Digital Signal Processing Reference
In-Depth Information
Fig.
9.10
. Two branches are shown from a
0
. One branch is at next node a
1
rep-
resenting decoded symbol as '00' and other branch is at b
1
representing decoded
signal as '11'.
Fig. 9.10
Viterbi decoder for
1st four coded bits
1
st
di-bit
Y=11
2
nd
di-bit
Y=01
Cumulative path
discrepancy
a
1
00(1)
00(2)
(3)
a
2
a
0
11(1)
b
1
11(0)
b
2
(3)
00(2)
c
2
(2)
Discrepancy
metric
11(0)
(0)
d
2
The branch from a
0
to b
1
represents decoded output as '11', which is same as
the 1st received duple ('11'). Hence, there is no discrepancy between the received
and the decoded signal. Therefore the measured metric of that branch is zero. This
metric is shown in 1st parentheses along the path of transition. When the next part
of bits Y
01 is received at nodes a
1
or b
1
, then from nodes a
1
and b
1
four possible
next states a
2
,b
2
,c
2
and d
2
are possible. Figure
9.11
shows all these transitions,
their decoded outputs and branch metrics corresponding to those decoded outputs.
The encircled number near a
2
,b
2
,c
2
and d
2
show path metric emerging from a
0
.
Here, the path metric of path a
0
b
1
d
2
is zero.
The next figure is showing the compact diagram for the mapping of the viterbi
decoding. Here s1, s2, s3, s4 are actually the states a, b, c and d with the designated
levels, as signified.
=
Fig. 9.11
Path mapping for viterbi decoder
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