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A ternary channel emits 3 symbols x1, x2 and x3 with probabilities Px(x1) = 0.4 and Px(x2) = Px(x3) = Q. The mutual information I(x|y) (in bits/symbol) would be given as (p is given to be 0.8)
  • a)
    1.1375
  • b)
    1.1378
  • c)
    1.1379
  • d)
    1.374
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A ternary channel emits 3 symbols x1, x2 and x3 with probabilities Px...
Probabilities P,Q and Q are 0.4,0.3 and 0.3
We know that mutual information is given as follows,
I(x ∣ y) = H(x) − H(x ∣ y)
And Entropies are defined as,
H(x) = ∑−P (xi) log2 ⁡P(xi)
We get Hx as 1.571 bits/symbol.
And,
H(x ∣ y)= ∑ij − P(yj) P(xi ∣ yj) log2 ⁡P(xi)
We get Hx|y as 0.4332 bits/symbol
Mutual Information would be obtained as,
1(x ∣ y)=1.571−0.4332
=1.1378bits/symbol
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A ternary channel emits 3 symbols x1, x2 and x3 with probabilities Px(x1) = 0.4 and Px(x2) = Px(x3) = Q. The mutual information I(x|y) (in bits/symbol) would be given as (p is given to be 0.8)a)1.1375b)1.1378c)1.1379d)1.374Correct answer is option 'B'. Can you explain this answer?
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