Exams › GATE › General Aptitude
A source alphabet consists of \(N\) symbols. A source encoder increases the probability of the first symbol by a small amount \(\varepsilon\) and decreases that of the second by \(\varepsilon\). After encoding, the entropy of the source
- increases
- remains the same
- increases only if \(N=2\)
- decreases
Correct answer: decreases
Solution
Entropy is a concave function of the probability distribution and decreases when the distribution becomes less uniform. Increasing one symbol's probability and decreasing another's by the same amount makes the source slightly more skewed, so entropy decreases.
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