Trellis diagram of a convolutional code with constraint length equal to $3$ and code rate equal to $\frac{1}{2}$

A$)$ Draw the state diagram of this encoder. Recall that the dotted line means that a $"1"$ information bit is available, and the solid line means that a $"0"$ information bit is available.

B$)$ Determine the resulting bit sequence at the output of the decoder if the message sequence available at the input of the encoder is $11010001.$

C$)$ The following message $"1111001"$ is encoded using this convolutional code. The sequence $11110101101111$ is received... Using the Viterbi algorithm, determine the first seven bits decoded from the sequence, and the number of errors made in decoding.

D$)$ Simulate in Matlab the convolutional code specified by the Trellis diagram and recover the original bits using the Viterbi decoder.