Consider a binary symmetric channel (BSC) with a crossover probability of 0.20. If two such BSCs are cascaded, then the crossover probability of the resultant BSC will be _____
0.32

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Solution

The correct option is A 0.32

$P (y_{0} | x_{1}) = P (y_{1} | x_{0})$
$= P (z_{0} | x_{1}) P (y_{0} | z_{0}) + P (z_{1} | x_{1}) P (y_{0} | z_{1})$
$= (0.20 \times 0.80) + (0.80 \times 0.20) = 0.32$
So, the crossover probability of the resultant BSC = 0.32

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Consider a binary symmetric channel (BSC) with a crossover probability of 0.20. If two such BSCs are cascaded, then the crossover probability of the resultant BSC will be _____0.32

The correct option is A 0.32 P(y0|x1)=P(y1|x0) =P(z0|x1)P(y0|z0)+P(z1|x1)P(y0|z1) =(0.20×0.80)+(0.80×0.20)=0.32 So, the crossover probability of the resultant BSC = 0.32

Consider a binary symmetric channel (BSC) with a crossover probability of 0.20. If two such BSCs are cascaded, then the crossover probability of the resultant BSC will be _____
0.32

The correct option is A 0.32

$P (y_{0} | x_{1}) = P (y_{1} | x_{0})$
$= P (z_{0} | x_{1}) P (y_{0} | z_{0}) + P (z_{1} | x_{1}) P (y_{0} | z_{1})$
$= (0.20 \times 0.80) + (0.80 \times 0.20) = 0.32$
So, the crossover probability of the resultant BSC = 0.32