problem-set.doc

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Problem Set1

1. Draw a block diagram for a communications system and writesynopsis for each one.

2. List all network topologies and define advantages anddisadvantages for each one.

3. Name the network layer that performs the following functions:a) Has a local address that was built in by the LAN adapter card

manufacturer.b) Puts out and receives signals through an external port

(connector).c) Provides standard services to various computer programs.

d) It uses a hierarchical address assigned by the local networkmanager.e) Responsible for end-to-end connections across a multi-node

switched network or router network.

4. Assume that a computer sends a frame at the transport layer toanother computer and the destination port address is not running.According to what you read from chapter 2, what will happen to thatprocess?

5. What is the difference between Flow control in Transport and Datalink layer?

6. Why do we need the error control in transport and data link layer?

7. Determine the possible bit rate and the number of levels over achannel for these cases?a) B = 2.4K Hz, noiseless channel with L = 16.b) B= 2.4K Hz, SNR = 20 dB.c) B = 3.0K Hz, SNR = 40 db.

8. A signal goes from routers A, through B and C, and finally arrives atD. The signal loses 2 dB from A to B, again 5 dB from B to C, and

loses 3 dB from C to D. What is the total gain or loss from A to D?

9. What is the maximum data rate for a voice-grade line with abandwidth of 4K Hz and a SNR of 10000 to 1? What is the maximumdata rate if the SNR is now enhanced to 50 dB?

10. Calculate the transmission bandwidth for a video signal, thewidth and height are 200 and 150 pixels respectively with 128 color


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patterns and 16 level intensities. Further assume that 25 frames persecond are acceptable to the user.

11. We were hired to study the design of a 100K bps modem. Howmany signal levels would we need, assuming an availablebandwidth of 4k Hz?

12. What is the channel capacity for a device channel with a 300 Hzbandwidth and SNR is 3 dB?

13. Given a channel with capacity of 100M bps and a bandwidth of3M Hz. What is the signal to noise ratio required to achieve thiscapacity?

14. We want to design a 56kbps modem. What is the minimumnumber of signaling levels we need? Assume that a telephonechannel has a bandwidth of 3K Hz.

15. Suppose that data are stored on 1.4M Byte floppy diskettes thatweigh 30 g each. Suppose that an airline carries 10,000 kg of thesefloppies at a speed of 1000 km/h over a distance of 5000 km. Whatis the data transmission rate in bits per second of this system?

16. A digital signaling system is required to operate at 56,000 bps. Ifthe signal used has 8 levels, what is the minimum requiredbandwidth of the channel?

17. Given a channel with an intended capacity of 32M bps, thebandwidth of the channel is 4M HZ. What SNR in dB is required toachieve this capacity?

18. What is the Capacity (bits/sec) if the bandwidth is 2,400 bps andeach symbol has 8 states (levels)?

19. An image is 1024 x 768 pixels with 3 bytes/pixel. Assume theimage is uncompressed.a) How long does it take to transmit it over a 56 kbps modem

channel?b) How long does it take to transmit it over a 1-Mbps cable modem?c) How long does it take to transmit it over a 10-Mbps Ethernet?

Over 100-Mbps Ethernet?


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20. If a binary signal is sent over a 3K Hz channel whose signal-to-noise ratio is 20 dB, what is the maximum achievable data rate?

Problem Set2

Problem # 1

For a voice grade line, a digital signal with 16 levels is used.a) What is the Baud rate?b) What is the bit rate?

Problem # 2A digital signaling system is required to operate at 56000bps. If the signal used has 8 levels, what is the minimumrequired bandwidth of the channel?

Problem # 3What is the max required baud of a 2G bps encoding, whenusing

a)Differential Manchester encoding.b)60B/66B line encoding.

Problem # 4Derive an expression of the maximum effective data rateover a B bps line for the following:

a)Asynchronous communication

a. Send 1 character at a time.b. Start bit = 1c. Stop bit = 1.5d. Parity bit = 1

b)Synchronous communicationa. Data bits per frame = 128.


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b. Overhead per frame = 48 bits.

