Q$2$: Consider a rate $R=\frac{1}{2}$ of Convolutional code with constrain length $K=3$ and the generator polynomials are: $g1=[101],g2=[001].(25$M$)$

a$)$ Draw the hardware encoder diagram corresponding to this code.

b$)$ Determine the code sequence produce by the massage $[011].$

c$)$ Construct the state diagram, and trellis for the encoder.

d$)$ The convolution code is used for transmission over an AWGN channel. The received sequence is $0010101111.$ Using the Viterbi algorithm, find the most likely data sequence.