GATE 2014 EC (EC1) – Question 33
Find the capacity of a binary symmetric channel with crossover probability 0.5.
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Correct answer: -0.01 to 0.01
Explanation
A binary symmetric channel has capacity C=1−H2(p) bits per use. At p=1/2, H2(p)=−2(1/2)log2(1/2)=1, so **C=0**. The received bit is then equally likely to be either value regardless of the transmitted bit and carries no information about it.