GATE 2017 EC (EC2) – Question 31
Which of the following graphs shows the Shannon capacity (channel capacity), in bits, of a memoryless binary symmetric channel with crossover probability p?
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Correct answer: (C) Option C in the figure
Explanation
The capacity of a binary symmetric channel is $C=1-H_b(p)$ bits per use, where
$$H_b(p)=-p\log_2p-(1-p)\log_2(1-p).$$
At p=0 the channel is error-free, so C=1. At p=1 every bit is inverted deterministically and can be recovered, so C=1 again. At p=1/2 the output is independent of the input, giving C=0.
The curve is symmetric about p=1/2 and smoothly convex, rather than V-shaped. This is graph **C**.