For a discrete memoryless channel, input and output symbols are represented by random variables X and Y respectively. If H(V) represents the entropy of a random variable V, then which one of the following relations is always true?

H (X | Y) = H (Y | X)

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H (Y | X) \leq H (Y)

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H (X | Y) \geq H (X)

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H (Y | X) \geq H (X)

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Solution

The correct option is B $H (Y | X) \leq H (Y)$

$\begin{matrix} H (X | Y) \leq H (X) H (Y | X) \leq H (Y) \end{matrix}} \Rightarrow a l w a y s t r u e$

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Similar questions

I f X a n d Y a r e t w o d i s c r e t e r a n d o m v a r i a b l e s a n d H (V) r e p r e s e n t s t h e e n t r o p y o f t h e v a r i a b l e V, t h e n c o n s i d e r t h e f o l l o w i n g r e l a t i o n s : S e l e c t t h e c o r r e c t r e l a t i o n s u s i n g t h e c o d e s g i v e n b e l o w . R 1 : H (X) \geq H (X | Y) R 2 : H (X, Y) \geq H (X) + H (Y) R 3 : H (x) - H (Y) = H (X | y) - H (Y | X)

R 1 : H (X + 2) = H (X)

R 2 : H (X + Y | X) \geq H (Y | X)

s_{0}

s_{1}

μ_{2} = 20, μ_{2}^{1} = 276

X

X

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