Turbo Codes

Prasanta Kumar BarikComputer Science & Engg.

Regd No-0701106246

AgendaProject objectives and motivationsChannel CodingTurbo Codes TechnologyTurbo Codes PerformanceTurbo Coding ApplicationConclusion

Communication System Structural modular approachVarious componentsOf defined functions

ChannelCoding

Source Coding ModulationFormatting

Digitization Multiplexing Accesstechniques

send

receive

Channel CodingTo encode the information sent over a

communication channel in such a way that in the presence of

channel noise, errors can be detected and/or corrected.

Can be categorized intoBackward error correction (BEC)Forward error correction (FEC )

Objective: provide coded signals with better distance properties

Types of codingBlock codingConvolutional coding: codes differ from

block codes in the sense that they do not break the message stream into fixed-size blocks. Instead redundancy is added continuously to the whole stream. The encoder keeps M previous input bits in memory. Each output bit of the encoder then depends on the current input bit as well as the M stored bits.

Structured Redundency

Channel encoderInput word

k-bit

Output wordn-bit

Redundancy = (n-k)Code rate = k/n

codewordCode sequence

A Need for Better CodesEnergy efficiency vs Bandwidth efficiency Codes with lower rate (i.e. bigger

redundancy) correct more errors.then communication system can operate with a lower transmit power, transmit over longer distances, tolerate more interference, use smaller antennas and transmit at a higher data rate. These properties make the code energy efficient.

low-rate codes have a large overhead and are hence more heavy on bandwidth consumption. Also, decoding complexity grows exponentially with code length.

Shannon Theory

For every combination of bandwidth (W), channel type, signal power (S) and received noise power (N), there is a theoretical upper limit on the data transmission rate R, for which error-free data transmission is possible. This limit is called channel capacity or also Shannon capacity.

sets a limit to the energy efficiency of a code.

A decibel is a relative measure. If E is the actual energy and Eref is the theoretical lower bound, then the relative energy increase in decibels is

 .   Since,   A twofold relative energy increase equals

3dB. 

Turbo codes Turbo codes are a class of error correcting

codes codes introduced in 1993 that come closer to approaching Shannon’s limit than any other class of error correcting codes.

Turbo codes achieve their remarkable performance with relatively low complexity encoding and decoding algorithms.

Turbo Encoder

Input

RSC

RSC

Interleaver

Systematic codeword

random

X

Y1

Y2

Recursive Systematic CodersCopy of the data in natural order

Recursive

S1 S2 S3

Data stream

Systematic

Calculated parity bits

InterleaverThe interleaver’s function is to permute low

weight code words in one encoder into high weight code words for the other encoder.A “row-column” interleaver: data is written row-

wise and read columnwise.While very simple, it also provides little randomness.

A “helical” interleaver: data is written row-wise and read diagonally.

  An “odd-even” interleaver: first, the bits are left uninterleaved and encoded, but only the odd-positioned coded bits are stored. Then, the bits arescrambled and encoded, but now only the even-positioned coded bits arestored. Odd-even encoders can be used, when the second encoder producesone output bit per one input bit.

INPUTX1 X2 X3 X4 X5

X6 X7 X8 X9 X10X11 X12 X13 X14 X15

Helical interleaver outputX11

X7 X3 X14

X10

X1 X12

X8 X4 X15

X6 X2 X13

X9 X5

Row-column interleaver outputX1 X6 X1

1X2 X7 X1

2X3 X8 X1

3X4 X9 X1

4X5 X1

0X15

Odd-even interleaver outputEncoder output without interleaving

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10

X11

X12

X13

X14

X15

Y1 - Y3 - Y5 - Y7 - Y9 - Y11

- Y13

- Y15

Encoder output with row-column interleaving

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10

X11

X12

X13

X14

X15

- Z6 - Z2 - Z12

- Z8 - Z4 - Z14

- Z10

-

Final output of the encoder

Y1 Z6 Y3 Z2 Y5 Z12

Y7 Z8 Y9 Z4 Y11

Z14

Y13

Z10

Y15

Turbo DecodingCriterion

For n probabilistic processors working together to estimate common symbols, all of them should agree on the symbols with the probabilities as a single decoder could do

Turbo Decoder

Turbo Decoder The inputs to the decoders are the Log

likelihood ratio (LLR) for the individual symbol d.

LLR value for the symbol d is defined ( Berrou) as

Turbo DecoderThe SISO decoder

reevaluates the LLR utilizing the local Y1 and Y2 redundancies to improve the confidence

•The value z is the extrinsic value determined by the same decoder and it is negative if d is 0 and it is positive if d is 1•The updated LLR is fed into the other decoder and which calculates the z and updates the LLR for several iterations•After several iterations , both decoders converge to a value for that symbol.

Turbo DecodingCompare the LLR output, to see if the

estimate is towards 0 or 1 then take HD

How Do they Work (© IEEE spectrum)

How Do they Work (© IEEE spectrum)

Turbo Codes Performance

Turbo Codes ApplicationsDeep space explorationMobile 3G systems

In use in Japan UMTS

Conclusion : End of SearchTurbo codes achieved the theorical limits

with small gapGive rise to new codes : Low Density Parity

Check (LDPC)Need

Improvements in decoding delay

Reference

http://www.google.com[2] University of South Australia, Institute

for Telecommunications Research,Turbo coding research group. http://www.itr.unisa.edu.au/~steven/turbo/.

[3] S.A. Barbulescu and S.S. Pietrobon. Turbo codes: A tutorial on a new class of powerful error correction coding schemes. Part I: Code structures and interleaverdesign. J. Elec. and Electron.Eng., Australia, 19:129–142, September 1999.

Thank You…..