U. Glaeser

FIGURE 34.58 Viterbi algorithm detection on the PR4 trellis.
The Viterbi detector will start to search the trellis accumulating branch distance from sequence y. In
the first recursion of the algorithm, there are two paths of length 1 at the distance
from y. Next, each of the two paths of length 1 are extended in two ways forming four paths of length 2
at squared Euclidean distance from the sequence y
and this accumulated distance of four paths labels the four trellis states. In the next loop of the algorithm
each of the paths are again extended in two ways to form eight paths of length 3, two paths to each node
at level (depth) 3.
Node 00
Node 10
Node 01
© 2002 by CRC Press LLC
d( y,0)
( 0.9 – 0)
2
= = 0.81
d( y,1)
( 0.9 – 1)
2
= = 0.01
d( y, ( 0,0)
) 0.81 ( 0.2 – 0)
2
= + = 0.85
d( y, ( 0,1)
) 0.81 ( 0.2 – 1)
2
= + = 1.45
d( y, ( 1,0)
) 0.01 ( 0.2 – 0)
2
= + = 0.05
d( y, ( 1,1)
) 0.01 ( 0.2 – 1)
2
= + = 0.65
d( y, ( 0,0,0)
) 0.85 ( −0.6 – 0)
2
= + = 1.21
d( y, ( 1,0, – 1)
) 0.05 ( −0.6 + 1)
2
= + = 0.21 surviving path
d( y, ( 0,0,1)
) 0.85 ( −0.6 – 1)
2
= + = 3.41
d( y, ( 1,0,0)
) 0.05 ( −0.6 – 0)
2
= + = 0.41 surviving path
d( y, ( 0,1,0)
) 1.45 ( −0.6 – 0)
2
= + = 1.81
d( y, ( 1,1, – 1)
) 0.65 ( −0.6 + 1)
2
= + =
0.81 surviving path