State-diagram 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 2-stage shift register, hence the encoder has four states. The four states are labeled S0, S1, S2, S3. At the time unit i the state is represented by (ui-1,ui-2).

In Fig. 1 the four states are denoted by S0=(00), S1=(10), S2=(01), S3=(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 S0=(00), S1=(01), S2=(10) and S3=(11). In such convention we have a different trellis, but the convolution code features are the same.)

 

Make your own experiment

Please, find the encoder structure for above state-diagram with out simulation tool.