Upload
prasant-kumar-barik
View
198
Download
3
Tags:
Embed Size (px)
Citation preview
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…..