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The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition probabilities are as marked.
The parameter α lies in the interval [0.25, 1]. The value of for which the capacity of this channel is maximized is ________ (round off to two decimal places).
Correct answer is '1'. Can you explain this answer?
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Most Upvoted Answer
The transition diagram of a discrete memoryless channel with three in...
Given channel is a symmetric channel as shown below,
For a symmetric channel having N inputs, the channel capacity is,
Where, P is the probability. In this problem N = 3 and P = α.
∴ Channel capacity will be
C = log23 + αlog2α + (1 - α) log2 (1 - α)
Differentiating both sides with respect to α , we get
For maxima or minima dC/dα = 0
logα = log(1 - α)
α = 1 - α
2α = 1
α = 1/2
∴ Channel capacity will be minimum if α = ½
The minimum value of channel capacity will be
If α = 1 then
C = log2 3 - 0.5 - 0.415
C = 1.584 - 0.5 - 0.415 = 0.669
On plotting the graph between channel capacity C and probability α .
∴ We can conclude that if α = 1, then the channel capacity will be maximum.
Hence, the correct answer is 1.
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The transition diagram of a discrete memoryless channel with three in...
Given channel is a symmetric channel as shown below,
For a symmetric channel having N inputs, the channel capacity is,
Where, P is the probability. In this problem N = 3 and P = α.
∴ Channel capacity will be
C = log23 + αlog2α + (1 - α) log2 (1 - α)
Differentiating both sides with respect to α , we get
For maxima or minima dC/dα = 0
logα = log(1 - α)
α = 1 - α
2α = 1
α = 1/2
∴ Channel capacity will be minimum if α = ½
The minimum value of channel capacity will be
If α = 1 then
C = log2 3 - 0.5 - 0.415
C = 1.584 - 0.5 - 0.415 = 0.669
On plotting the graph between channel capacity C and probability α .
∴ We can conclude that if α = 1, then the channel capacity will be maximum.
Hence, the correct answer is 1.
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The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition probabilities are as marked.The parameter α lies in the interval [0.25, 1]. The value of for which the capacity of this channel is maximized is ________ (round off to two decimal places).Correct answer is '1'. Can you explain this answer?
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