Problem $3(10$ points$)$: Assume a frame of $F=100$ bits, with bit$-$error$-$rate $($BER$)$ equal to ${10}^{-3}.$

a$)(4$ points$)$ Compute the probability that the frame is received in error.

b$)(2$ points$)$ Compute the average number of erroneous bits in an average frame.

c$)(4$ points$)$ For the give BER, it is desired to design the frame size such that the frame error rate $($FER$)$

$($i$.$e$.$ Probability of frame being in error$)$ is $1\%$ or less. What should be the frame length in bits?

Problem $4(15$ points$)$:

A CRC is constructed to generate a $4-$bit FCS for a $9-$bit message given by $1-0010-1010.$ The generator

polynomial is specified by $G(x)=x^4+x^2+1.$

a$)(3$ points$)$ Draw the shift register corresponding the generator polynomial $G(x).$

b$)(4$ points$)$ Compute the CRC bits using the above data string and generator polynomial using the

polynomial division.

c$)(2$ points$)$ What is the transmitted frame Tt in in polynomial form?

d$)(2$ points$)$ Assume an error pattern represented by $E(x)=x^6+1,$ what would be the received

frame Tr in bits form and in polynomial form?

e$)(4$ points$)$ Is the error pattern in part $($d$)$ detectable or not? Why or why not?