Section 3.6. Exercises

3.6. Exercises

1.	Human voice frequency ranges from 16 Hz to about 20 KHz. Telephone companies use the most-significant 4,000 KHz portion of this spectrum to deliver voice conversation between two users. This downgrade in the quality of conversation allows the transmission links to save bandwidth remarkably. Using a three-level hierarchy of multiplexing (12:1, 5:1, and 10:1): How many voice conversation can this system carry? What would be the final transmission capacity of this system?
2.	Consider the integration of three analog sources and four identical digital sources through a time-division multiplexer that uses its entire 170 Kb/s maximum capacity. The analog lineswith bandwidths of 5 KHz, 2 KHz, and 1 KHz, respectivelyare sampled, multiplexed, quantized, and 5-bit encoded. The digital lines are multiplexed, and each carries 8 Kb/s. For the analog sources, find the total bit rate. For the digital sources, find the pulse- stuffing rate. Find the frame rate if a frame carries eight sampled analog channels, four digital data channels, a control channel, and a guard bit.
3.	Assume that two 600 b/s terminals, five 300 b/s terminals, and a number of 150 b/s terminals are to be time-multiplexed in a character-interleaved format over a 4,800-b/s digital line. The terminals send 10 bits/character, and one synchronization character is inserted for every 99 data characters . All the terminals are asynchronous, and 3 percent of the line capacity is allocated for pulse stuffing to accommodate variations in the terminal clock rate. Determine the number of 150 b/s terminals that can be accommodated. Sketch a possible framing pattern for the multiplexer, assuming three characters per 150 b/s terminal.
4.	Consider a time-division multiplexer having a frame time of 26 µ s. Each user channel has 6 bits, and each frame has 10 bits of overhead information. Assume that the transmission line carries 2 Mb/s of information. How many user channels can be accommodated on the line? Consider ten sources in this system, and assume a probability of 0.9 that a source is busy. What is the clipping probability?
5.	Consider a synchronous TDM with eight inputs, each becoming an average of 2 µ s active and 6 µ s inactive. Frames can receive four channels only. Find the probability that a source is active. Find the probability that three channels of the frame are in use. Find the blocking probability for this multiplexer. Find the average number of used channels in the frame.
6.	For a four-input statistical TDM, consider two different frame sizes of 2 and 3. Sketch one set of three plots, each showing the clipping probability versus = 0.2, 0.4, 0.6, 0.8.
7.	Consider a statistical TDM in which 11 sources and 10 channels are present. Find the clipping probability, assuming a probability of 0.9 that a given source is busy.
8.	Find the average clipping time for each burst of information in statistical TDMs.
9.	A string of 110011101 arrives at the line coder of a modem. Give the output form if the line coder is designed by: Natural NRZ Polar NRZ Manchester NRZ
10.	A string of 100101011 arrives at the modulation unit of a modem. Give the output signal if the modulator is designed by: ASK FSK PSK
11.	We want to design the input port processor of a high-speed router and analyze the delay. Incoming packets to IPP are fragmented into smaller segments, with each segment consisting of d bits data plus 50 bits of header. The switch fabric requires segments to be transmitted at r b/s. To achieve the highest possible speed: Is there any way to optimize the transmission delay D of each segment in terms of d and r ?How? Is propagation delay in the switch fabric significant compared to D ? Why?
12.	Computer simulation project. To simulate the routing table of routers, write a computer program to construct a look-up routing table with ten entries. Each entry must contain a sequence number, time, destination address, cost of a destination node (given a certain network), and router port number. Your program should demonstrate the updating mechanism on a frequent basis.