Consider a channel where $x_{n} \in\{0,1\}$ is the input and $y_{n}=x_{n} * z_{n}$ is the output, where $*$ is $\text{EX-OR}$ operation, and $P\left(z_{n}=x_{n-1}\right)=P\left(z_{n}=y_{n-1}\right)=\frac{1}{2}$. Note that communication starts at time $n=0$, and assume $x_{-1}=y_{-1}=0$. Then the capacity of the channel in bits is
- $\frac{1}{2}.$
- $1$.
- $<1.$
- $\geq 0.$
- Both $(c)$ and $(d)$.