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2Introduction
z
−1
z
−1
z
−1
B
A
X
z
−1
z
−1
z
−1
B’
A’
X’
Interleaver
Puncture
and
repetition
X
P1
P2
P3
Information
Switches in upper position for information bits and in lower position for tail bits
Introduction
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EncodingisdoneasshowninFigure1.The3GPPandIS2000turboencodersemploytworecursive,
systematic,convolutional(RSC)encodersconnectedinparallel,withaninterleaver(theturbointerleaver)
precedingthesecondrecursiveconvolutionalencoder.Thetworecursiveconvolutionalcodesarecalled
theconstituentencodersoftheturbocodeandhaveaconstraintlengthK=4.
Figure1.3GPPandIS2000Turbo-EncoderBlockDiagram
Theoutputsoftheconstituentencodersarepuncturedandrepeated(Fdenotestheframesize,XandX'
aresystematicdata,A,B,A',andB'areparitydata,X',A',andB'aretheinterleavedversionsofX,A,and
Bdata):
•Datarate1/2(2×Fbits):
X
0
A
0
X
1
A'
1
X
2
A
2
X
3
A'
3
…
•Datarate1/3(3×Fbits):
X
0
A
0
A'
0
X
1
A
1
A'
1
X
2
A
2
A'
2
X
3
A
3
A'
3
…
•Daterate1/4(4×Fbits):
X
0
A
0
B
0
B'
0
X
1
A
1
A'
1
B'
1
X
2
A
2
B
2
B'
2
X
3
A
3
A'
3
B'
3
…
Forthetailbits,thesequenceis:
•IS2000tailrate1/2and3GPPtailrate1/3:12bits
X
F
A
F
X
F+1
A
F+1
X
F+2
A
F+2
X'
F
A'
F
X'
F+1
A'
F+1
X'
F+2
A'
F+2
•IS2000tailrate1/3:18bits(systematicbitrepeatedtwice)
X
F
X
F
A
F
X
F+1
X
F+1
A
F+1
X
F+2
X
F+2
A
F+2
X'
F
X'
F
A'
F
X'
F+1
X'
F+1
A'
F+1
X'
F+2
X'
F+2
A'
F+2
•IS2000tailrate1/4:24bits(systematicbitrepeatedtwice)
X
F
X
F
A
F
B
F
X
F+1
X
F+1
A
F+1
B
F+1
X
F+2
X
F+2
A
F+2
B
F+2
X'
F
X'
F
A'
F
B'
F
X'
F+1
X'
F+1
A'
F+1
B'
F+1
X'
F+2
X'
F+2
A'
F+2
B'
F+2
Thedecodingprocessisaniterativealgorithmbasedonsimpledecodersindividuallymatchedtothe
RSCcodes.Ageneric3GPPandIS2000turbodecoderisshowninFigure2.
Eachdecodersendsaposteriorilikelihoodestimatesofthedecodedbitstotheotherdecoder,and
10TMS320C6457Turbo-DecoderCoprocessor2SPRUGK1–March2009
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