Question $(3$A$)-$ A data D$($X$)=$ X$11+$X$+$X$6+$X$5+$X$4+$X$3+$X$+1$ is to be transmitted and the given pattern is P$($X$)=$ X $+$ X$4+$ X$^3+$X$^2+$X$+1.$ What is the transmitted message? The receiver receives the message with an error in the $7$th bit from the MSB of the received message, detect that there is an error using modulo $2$ arithmetic.

Question $(3$B$)-$ Which are the most significant transmission impairments that occurs? Briefly explain each of the impairment with an example.

Question $(3$C$)-$ Given a channel with an intended capacity of $20$ Mbps$,$ the bandwidth of the channel is $3$ MHz$.$ Assuming white thermal noise, what signal$-$to$-$noise ratio is required to achieve this capacity?