Exercise 4.7Calculate the system entropies where I is the binary erasure channel (BEC), introduced in §4.1,and the input probabilities of 0 and 1 are p and p. Show that this channel satisfies (4.9) and(4.10).H(BA) ≤H(B),H(AB) ≤ H(A),(4.9)(4.10) H(B | A) ≤ H(B),(4.9)d only if P = or p = 0, 1. This means that the uncertaintydecreases when A is known. Similarly, H(A | B) = H (p) +(p) (since H(q) ≥ H(P)), soH(AB) ≤ H (A),(4.10)

To start, let's first define the system entropies involved in this problem. The entropy of the input…

Answered: Exercise 4.7 Calculate the system…

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Exercise 4.7 Calculate the system entropies where I is the binary erasure channel (BEC), introduced in §4.1, and the input probabilities of 0 and 1 are p and p. Show that this channel satisfies (4.9) and (4.10). H(BA) ≤ H(B), H(AB) ≤ H(A), (4.9) (4.10)