Exercises

Approach

For the multiple choice items, identify the definition each term actually denotes: a channel is a physical path, bandwidth is measured in hertz, a symbol is a unit of a signal, and a baud counts symbols per second. For the fill-in-the-blanks, recall the two signal types, the roles of the source and the sink, the six stages of the communication system, and the direction of the bandwidth–rate relationship.

Steps

1. Read each option as a stand-alone definition rather than as a plausible-sounding phrase.
2. For the bandwidth item, separate the two meanings of bandwidth and pick the unit that belongs to the physical one.
3. For the symbol item, keep the unit of the signal distinct from the unit of the data.
4. For the baud item, remember that a baud counts symbols, not bits.
5. Write the fill-in-the-blanks from the definitions given earlier in the chapter.

Answer

1. B — the unit of bandwidth is Hz
2. A — a symbol is the smallest unit of a signal
3. B — a baud is the number of symbols transmitted per second
4. A — a channel is the physical path over which data travels

Fill in the blanks:

1. Analog signal, digital signal
2. Sender, receiver
3. Source, transmitting device, channel, receiving device, sink, noise source
4. Higher

Approach

Apply each theorem to the situation it describes: Nyquist gives the symbol rate of an ideal noiseless channel, Shannon gives the data rate of a noisy channel. For the analysis items, separate the factors that are fixed by the path from the factors that vary with load, and then account for the overhead that the two theorems ignore.

Steps

1. For the Nyquist calculation, substitute $W = 4000$ and $M = 4$ into $C = 2W \log_2 M$.
2. For the Shannon calculation, first convert the SNR from decibels to a ratio, then substitute into $C = W \log_2(1 + S/N)$.
3. For the real rate, apply real rate = theoretical rate × encoding efficiency × (1 − overhead ratio).
4. For the comparison item, note that Nyquist assumes no noise while Shannon includes it, and that they differ in output unit.
5. For the capacity factors, list bandwidth, SNR, and encoding scheme.
6. For the last item, list protocol overhead, encoding efficiency, equipment limits, and network congestion.

Answer

1. Nyquist theorem calculation:

   $C = 2W \log_2 M = 2 \times 4000 \times \log_2 4 = 16000 \text{ baud}$

2. Shannon theorem calculation:

   $\frac{S}{N} = 10^{30/10} = 1000$ $C = W \log_2(1 + \frac{S}{N}) = 3000 \times \log_2(1 + 1000) \approx 29910 \text{ bps}$

3. Real transmission rate calculation:

   $\text{Real rate} = 10000 \times 0.8 \times (1 - 0.1) = 7200 \text{ bps}$

For the analysis items:

• The Nyquist theorem applies to ideal channels with little or no noise and gives the symbol rate in baud; the Shannon theorem applies to real noisy channels and gives the data rate in bps, and its limit is always the tighter of the two.
• The main factors affecting channel capacity are the bandwidth, the signal-to-noise ratio, and the encoding scheme, since a wider bandwidth, a higher SNR, and a more efficient encoding all raise the capacity.
• The real rate is lower because the theorems ignore protocol overhead such as frame headers and checksums, the redundancy of error-correcting codes, the processing limits of the equipment, and the loss of throughput under congestion.

Approach

Match each scheme to the physical property it varies: Manchester encoding is defined by where the transition occurs, ASK by the amplitude, FSK by the frequency, PSK by the phase, and QAM by the amplitude and phase together. The number of bits per symbol follows from $n = \log_2 M$.

Steps

1. For the Manchester item, recall that the transition sits in the middle of the bit period, which is what carries the clock.
2. For the ASK item, match the abbreviation to the property it varies.
3. For the QPSK item, count the phases: four phases, so $n = \log_2 4 = 2$ bits per symbol.
4. For the fill-in-the-blanks, fill in the two goals of encoding, the direction of the conversion, the two BPSK phases, and the two QAM properties.

Answer

1. A — one transition in the middle of every bit period
2. A — amplitude shift keying
3. B — 2 bits of data

Fill in the blanks:

1. Reliability, efficiency
2. Digital, analog
3. 0, 180
4. Amplitude, phase

Approach

Compare the three techniques on how a path is obtained and what that costs. Circuit switching reserves a path for the whole session, so its delay is small but its resource use is poor; packet switching shares the network, so its resources are used efficiently but its delay is unpredictable. The datagram and the virtual circuit are the two modes of packet switching.

