If the code is used with hard decision decoding on a

Question

A k = 1, K = 3, and n = 2 convolutional code is characterized by g₁ = [001] and g₂ = [101].

1. Draw the state diagram for the encoder.

2. Determine the transfer function of the code in the form T (Y, Z).

3. Is this code a catastrophic code? Why?

4. Determine the free distance of the code.

5. If the code is used with hard decision decoding on a channel with crossover probability of p = 10^-3, determine an upper bound on the average bit error probability of the code.