Question Five:

$(5$ marks$)$

Consider the following irregular PAM constellation diagram shown in Figure $2.$ The transmission is affected by additive white Gaussian noise with a mean of zero and a variance $($power$)$ of $\frac{N_0}{2}.$

a$.$ Draw me decision regions. $(1$ mark$)$

b$.$ Find an expression of the probability of error as a function of the bit energy. Assume that the four symbols are equiprobable.

$(2$ marks$)$

c$.$ Determine the average energy per bit and rewrite the error probability in terms of this value. $(2$ marks$)$