3. (a) You are a network administrator of a company, where there are 40 users in total sharing a 20 Mbps network. On average, each user is active 12% of the time and needs 1 Mbps during active transmission. If the network uses packet switching technology, derive the probability that a user will not be able to obtain the network service immediately. (Hint: Show your answer with a formula containing a sum of multiple probabilities.) (5 Marks) Consider a 12-bit data sequence 101000001111 and a generator polynomial (b) g(x) = x +x+1 (i) Suppose the transmitter uses Differential Encoding as the line coding scheme, plot the encoded signal of the transmitted codeword. Assume the first bit is encoded as V+. (ii) Find the following three undetectable error patterns by using this generator polynomial: a 2-bit error, a 3-bit error, a 4-bit error. (12 Marks) (c) Use Bipolar with 8 Zeros Substitution (B8ZS) as an example to briefly explain the four design goals of a scramble code. (4 Marks) (d) Perform de-framing and byte de-stuffing for the following sequence that is to be received by the receiver. Note that the sequence is represented in hexadecimal format. Show your final answer in hexadecimal format. 7E7D5ED57D5DA7D87E (4 Marks)