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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?
    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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    Community 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 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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    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? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about 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? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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