Consider the following example (see Fig. 5.26).
244 CHAPTER FIVE
Input Output
1 11 10 11 00
1 11101100
0 00000000
1 11 10 11 00
1 11101100
.
. 11 01 01 00 01
.
Coded Sequence
FIGURE 5.26 Convolutional encoder output by overlapping impulse responses.
An alternative method commonly used to describe and analyze
convolutional codes is the state diagram or state machine.
The state of the convolutional encoder is defined as the K 1
right-most bits used to calculate the output coded bits.
Continuing with the previous R 1/2, K 3 coder we can show
there are 2(31) 4 states. The encoder state diagram is shown in
Fig. 5.27, where the solid line corresponds to a state transition
when the input bit 0. The state diagram shows all the possible
transitions and various output-coded bits corresponding to their
respective input bits [1].
When the input bit is a 1 the corresponding state transition is
shown by a dashed line. Similarly an input bit of 0 produces state
transitions shown by a solid line. The output-coded bits are written
next to the state transition line. For example, consider the
case where the present state is 11 and a 0 bit is input into the
encoder. This will move the state to 01 and output to a coded bit
sequence of 01.
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