Turbo Codes

Turbo codes

1. INTR INTROD ODUC UCTIO TION N

TURBO CODES constitute major development in the field of Forward Error 

Correction (FEC).

In electrical engineering and digital communications turbo codes are a class of  high performance performance error correction correction code developed developed in 1993 which are finding finding use in deep satellite communication and other applications where designers seek to achieve maximal information transfer over a limited bandwidth communication link in the  presence of data corrupting noise.

Exhibiting performance approaching the Shannon limit, Turbo Codes (TC) have the TC block set features efficient encoder and decoder designs seen rapid adoption in the design of digital communication systems. systems. Desirable and Designable Designable introduces the basics of turbo codes in their different flavors (more specifically,  parallel concatenated convolutional turbo codes and block turbo codes). Through the 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 implem implemen ented ted and and the the attra attracti ctive ve perf perfor orma manc ncee resu result ltss that that can can be achiev achieved ed in throughput, latency .

The last ten years have seen the appearance of a new type of correction code the tur turbo bo cod code. e. Thi Thiss rep repres resent entss a sig signifi nifican cantt dev develo elopme pment nt in the fie field ld of erro errorrcorrecting codes. The principle of decoding is to be found in an iterative exchange of  information inform ation between elementary decoders, decoders, called extrinsic information, information, and it is 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, wireless networks

and local radio loops. Future applications could

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

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Turbo codes

2.

THE “TURBO PRINCIPLE”

Allows a single very complex operation (decoding a turbo code) to be split into two much simpler operations operat ions (decoding component codes).

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

3. ERROR ERROR DETECTION DETECTION AND CORREC CORRECTION TION Errors can be categorized as follows:

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a). Single bit: one one bit error 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.

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For common methods of error detection are the following:

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a). Vertical Vertical redundancy check(VRC)  b). Longitudinal redundancy check (LRC) c). Cyclic redundancy check (CRC) d). Checksum In VRC an extra bit is added to the data unit.

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

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

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

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division. Checksum Checksum is is used used by the higher higher layer protocols protocols (

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TCP/IP) TCP/IP) for for error error detection. detection.

a). To To divides the data into sections .  b). Add the sections together using one's complement arithmetic. c). Take Take the complement of the final sum; this is the checksum. The hamming code is a single bit error correction method using redundant bits.

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Turbo codes

4. TYPE TYPES S OF ERRO ERRORS RS

Wherever Wherever an electromagnetic electromagnetic signal signal flow one point point to another ,it is subject subject to unpred unpredicta ictable ble inferen inference ce from from heat,ma heat,magne gnetism tism and other other forms forms of electric electricity ity.Th .This is inference can change the shape or timing of the signal.There are two types of errors :single :single bit error and burst error.In error.In single single bit error a ‘0’ is changed changed to ‘1’ or a ‘1’ is is changed to ‘0’.In burst error ,multiple bits are changed.

errors

Single bit

Burst

Fig(1) : Types of errors

4. A) SINGLE BIT ERROR  The term single bit error means that only one bit of given data unit is changed from 1 to 0 or from 0 to 1. In single bit error only one bit in the data unit has changed.

0

0

0

0

1

0

1

0

0

1

0

↑ 0 changed to 1 ↑ 0

0

0

0

0

Fig (2): Single Bit Error 

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Turbo codes Figure shows the effect of a single bit bit error as a data unit.For a single bit error to occur ,the noise must must have a duration of ‘1’ microsecond.A single  bit error can happen if we are sending data using parallel transmission.

Example:

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

BURST ERROR 

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

0

0

0

1

↓

0

0

1

0

1

0

1

1

1

0

↓

1

1

Fig (3): Burst Error 

Figure shows the effect effect of burst error on a data unit.In this case ‘00011010 ‘00011010 ‘ was send but ‘00111 ‘0011111 110’ 0’ was received.The received.The length of the burst is measured measured from the first corrupted corrupted bit bit to the last corrupted corrupted bit.Burst bit.Burst error is most likely to happen in a serial communication.the number of bits affected depends on the data rate and duration of noise.

5.

ERROR DETECTION

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Turbo codes

Detection: We can de detect many errors during transmission t ransmission

Redundancy: 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 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. Erro Errorr detec detectio tion n uses uses the the conc concep eptt of redud redudun unda dancy ncy,, mean meanss addi adding ng extra extra bits bits to detecting errors at the destination.

Detectio Dete ction n Meth ethods ods

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

5. A) Vertical Vertical redundancy check:

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 is most common and least expensive mechanism.

