For an integer $I$, the input-output relationship of a discrete memoryless channel is given by:
$Y = X + Z$ (mod $I$, i.e. sum indicates a modular addition)
where $I ≥ 2$, and
• $X$ is an integer chosen from the alphabet $A_x = \{1,\dots,2I\}$,
• $Z$ is noise which is a uniform Bernoulli random variable. This means that $A_z = \{0,1\}$, and
$$\Pr\{Z = 0\} = \Pr\{Z = 1\} = 0.5.$$
How can we calculate the capacity of this channel?