Question

Consider the binary symmetric channel shown in the figure below:



A decision device is used at the receiver end. which is making decision in favour $m_0$. when $r_0$ is received and in favor of $m_1$. when $r_1$ is received. If any symbols $m_0$ and $m_1$ are equiprobable, then the average probability of error in decision making at the output of the channel will be equal to

• A. 0.8
• B. 0.4
• C. 0.2
• D. 0.1

Answer 1

The correct option is C 0.2

The average probability of error can be given as,

$P_e=P\left(r_0|m_1\right)P\left(m_1\right)+P\left(r_1|m_0\right)P\left(m_0\right)$
$=\left(0.2\right)\left(0.5\right)+\left(0.2\right)\left(0.5\right)$
$=0.2$