Let us assume the input
message sequence is defined as m, and given by m 1 1 0 11. The states of the encoder are shown in
Fig. 5.23 for the first 5-bit streams.
The input/output bit sequence can be presented in a concise form (see Fig. 5.24).
PERFORMANCE IMPROVEMENT TECHNIQUES 243
(Y1, Y2) = (1, 1) Tb Tb
+
+
1 0 0
(Y1, Y2) = (0, 1) Tb Tb
+
+
1 1 0
(Y1, Y2) = (0, 1) Tb Tb
+
+
0 1 1
(Y1, Y2) = (0, 0) Tb Tb
+
+
1 0 1
(Y1, Y2) = (0, 1) Tb Tb
+
+
1 1 0
FIGURE 5.23 Rate 1/2, convolutional code state machine.
Tb Tb
+
+
Input Bit Sequence Output Bit Sequence
11 01 01 00 01 01 11 00 M = 11011000
FIGURE 5.24 Convolutional encoder input and output bit stream.
(Y1, Y2) = 11 10 11 00 m = 1000 FEC
Encoder
FIGURE 5.25 Rate1/2, K 3 convolutional encoder impulse response.
We mentioned earlier in this section that the output can be viewed as the convolution of the input
bit stream with the impulse response of the convolutional encoder. In Fig. 5.25 we present the impulse
response for the encoder using a particular example.
It was also mentioned that the FEC encoder polynomial was time invariant. Hence once the
impulse response of the encoder is known, it can be used at any time.
Since convolutional codes are linear we will show the output to be a superposition of the impulse
responses, simply shifted in time.
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