Question: Prob. 2. A binary channel has binary input X and the transition probabilities given as Q=[0.50.50.70.30.20.8]. (a) How many possible values can the input take?

Prob. 2. A binary channel has binary input X and the transition probabilities given as Q=[0.50.50.70.30.20.8]. (a) How many possible values can the input take? How many possible outcomes does the output Y have? (b) Draw the channel transition diagram, and label the transition probability. (c) Find the capacity of the channel and the optimal channel input distribution. Try to calculate it analytically by taking the derivative of the formula. If you cannot complete the computation by hand, explain why the step is hard and then use software(Matlab or Python) to find it numerically. Prob. 2. A binary channel has binary input X and the transition probabilities given as Q=[0.50.50.70.30.20.8]. (a) How many possible values can the input take? How many possible outcomes does the output Y have? (b) Draw the channel transition diagram, and label the transition probability. (c) Find the capacity of the channel and the optimal channel input distribution. Try to calculate it analytically by taking the derivative of the formula. If you cannot complete the computation by hand, explain why the step is hard and then use software(Matlab or Python) to find it numerically

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