Steps

1. For the first item, pick the property that follows from reserving a dedicated path.
2. For the second item, pick the property that follows from statistical multiplexing across many users.
3. For the third item, apply the definition of a datagram: independent routing, so no connection and no ordering guarantee.
4. For the fill-in-the-blanks, fill in the traffic types, the two phases of a virtual circuit, and the missing connection and the arrival order.

Answer

1. B — low transmission delay
2. B — high resource utilisation
3. C — every packet chooses its route independently

Fill in the blanks:

1. Real-time, bursty
2. Established, released
3. A connection established, out of order

Approach

Recall the figures and the classification for each medium. Twisted pair is limited to about 100 metres, optical fibre reaches the highest bandwidth, and wireless is the medium most exposed to interference.

Steps

1. For the first item, use the 100-metre figure given for twisted pair.
2. For the second item, note that fibre reaches the THz range, which puts it far above the other media.
3. For the third item, pick the property that follows from propagating through the air.
4. For the fill-in-the-blanks, list the shielding classes of twisted pair, the mode classes of fibre, and the four performance metrics.

Answer

1. B — 100 metres
2. D — extremely high
3. B — easily affected by interference

Fill in the blanks:

1. UTP, STP
2. Single-mode fibre, multi-mode fibre
3. Bandwidth, attenuation, delay, interference resistance

Approach

Identify the layer each device works at, then apply what a physical layer device is allowed to do: it handles the signal, not the data.

Steps

1. For the first item, recall that a repeater regenerates the signal at the physical layer.
2. For the second item, note that a hub is a multi-port repeater wired as a star.
3. For the third item, pick the capability that requires an address, which physical layer devices do not have.
4. For the fill-in-the-blanks, list the two repeater functions, the hub topology, and the three limitations.

Answer

1. A — the physical layer
2. A — a multi-port repeater
3. C — filter data

Fill in the blanks:

1. Amplifying signals, forwarding signals
2. Star
3. Filter data, route data, convert data

Approach

Work from the requirements to the design: the distance limit rules out fibre and picks twisted pair, the device count and the low budget point to a hub or a switch, and the star topology keeps any single link failure from taking the network down. For the diagnosis, turn each symptom into a set of candidate causes, then work through detection, repair, and prevention.

Steps

1. Match the 100-metre distance limit against the reach of each medium.
2. Match the number of devices against the port count of the available equipment.
3. Choose the topology that isolates link failures.
4. List the causes behind each symptom: damaged cables, loose connectors, electromagnetic interference, and device faults.
5. For each cause, give the detection step, the repair step, and the preventive measure.

Answer

Network design:

1. Transmission medium: twisted pair (Cat5e or Cat6)
2. Network device: a hub or a switch
3. Topology: star topology
4. Performance guarantee: use high-quality cabling, lay it out carefully, and keep it away from interference sources

Fault diagnosis:

1. Possible causes: damaged cables, loose connectors, electromagnetic interference, device faults
2. Diagnostic methods: test with a tester, check the connection state, monitor the signal quality
3. Solutions: replace the damaged cable, reconnect the connectors, remove the sources of interference, replace the faulty device
4. Preventive measures: inspect regularly, lay the cabling out carefully, use shielded cable, and maintain the equipment on a schedule

Approach

Model each stage of the signal path as a separate method so that the stages can be tested one at a time, and model each transmission medium as a table of parameters so that the same simulation can be run over different media.

Steps

1. Create a class that holds the original, the amplified, and the reshaped signal.
2. Implement a generator that samples a sine wave, an amplifier that applies a gain, a reshaping step that adds noise, and a forwarding method that returns the processed signal.
3. Cover the four stages with a test run that prints each intermediate result.
4. For the simulation, create a class that holds a dictionary of media, each with its attenuation and noise parameters.
5. Implement a transmission method that applies attenuation, adds noise, and detects errors, and an analysis method that reports the success rate.
6. Run the simulation over twisted pair, fibre, and wireless.

