Question

Consider the discrete memoryless channel shown below.

$\text{The probabilities}P\left(x_1\right)=0.40\text{and}P\left(x_0\right)=\mathrm{0.60.}\text{If it is known that the transmitted symbol is}{x}_1,\text{then the average information that can be obtained by reading the corresponding output symbols is \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_bits/symbol.}$

• A. 0.97

Answer 1

The correct option is A 0.97
$\text{When it is known that the transmitted symbol is}{x}_1\text{, the corresponding output symbols exist with probabilities,}$

$P\left(y_0|x_1\right)=0.40$
$P\left(y_1|x_1\right)=0.60$
$\text{Required entropy}=H(Y|X=x_1)\text{= Entropy [0.40, 0.60]}$
$=-\left[0.40{\log }_2\right(0.40)+0.60{\log }_2(0.60\left)\right]\text{bits/symbol}$
$=0.97\text{bits/symbol}$