Solve the following problem:
The block diagram of a binary convolutional code is shown in Figure .
1. Draw the state diagram for the code.
2. Find the transfer function of the code T (Z).
3. What is dfree, the minimum free distance of the code?
4. Assume that a message has been encoded by this code and transmitted over a binary symmetric channel with an error probability of p = 10-5. If the received sequence is
r = (110, 110, 110, 111, 010, 101, 101)
using the Viterbi algorithm, find the most likely information sequence, assuming that the convolutional code is terminated at the zero state.
5. Find an upper bound to the bit error probability of the code when the above binary symmetric channel is employed. Make any reasonable approximation.