Performance:

VRC cannot detect errors where the total number of bits changed is even. If any two  bits change in transmission ,the changes cancel each other and the data unit will pass pass a parity check even though the data unit is damaged.The damaged.The same holds true for any even number of errors.VRC can detect all single-bit errors.It can detect burst errors only if  the total number of errors in each data unit is odd.

5. B) Longitudinal redundancy check:

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Turbo codes

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.

Performance:

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  will not detect an error.

5. C) Cyclic redundancy check:

CRC CRC is base based d on bina binary ry divi divisi sion on.. In CRC CRC a no: no: of redun redunda dant nt bits bits,, called called CRC remainder is appended to the end of data units so that the redundancy data unit   beco become mess exact exactly ly divi divisi sibl blee by a seco second nd,, pred predete etermi rmine ned d bina binary ry numb number er.. As its 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 have been damaged in transmit and must be rejected.

Performance

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

5. D) Checksum The The error error detec detecti tion on meth method od used used by the the high higher er layer layer prot protoc ocol olss is called called checksum. In the sender the checksum generator subdivides the data units in to equal segm segmen ents ts of n bits bits.. Thes Thesee segm segmen ents ts are adde added d toge togeth ther er usin using g 1’s 1’s compl complem emen entt 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 transmitted across the network. So if the sum of the data segment T, The checksum will be –T.

6. ERRO ERROR R CORRE CORRECT CTIO ION N Nehru College of Engineering And Research Centre

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Turbo codes

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 use an error correcting code, which automatically corrects certain errors.It requires 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 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 data data and and redun redunda dancy ncy.. The The numb number er of redun redunda dancy ncy bits bits requi required red to make make thes thesee corrections, in dramatically higher than that required for single bit correction.

7. BTC: BTC: BLOCK BLOCK TURB TURBO O CODE CODE Nehru College of Engineering And Research Centre

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Turbo codes 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 gain gain for rather high high coding coding rate (R > 0.7) 0.7) and less subject subject to an error error floor than than Convolution Turbo Codes (CTC).

8. CONV CONVOLU OLUTIO TIONAL NAL CODE CODE In telecommunication, a convolutional code is a type of error-correcting code in whic which h (a) (a) each each m-bit -bit inform informati ation on symbo symboll (each (each m-bit -bit strin string) g) to be enco encode ded d is transformed into an n-bit symbol, where m/n is the code rate (n ≥ m) and (b) the transformation is a function of the last information symbols, where k  is the constraint length of the code.

d

RSC1 Interleaver

RSC2 FIG(4) : Convolutional Code

The origin original al Turbo Turbo code code used used a parall parallel el concate concatenat nation ion of two relativ relatively ely simple simple 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 “Inter “Interleav leaver er gain” gain” which which produc produces es a random random-lik -likee overall overall codewo codeword rd or floor floor than than Convolution Turbo Codes (CTC).

9. TURB TURBO O DECO DECODI DING NG

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Turbo codes •

Decoder Decoderss are are asso associat ciated ed with with each compon component ent encode encoderr.

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Deco Decode ders rs take take turn turnss estim estimati ating ng and and exch exchan angi ging ng dist distrib ribut utio ion n on info inform rmati ation on  bits.

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

Fig(5) : Turbo Decoding 

Interleaver

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The interleaver’s interleaver ’s function is to permute low weight code words in one encoder  into high weight code words for the other encoder.

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Most input sequences are associated with parity sequences that are not selfterminating.

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Turbo codes Input sequences with self-terminating parity sequences form terminating terminating code words. words. The origin original al Turbo Turbo code code used used a parall parallel el concate concatenat nation ion of two relativ relatively ely simple simple recursive systematic convolutional (RSC) codes with large interleaving.

Although the component codes are weak, the output turbo code word is very   pow powerf erful ul due due to the the “Int “Interl erleav eaver er gain gain”” which which prod produc uces es a rand random om-l -lik ikee over overall all codeword.

Fig(6) : Concatenated encoder and decoder 

The encoder is formed by the parallel concatenation of two convolutional 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 elementary decoder passes to the other soft (probabilistic) information about each bit of the sequence to decode. This soft information, called extrinsic information, is updated at each iteration.

