There is a discrete memoryless channel (DMC) with the channel input X E x = {l,2,3,4}. The channel output Y follows the following probabilistic rule. 1' : X probability % 2x probability % Answer the following questions. (a) Draw the schematic of the channel and clearly show possible channel outputs and the channel transition probabilities. [5 marks] (b) Write the mutual information 1(X ;l' ) as a function of the most general input probability distri- bution. [10 marks] (c) Find a way of using only a subset of the channel inputs such that the channel turns into a noiseless channel and the maximum mutual information (you need to quantify its value) can be achieved with zero error. [5 marks]