Question

In a communication channel encoder every data bit is repeated five times independently and at the receiver, a majority vote decides the value of each data bit. If the uncoded bit error probability is ${10}^{-3}$, then the coded bit error probability will be

• A. ${10}^{-8}$
• B. ${10}^{-6}$
• C. ${10}^{-5}$
• D. ${10}^{-10}$

Answer 1

The correct option is A ${10}^{-8}$

$P_o={\sum }_{i=3}^5\left[\begin{array}{c}5\\ i\end{array}\right]p^i(1-p{)}^{5-i}$

$=\left(\begin{array}{c}5\\ 3\end{array}\right)\left({10}^{-3}{)}^3\right(1-{10}^{-3}{)}^2+\left(\begin{array}{c}5\\ 4\end{array}\right)\left({10}^{-3}{)}^4\right(1-{10}^{-3})+({10}^{-3}{)}^5$

$\approx {10}^{-8}$