A$.$ a$.$ Consider a communication system that uses a Cyelic Redundancy Check $($CRC$)$

$14+3$

method to transmit a message $11001001$ with the polynomial function $x^1+1$ to

$=71$

detect errors in data transmission. Use polynomial long division to determine the message that should be transmitted from the sender side. Next, oorrupt the lef$-$most thind bit of the transmitted message and show that the error is detected by the receiver using the CRC teelnique.

b$.$ How do Dense Wavelength Division Multiplexing $($DWDM$)$ and Coarse

$3$

Wavelength Division Multiplexing $($CWDM$)$ differ in terms of their principles, applications, and advantages, and what are the key factors influencing the choice between these two technologies in optical networking?