GATE 2014 EC (EC3) – Question 62
A binary X has P(X = 1) = 1/3 and enters the shown cascade of two independent identical BSCs, each crossover probability 1/2. Outputs are Y₁,Y₂. Find H(Y₁) + H(Y₂) (bits).
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Correct answer: 1.9 to 2.1
Explanation
A BSC with crossover probability1/2outputs an unbiased bit independently of its input distribution. Therefore Y1is uniform and has entropy1bit even though P(X=1)=1/3. The second such channel also makes Y2uniform with entropy1bit. Hence **H(Y1)+H(Y2)=2bits**.