Statediagram description of convolutional
codes
Operation of a convolutional encoder can be described by a state
diagram. The state of the encoder is defined as the content of it's
shift register.
Fig. 1 State diagram of a (2,1,2) convolutional
encoder given in Fig. 2, less. 1.
Consider the encoder of the (2,1,2) convolutional
code given in Fig. 2 less. 1. The
state of the encoder is the content of the 2stage shift register,
hence the encoder has four states. The four states are labeled S_{0},
S_{1}, S_{2},
S_{3}.
At the time unit i the state is represented
by (u_{i1},u_{i}_{2}).
In Fig. 1 the four states are
denoted by S_{0}=(00),
S_{1}=(10), S_{2}=(01),
S_{3}=(11).
Figure 1 demonstrates the encoder's operation
for the duration of the first ten clock cycles tabulating the input
bits, the shift register states, and the corresponding output bits.
(We would certainly agree that S_{0}=(00),
S_{1}=(01), S_{2}=(10)
and S_{3}=(11). In such convention
we have a different trellis, but the convolution code features are
the same.)
Please, find the encoder structure for above statediagram
with out simulation tool.