Answer

For the signal processing program, build a SignalProcessor class whose constructor keeps three fields — the original signal, the amplified signal, and the reshaped signal — and give it four methods:

1. generate_signal(frequency, duration, sample_rate) samples a sine wave with NumPy and stores it as the original signal.
2. amplify_signal(gain) multiplies the original signal by the gain and stores the result.
3. reshape_signal(noise_level) adds normally distributed noise to the amplified signal and stores the result.
4. forward_signal() returns the reshaped signal.

Each method returns None when the stage it depends on has not run yet, and the test code calls the four methods in order, then plots the original, the amplified, the reshaped, and the forwarded signal.

For the network simulation program, build a NetworkSimulator class whose constructor holds a dictionary of transmission media, each with an attenuation and a noise value, and give it two methods:

1. transmit_packet(packet, medium, distance) returns None for an unknown medium, otherwise attenuates the packet by attenuation × distance, adds noise proportional to the medium’s noise value, and returns None when the simulated 10% error rate triggers.
2. analyze_performance(packets, medium, distance) runs every packet through transmit_packet, counts the successful transmissions, and returns the success rate together with the total and successful packet counts.

The test code generates 100 random packets and runs the analysis over twisted pair, fibre, and wireless, printing the success rate for each medium.

The complete listings of both programs are given in the answer key at the end of this page.

Approach:

This block consolidates the answers to every physical-layer exercise, covering eight groups in turn: basic concepts, transmission theory, encoding and modulation, switching techniques, transmission media, physical-layer devices, comprehensive application and programming practice. Within each group the multiple-choice, fill-in-the-blank, calculation and design questions are answered in order, and the capacity limits are obtained from the Nyquist and Shannon theorems.

Steps:

1. Answers to the Basic Concept Questions

1.1 Multiple Choice Answers

1. A — a channel is the physical path over which data travels
2. B — the unit of bandwidth is Hz
3. A — a symbol is the smallest unit of a signal
4. B — a baud is the number of symbols transmitted per second

1.2 Fill in the Blanks Answers

1. Analog signal, digital signal
2. Sender, receiver
3. Source, transmitting device, channel, receiving device, sink, noise source
4. Higher

2. Answers to the Transmission Theory Questions

2.1 Calculation Answers

1. Nyquist theorem calculation: $C = 2W \log_2 M = 2 \times 4000 \times \log_2 4 = 16000 \text{ baud}$

2. Shannon theorem calculation: $\frac{S}{N} = 10^{30/10} = 1000$ $C = W \log_2(1 + \frac{S}{N}) = 3000 \times \log_2(1 + 1000) \approx 29910 \text{ bps}$

3. Real transmission rate calculation: $\text{Real rate} = 10000 \times 0.8 \times (1 - 0.1) = 7200 \text{ bps}$

3. Answers to the Encoding and Modulation Questions

3.1 Multiple Choice Answers

1. A — one transition in the middle of every bit period
2. A — amplitude shift keying
3. B — 2 bits of data

3.2 Fill in the Blanks Answers

1. Reliability, efficiency
2. Digital, analog
3. 0, 180
4. Amplitude, phase

4. Answers to the Switching Technique Questions

4.1 Multiple Choice Answers

1. B — low transmission delay
2. B — high resource utilisation
3. C — every packet chooses its route independently

4.2 Fill in the Blanks Answers

1. Real-time, bursty
2. Established, released
3. A connection established, out of order

5. Answers to the Transmission Media Questions

5.1 Multiple Choice Answers

1. B — 100 metres
2. D — extremely high
3. B — easily affected by interference

5.2 Fill in the Blanks Answers

1. UTP, STP
2. Single-mode fibre, multi-mode fibre
3. Bandwidth, attenuation, delay, interference resistance

6. Answers to the Physical Layer Device Questions

6.1 Multiple Choice Answers

1. A — the physical layer
2. A — a multi-port repeater
3. C — filter data

6.2 Fill in the Blanks Answers

1. Amplifying signals, forwarding signals
2. Star
3. Filter data, route data, convert data

7. Answers to the Comprehensive Application Questions

7.1 Network Design Answers

1. Transmission medium: twisted pair (Cat5e or Cat6)
2. Network device: a hub or a switch
3. Topology: star topology
4. Performance guarantee: use high-quality cabling, lay it out carefully, and keep it away from interference sources

