GATE 2017 EC (EC2) – Question 62
Consider the binary memoryless channel characterized by the transition-probability diagram shown. The channel is
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Correct answer: (C) useless
Explanation
For either input symbol, the diagram gives output probabilities $P(Y=0\mid X)=0.25$ and $P(Y=1\mid X)=0.75$.
The conditional distribution is identical for both inputs, so observing the output supplies no information about which input was sent. Input and output are independent for every input distribution, giving mutual information and capacity zero.
The channel is therefore **useless, C**. It is not deterministic, because either output can occur for either input.