(a) Given the BSC in Figure 4, with $P(x_1) = \alpha$. Show that (i)…

Question

(a) Given the BSC in Figure 4, with $P(x_1) = \alpha$. Show that

(i) $I(X; Y) = H(Y) + p \log_2(p) = (1-p) \log_2(1-p)$

(ii) $I(X; Y) \text{ when } \alpha = 0.5 \text{ and } p = 0.1$

(b) A DMS X with five symbols $x_1, x_2, x_3, x_4 \text{ and } x_5$ having probabilities $0.2, 0.15, 0.05, 0.1, 0.5$.

(i) Construct a Shannon - Fano coding for x and calculate code efficiency.

(ii) Repeat for Huffman coding. ( 10, 10 )