7.2 Fault Diagnosis Answers

1. Possible causes: damaged cables, loose connectors, electromagnetic interference, device faults
2. Diagnostic methods: test with a tester, check the connection state, monitor the signal quality
3. Solutions: replace the damaged cable, reconnect the connectors, remove the sources of interference, replace the faulty device
4. Preventive measures: inspect regularly, lay the cabling out carefully, use shielded cable, and maintain the equipment on a schedule

8. Answers to the Programming Exercises

8.1 Signal Processing Program Example

import numpy as np
import matplotlib.pyplot as plt

class SignalProcessor:
    def __init__(self):
        self.signal = None
        self.amplified_signal = None
        self.reshaped_signal = None

    def generate_signal(self, frequency, duration, sample_rate):
        """Generate an analog signal"""
        t = np.linspace(0, duration, int(sample_rate * duration))
        self.signal = np.sin(2 * np.pi * frequency * t)
        return self.signal

    def amplify_signal(self, gain):
        """Amplify the signal"""
        if self.signal is not None:
            self.amplified_signal = self.signal * gain
            return self.amplified_signal
        return None

    def reshape_signal(self, noise_level=0.1):
        """Shape the signal"""
        if self.amplified_signal is not None:
            noise = np.random.normal(0, noise_level, len(self.amplified_signal))
            self.reshaped_signal = self.amplified_signal + noise
            return self.reshaped_signal
        return None

    def forward_signal(self):
        """Forward the signal"""
        if self.reshaped_signal is not None:
            return self.reshaped_signal
        return None

# Test code
processor = SignalProcessor()
signal = processor.generate_signal(10, 1, 1000)
amplified = processor.amplify_signal(2)
reshaped = processor.reshape_signal(0.05)
forwarded = processor.forward_signal()

# Plot the results
plt.figure(figsize=(12, 8))
plt.subplot(4, 1, 1)
plt.plot(signal)
plt.title('Original signal')
plt.subplot(4, 1, 2)
plt.plot(amplified)
plt.title('Amplified signal')
plt.subplot(4, 1, 3)
plt.plot(reshaped)
plt.title('Reshaped signal')
plt.subplot(4, 1, 4)
plt.plot(forwarded)
plt.title('Forwarded signal')
plt.tight_layout()
plt.show()

8.2 Network Simulation Program Example

import random
import time

class NetworkSimulator:
    def __init__(self):
        self.transmission_media = {
            'twisted_pair': {'attenuation': 0.1, 'noise': 0.05},
            'fiber': {'attenuation': 0.01, 'noise': 0.01},
            'wireless': {'attenuation': 0.3, 'noise': 0.2}
        }

    def transmit_packet(self, packet, medium, distance):
        """Transmit a packet"""
        if medium not in self.transmission_media:
            return None

        # Calculate the attenuation
        attenuation = self.transmission_media[medium]['attenuation'] * distance
        attenuated_packet = packet * (1 - attenuation)

        # Add the noise
        noise = self.transmission_media[medium]['noise'] * random.random()
        noisy_packet = attenuated_packet + noise

        # Error detection
        if random.random() < 0.1:  # 10% error rate
            return None

        return noisy_packet

    def analyze_performance(self, packets, medium, distance):
        """Analyse the performance"""
        successful_transmissions = 0
        total_packets = len(packets)

        for packet in packets:
            result = self.transmit_packet(packet, medium, distance)
            if result is not None:
                successful_transmissions += 1

        success_rate = successful_transmissions / total_packets
        return {
            'success_rate': success_rate,
            'total_packets': total_packets,
            'successful_packets': successful_transmissions
        }

# Test code
simulator = NetworkSimulator()
packets = [random.random() for _ in range(100)]

# Test the different transmission media
for medium in ['twisted_pair', 'fiber', 'wireless']:
    performance = simulator.analyze_performance(packets, medium, 100)
    print(f"{medium}: success rate {performance['success_rate']:.2%}")

Answer:

The answers listed above cover concept identification, channel-capacity computation, encoding and modulation, switching and media selection, physical-layer device functions, network design and programming examples.