 Solution

ID: past-exam-of-the-information-theory-course-of-the-university-of-oxford/2021/3/d/solution

I (X; Y) = H (X) - H (X ∣ Y) \leq H (X) \leq lo g_{2} ∣ X ∣ = 1.

Taking the maximum over input laws proves $C \leq 1$ bit per channel use. This bound comes from the binary input alphabet itself; no specific transition probabilities or decoder are needed.

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