A simple way to track the state transitions is to label each
state. We can define each state as
The next method used to analyze the encoder is the tree diagram. This basically adds the notion of a
time line to the state diagram, where time increases as we traverse the tree diagram toward the right side
of the page. In Fig. 5.28 we show the tree diagram of the FEC encoder with R 1/2 and K 3.
Here we show the first 5 bits of the input and all the possible output combinations. For the input
sequence of 11011 we have outlined the corresponding path in the tree diagram. The ability to show
a time line is also disadvantageous. By this we mean as the number of input bits increases the size of
the tree diagram dramatically and drastically grows out of control.
The last method used to analyze and describe the convolutional encoder is the trellis diagram. This
trellis diagram comes about by viewing the repetitive structure of the tree diagram. By viewing the
tree diagram we can see the states repeat after K branches (or transitions). Because of the property we
can still maintain the time line aspect with a manageable means of description. The trellis diagram is
shown in Fig. 5.29 with the number of states equaling 2(K1) 22 4 states.
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