Page 347 - Satellite Communications, Fourth Edition

Error Control Coding 327

(00)
(00) 0 0 0
Key
0 0 0 (11)
(U1 U2) 1 0 0
(00)
S1 S2 S3
0 0 0
(01)
(11) 0 1 0
1 0 0 (10)
(00) 1 1 0
0 0 0
(11)
(01) 0 0 1
0 1 0 (00)
(11) 1 0 1
1 0 0
(10)
(10) 0 1 1
1 1 0 (01)
(00) 1 1 1
Data 0 0 0
in
(00)
(11) 0 0 0
0 0 1 (11)
1 0 0
(01)
0 1 0
(01)
(00) 0 1 0
1 0 1 (10)
1 1 0
(11)
1 0 0
(11)
(10) 0 0 1
0 1 1 (00)
(10) 1 0 1
1 1 0
(10)
(01) 0 1 1
1 1 1 (01)
1 1 1
Figure 11.3 The tree diagram for the rate 1/2 convolutional encoder.
intended, it takes the lower branch, and then it can match all the fol-
lowing pairs with the branches in the decoding tree. On the basis of max-
imum likelihood, this would be the preferred path, and the correct input
1001 would be deduced.