shown to codes based on the (8, 4, 3, 8) UM Hamming code are developed and shown to possess better performance potential in some senses. The standard turbo decoding possess better performance potential in some senses. The standard turbo decoding

algorithms, however, do not appear to achieve

algorithms, however, do not appear to achieve this potential.this potential.

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14.

THE MODEL

OSI is the model.It allows for communication across all types of OSI is the model.It allows for communication across all types of computer systems.It consist of seven but related layers,each of which defines the computer systems.It consist of seven but related layers,each of which defines the process of moving information across a network.The OSI model is not a protocol ;it is process of moving information across a network.The OSI model is not a protocol ;it is

a model

a model for understandinfor understanding and g and designing designing a network a network architecture that is architecture that is interoperable.interoperable.

15.LAYERED ARCHITECTURE

The OSI model is built of seven ordered layers:

a.

a. PhPhysysicical al lalayyer er b

b.. DaData ta lilink nk lalayyer er cc.. NNeettwwoorrk lk layayeer r d.

d. TTraransnspoport rt lalayyer er e.

e. SeSessssioion n lalayyer er f.

f. PrPresesenentatatition lon layayer er g.

g. ApApplplicicatatioion ln layayer er

PHYSICAL

PHYSICAL LALAYER:YER:

Thi

This s is is the lowesthe lowest t laylayer er in in a a comcommunmunicatication systeion system m and is and is resresponponsibsible le for thefor the conversion of a stream of bits into signal that can be transmitted on the other conversion of a stream of bits into signal that can be transmitted on the other side. The receiver at the other physical layer converts back the signals to streams. side. The receiver at the other physical layer converts back the signals to streams.

DATA LINK LAYER: DATA LINK LAYER:

The main task of this layer includes multiplexing of different data streams, The main task of this layer includes multiplexing of different data streams, correction of transmission errors .The data link layer is responsible for a reliable correction of transmission errors .The data link layer is responsible for a reliable point to point connection between two devices or a point to multipoint connection point to point connection between two devices or a point to multipoint connection between one sender and several receivers.

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NETWORK LAYER: NETWORK LAYER:

This third layer is responsible for routing packets through a network or This third layer is responsible for routing packets through a network or establishing a connection between two entities over many other systems.Important establishing a connection between two entities over many other systems.Important functions are addressing, routing, device location etc.

functions are addressing, routing, device location etc.

TRANSPORT

TRANSPORT LALAYER:YER:

This layer is used in the reference model to establish an end to end This layer is used in the reference model to establish an end to end connection .Topics like flow and congestion control are relevant,especially if the connection .Topics like flow and congestion control are relevant,especially if the transport protocols known from the Internet

transport protocols known from the Internet ,TCP and UDP are over the link.,TCP and UDP are over the link.

SESSION LAYER: SESSION LAYER:

The session layer is the network dialog controller. It establishes maintains the The session layer is the network dialog controller. It establishes maintains the interaction between communicatng systems.It allows the communication between two interaction between communicatng systems.It allows the communication between two processes to take place in half-duplex or full-duplex.

processes to take place in half-duplex or full-duplex.

PRESENTATION LAYER: PRESENTATION LAYER:

This layer is responsible for

This layer is responsible for translation, encryption and compression.translation, encryption and compression. Translation:

Translation:

The information should be changed to bit streams before being transmitted. The information should be changed to bit streams before being transmitted. Encryption:

Encryption:

To carry information, a system must be able assure privacy. Encryption means To carry information, a system must be able assure privacy. Encryption means that the sender transforms the original information to another form and sends the that the sender transforms the original information to another form and sends the resulting message over the network.

resulting message over the network. Compression:

Compression:

Data compression reduces the number of bits to be transmitted. Data compression reduces the number of bits to be transmitted.

APPLICATION LAYER: APPLICATION LAYER:

The application layer enables the user, to access the network, it provides user The application layer enables the user, to access the network, it provides user interface and support for mail such as electronic mail, file transfer, shared database interface and support for mail such as electronic mail, file transfer, shared database management system etc.

management system etc.

(16)

16.CONCLUSION

•

• Today, many modern systems use TURBO CODES.Today, many modern systems use TURBO CODES. •

• We can use turbo codes for compression of binary sequences. Networks mustWe can use turbo codes for compression of binary sequences. Networks must

b

be e abable to trale to transnsfefer r dadata frota from one devm one devicice e to anto anototheher r wiwith coth compmpleletete accuracy.Anytime data are transmitted from source to destination; they can accuracy.Anytime data are transmitted from source to destination; they can become corrupted in passage. For reliable communication, errors must be become corrupted in passage. For reliable communication, errors must be

deleted and corrected. Error detect

deleted and corrected. Error detect ion and ion and correctcorrection are ion are implemeimplemented either nted either at the data link layer or the transport layer of the OSI model.

(17)

17.REFERENCES

Websites:

1)

1) wwwwww.w.wikikipeipedidia.a.ororgg 2)

2) wwwwww.i.ieeeee.e.ororgg 3)

3) wwwwww.t.tururbobo-co-codedes.s.cocomm 4)

4) wwwwww.li.lib-b-asasc.ec.ekmkm.o.orgrg