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Turbo codes

10.THE MINIMUM DISTANCE OF TURBO-LIKE CODE We derive worst-case upper bounds on the minimum distance of parallel concatenated concatenated Turbo codes, codes, serially serially concatenated concatenated Turbo codes, codes, repeat-accumu repeat-accumulate late codes, codes, repeatrepeat-con convol volute ute codes, codes, and general generalizat ization ionss of these these codes codes obtain obtained ed by allowin allowing g non-li non-linea nearr and large-m large-memo emory ry constit constituen uentt codes. codes. We show show that that paralle parallellconcatenated

Turbo urbo code codess and and repeat repeat-co -conv nvol olut utee code codess with with subsub-li line near ar memor memory y are asymptotically bad. We also show that depth-two serially concatenated codes with 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 conca concate tena natin ting g a repeti repetiti tion on code code with with two two accum accumul ulato atorr code codess thro throug ugh h rando random m  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 turbo codes, whose performance in terms of bit error probability has been shown to be 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 improved when soft outputs from the decoders are used in an iterative decoding  process.

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Turbo codes 12. ADVANTAGES

& DISADVANTAGES

ADVANTAGES Of all practical error correction methods known to date, turbo codes and lowdensity parity-check codes (LDPCs) come closest to approaching the Shannon limit, the theoretical limit of maximum information transfer rate over a noisy channel. 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 transmit at a certain data rate. Their main drawbacks are the relatively high decoding complex complexity ity and relativ relatively ely high high latency latency,, which which make make them them unsuit unsuitable able for some some applications. For satellite use, this is not of great concern, since the transmission distance itself introduces latency due to the finite propagation speed. Prior to Turbo codes, because practical implementations of LDPCs had not  been developed, the most widespread technique that approached the Shannon limit combined Reed-Solomon error correction block codes. DISADVANTAGES

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Their Their main main draw drawba back ckss are the the relat relativ ively ely high high deco decodi ding ng compl complex exity ity and and relatively high latency latenc y, which make them unsuitable for some applications. For  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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Turbo codes 13. TURBO

CODES : PRINCIPLES AND AND APPLICATIONS

This is intended for use by advanced level students and professional engineers involved in coding and telecommunication research. The material is organized into a coherent framework, starting with basic concepts of block and Convolutional coding, and gradua gradually lly increas increasing ing in a logical logical and progre progress ssive ive manner manner to more more advanc advanced ed material, including applications

The application of turbo-codes in digital communication systems, mainly in three parts. The first part considers systems of combined turbo-code and a nd modulation.

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 (SNR) are achieved at no extra cost of energy, complexity, or delay. Conventional turbocodes with binary signaling divide the bit energy equally among the transmitted turboencoder 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 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 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 of the standard deviation over the mean of the bound is asymptotically constant (for  large large inte interle rleav aver er lengt length, h, N), N), decre decreas ases es with with N, and and incre increas ases es with with SNR. SNR. The The distribution of the bound is also computationally developed.

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 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. 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  possess better performance potential in some senses. The standard turbo decoding algorithms, however, do not appear to achieve this potential.

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Turbo codes 14. THE

MODEL

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  process of moving information across a network.The OSI model is not a protocol ;it is a model for understanding understanding and designing a network architecture that is interoperable.

15.LAYERED ARCHITECTURE The OSI model is built of seven ordered layers:

a. Phys Physic ical al lay layer   b.  b. Data Data link link lay layer  c. Network lay layeer  d. Trans ranspo port rt lay layer  e. Sess Sessio ion n lay layer  f. Pres Presen enta tati tion on lay layer  er  g. Appl Applic icat atio ion n lay layer  er 

PHYSICAL LAYER: LAYER:

This This is the lowest lowest layer layer in a commun communicat ication ion system system and is respon responsib sible le for the 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.

DATA LINK LAYER:

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  point to point connection between two devices or a point to multipoint connection  between one sender and several receivers.

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Turbo codes NETWORK LAYER:

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

TRANSPORT LAYER: LAYER:

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

SESSION LAYER:

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

PRESENTATION LAYER:

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

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

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 resulting message over the network. Compression:

Data compression reduces the number of bits to be transmitted.

APPLICATION LAYER:

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 management system etc. Nehru College of Engineering And Research Centre

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Turbo codes

16.CONCLUSION

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Today, many modern systems use TURBO CODES.

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We can use turbo codes for compression of binary sequences. Networks must   be be able able to trans transfe ferr data data from from one devic devicee

to anot anothe herr with with comp comple lete te

accuracy.Anytime data are transmitted from source to destination; they can  become corrupted in passage. For reliable communication, errors must be deleted and corrected. Error detect ion and correction correction are implemented implemented either  at the data link layer or the transport layer of the OSI model.

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Turbo codes

17.REFERENCES

Websites:

1) www www.wik .wikipe ipedi dia. a.or org g 2) www www.iee .ieee. e.or org g 3) www www.tur .turbo bo-co -code des. s.co com m 4) www www.lib.lib-as asc.e c.ekm km.o .org rg

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