Digital Signal Processing Reference
In-Depth Information
(
a
)
(
b
)
FIGURE 10.48.
CCS plots of output using case 3: (
a
) convolutional encoder with AWGN
(sigma
=
3.0); (
b
) Viterbi decoder.
in the noise level with
s=
3.0, the decoder output is degraded, as shown in Figure
10.48.
Figure 10.49 illustrates case 4 using cosine (666
1500) as input. With the
technique.gel
slider selected for Viterbi decoding, the encoder output appears
between the 0 and 1 voltage levels, as shown in Figure 10.49
b
, since the input is of
plain binary form. The decoded output is the restored input cosine signal shown in
Figure 10.49
c
. There is no additive noise added in this case.
This project can be extended for real-time input and output signals.
+
Illustration of the Viterbi Decoding Algorithm
Much of the material introduced here can be found in Ref. 41. To illustrate the
Viterbi decoding algorithm, consider the basic Viterbi symbol inputs. Each time a
triad of channel symbols is received, a metric is computed to measure the “distance”
between what is received and all of the possible channel symbol triads that could
have been received. Going from
t
1, there are only two possible channel
symbol triads that could have been received: 000 and 111. This is because the con-
volutional encoder was initialized to the all-0s state, and given one input bit
=
0 to
t
=
1 or
0, there are only two states to transition to and two possible outputs of the encoder:
000 and 111.
The metric used is the Hamming distance between the received channel symbol
triad and the possible channel symbol triad. The Hamming distance is computed by
=
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