Problem # 5An analog signal is to be converted into digital form. Theanalog signal represents frequencies in the range 200 Hz to2000 Hz. If the signal is quantized using 8 bits per sample,what is the data rate of the new digital signal?Problem # 6Encode the following bit stream. Note that the previoussignal levels are indicated when appropriate.

1 1 1 0 1 0 0 0

Usinga) NRZ-L, NRZ-I, RZ.b) Bipolar AMI.c) Manchester.d) Differential Manchester.

Problem # 7Using HDB3 to encode the following bit string (You mayassume that this is the very first sequence of 4 zeros)

1 1 1 0 0 0 0 1

Problem # 8What are the modulated signals for the sample signal below.(You can choose the carrier frequencies, but make sure theyare distinguishable).


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Problem # 9PCM system uses a uniform quantizer followed by an 8 bitbinary encoder. The bit rate of the system is equal to 256Kbps.

a) What is the Maximum message bandwidth for which thesystem operates satisfactory?b) Determine the signal to quantized noise ratio when a

full load sinusoidal modulating wave of frequency 1MHz is applied to the input?

c) You passed the output digits of PCM system into a BlockCoding 8Bit/10Bit, what is the current Data Rate andBandwidth?

d) You passed the output digits of Block Coding into NRZ-ILine Coding What is the Min. channel Bandwidth

required? Hint: return to the figure 5.3 from the textbook.

Problem # 10What is the data rate of a T1 line?

Problem # 11a)What is the main problem in synchronous time-division

multiplexing, where every channel receives a fixed time

slot?

b)Using frequency division multiplexing, what is theminimum required bandwidth if 30 channels are to bemultiplexed, where each channel has a bandwidth of4kHz?

Problem # 12A Character-interleaved time-division multiplexer is used tocombine the data streams of a number of 110-bpsasynchronous terminals for data transmission over a 2400bps digital line. Each terminal sends asynchronous characterconsisting of 7 data bits, 1 parity bit, 1 start bit, and 2 stopbit. Assume that one synchronization character is sent every19 data character and, in addition, at least 3% of the line


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capacity is reserved for pulse stuffing to accommodatespeed variations from the various terminals.

a) Determine the number of bits per character.b) Determine the number of terminals that can be

accommodated by the multiplexer.

Problem # 13Assume that we have a collection of 28Kbps DTEs we needto multiplex together on a 56Kbps line. Assuming that all ofthe terminals transmit an average of 23% of the time andthe multiplexer compresses data at its inputs to 70% (notby 70%). What is the maximum number of terminals we canreasonably expect to support using statistical time divisionmultiplexing in this situation? Note, you should use the rule

of thumb of an 80% utilization.

Problem # 14You are required to design a communication system that has920-945 MHz bandwidth; each channel has a bandwidth of30 kHz, 64 kbps. Determine

a) Maximum number of users for FDM technique.b) Maximum number of users for FHSS technique (assume

Bss = 25M Hz, B = 30kHz).

c) Maximum number of bits in PN sequence for FHSS?

Problem# 15We need to use synchronous TDM and combine 20 digitalsources; 5 with a bit rate of 120 kbps, 10 with a bit rate 60kbps, and the last 5 with a bit rate of 110 kbps. Design asynchronous TDM for these sources, and then determine thefollowing:

a) The output frame rate?b) The output data rate?c) Efficiency of the system?

Problem # 16A synchronous TDM is used to multiplex digital and analogsources. Assume the following sources are to be multiplexed:


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Source 1: Analog, 4 KHz bandwidthSource 2: Analog: 6 KHz bandwidthSources 3-10: 1100 bps synchronousShow a block diagram of the TDM system using the given

sources with the assumption that Pulse stuffing is used.Calculate the output capacity in Kbps.

Problem # 17Show a block diagram for a TDM PCM that will accommodatefour 300-bps, synchronous, digital inputs and one analoginput with a bandwidth of 500 Hz. Assume that the analoginput with a bandwidth of 500 Hz. Assume that the analogsample will be encoded into 4-bit PCM words.

Problem # 18Find the number of the following devices that could beaccommodated by a T1-type TDM line if 1 percent of the linecapacity is reserved for synchronization purposes.

a) 110-pbs printer terminalsb) 300 bps computer terminalsc) 64-kpbs PCM voice frequency lines

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