Your design team is given the following generator polynomials of a binary convolutional encoder with rate 1/3:

g₁(D) = 1 + D² + D³

g₂(D) = D+ D³

g₃(D) = 1 + D³

a ) Design the convolutional encoder and draw the block diagram of the convolutional encoder. Label the design carefully.

b) How many zeros do we need to append at the end of the above bit stream? Why?

c) Draw the state diagram for the above convolutional encoder.

d) Draw the Trellis diagram for the above convolutional encoder. The summary of the trellis must be shown in a table indicating present state, input bit, next state and output.

e) Encode any 6-bit binary message using the Trellis designed in (d).

f) Decode the encoded message in (e) using the Viterbi algorithm. Show the followed path on the Trellis diagram clearly.

g) How many bits are received with error after decoding in part (f)?