Bipartite Graphs

1
Bipartite Graphs
Control nodes Variable nodes Parallel Turbo
decoder Serial Turbo decoder Turbo
equalization ISI cancalation Conclusions
2
Bipartite graph
variable nodes
control node
Input a priori probability Output Extrinsic
probability
Control node
Input Extrinsic probability Output a priori
probability
Variable node
3
Node update
Variable node
The probabilities comming from different foctor
nodes are independant
Control node
This is a equivalent to a partial summation
4
SISO
Ce sont les probabilité "extrinsèques" dans un
Turbo décodeur
Probabilité a priori des bits d'information
Probabilité a posteriori des bits d'information
Probabilité extrinsèque des bits d'information
SISO
Probabilité a priori des bits codés
Probabilité a posteriori des bits codés
Probabilité extrinsèque des bits codés
5
Parallel Turbo coder
Coder 1
Turbo decoder
AWGN Channel
Pronbability evaluation
Coder 2
AWGN Channel
Pronbability evaluation
6
Parallel Turbo decoder
A priori of coded bits
Decoder 1
Output
Variable node
A posteriori of information bits
A priori of information bits
Extrinsic of information bits
Decoder 2
A priori of information bits
Variable node
Extrinsic of information bits
A priori of coded bits
7
Observation of coded symbols
Variable node
Factor node
Variable node
Variable node
Simplified notation
8
Bipartite graph of parallel Turbo decoder
Info bit
Coded bit
Coded bit
Variable nodes
Decoder D1
Decoder D2
A priori
Extrinsic and app
APP of information bits
9
Serial Turbo coder
RSC coder
NRNSC coder
RSC
AWGN Channel
Pronbability evaluation
AWGN Channel
Pronbability evaluation
10
Serial Turbo decoder
Inner decoder RSC
A priori of coded bits
A priori of information bits
Outer decoder NRNSC
A posteriori of information bits
Output
Extrinsic of coded bits
11
Bipartite graph of serial Turbo decoder
Inner Coded bit
Outer coded bits Inner Systematic bits
A posteriori of Information bits
Inner_decoder
Outer_decoder
12
Turbo equalization
Extrinsic probabilities of Coded bits
A posteriori of information bits
Received Signal
interleaver
SISO decoder
SISO equalizer
De interleaaver
A priori probabilities of Coded bits
13
Bipartite graph
A priori probabilities of Coded bits
A posteriori of information bits
De interleaver
SISO decoder
SISO equalizer
interleaver
Extrinsic probabilities of Coded bits
Observation
14
Bipartite graph
ISI Canceler
ISI Canceler
decoder
ISI Canceler
15
Node update
APP or extrinsic
ISI Node
ISI cancellation
Matched filter
Extrinsic probability
16
Conclusion
The bipartite graph explain the message passing
algorithm
From the A priori probabilities and the
Extrinsic probabilities