BE Computer Engineering (Pokhara University) Data Communication (PU, CMM 220) Question Paper 2079 Nepal

(a) Analog vs Digital Signals; Bit Rate, Baud Rate, Bandwidth (8)

Analog vs Digital Signals

Bit Rate, Baud Rate, Bandwidth

• Bit rate = number of bits transmitted per second (bps).
• Baud rate (signal rate) = number of signal elements (symbols) transmitted per second (baud).
• Relationship: If each signal element carries $r$ bits, then

$$\text{Bit rate} = \text{Baud rate} \times r, \qquad r = \log_2 L$$

where $L$ is the number of distinct signal levels. So baud rate $\le$ bit rate always.

• Bandwidth is the range of frequencies a medium passes (Hz). The Nyquist limit links bandwidth to signal rate: $C = 2B\log_2 L$, so higher bandwidth permits a higher baud rate and hence a higher bit rate.

Examples:

1. A system sending 2 bits per symbol (4 levels, QPSK) at 1000 baud gives a bit rate of $1000 \times 2 = 2000$ bps, while the baud rate is only 1000.
2. A binary system ($L=2$, $r=1$) at 1000 baud gives 1000 bps — here bit rate = baud rate.
3. For a 3 kHz telephone channel with 4 levels, Nyquist gives $C = 2 \times 3000 \times \log_2 4 = 12000$ bps.

(b) Guided vs Unguided Media; Optical Fiber (7)

Guided vs Unguided

Optical Fiber — Construction

Described structure (centre outwards):

• Core: thin glass/plastic strand of higher refractive index $n_1$ that carries the light.
• Cladding: glass of lower refractive index $n_2$ surrounding the core.
• Buffer coating / jacket: plastic protective outer layers.

Operating principle: Light is launched into the core at an angle greater than the critical angle, so at the core–cladding boundary it undergoes total internal reflection ($n_1 > n_2$). The ray bounces along the core to the far end, where a photodetector converts it back to an electrical signal. Modes: single-mode (very thin core, one ray path, long distance) and multimode (wider core, many paths).

Two advantages over coaxial cable

1. Much higher bandwidth and far lower attenuation, allowing higher data rates over longer distances without repeaters.
2. Immunity to electromagnetic interference (light, not electric current) and greater security from tapping.

(a) Pulse Code Modulation (PCM) (9)

PCM converts an analog signal into a digital bit stream in three stages.

Block diagram (described):

Analog input → [Low-pass / anti-alias filter] → [Sampler (PAM)] → [Quantizer] → [Encoder] → PCM digital output

1. Sampling

The continuous analog signal is sampled at regular intervals, producing a Pulse Amplitude Modulated (PAM) sequence. To reconstruct the signal without loss, sampling must obey the Nyquist theorem.

2. Quantization

Each sampled amplitude is rounded to the nearest of a finite set of levels ($L = 2^n$ levels for $n$-bit encoding). The rounding error introduced is called quantization noise.

3. Encoding

Each quantized level is mapped to an $n$-bit binary code word, giving the serial PCM bit stream.

Nyquist Sampling Theorem

A band-limited signal with maximum frequency $f_{max}$ can be perfectly reconstructed from its samples if it is sampled at a rate $f_s \ge 2 f_{max}$. The minimum rate $f_s = 2f_{max}$ is the Nyquist rate.

(b) Numerical (6)

Given: bandwidth (max frequency) $f_{max} = 4\text{ kHz}$, bits per sample $n = 8$.

Minimum sampling rate (Nyquist rate):

$$f_s = 2 f_{max} = 2 \times 4000 = 8000 \text{ samples/s} = 8\text{ kHz}$$

Bit rate of PCM output:

$$R = f_s \times n = 8000 \times 8 = 64000 \text{ bps} = 64\text{ kbps}$$

Results: minimum sampling rate = 8 kHz, PCM bit rate = 64 kbps.

(a) Comparison of Switching Techniques (9)

(b) Stop-and-Wait ARQ (6)

Working: The sender transmits one frame and then stops, waiting for an acknowledgment (ACK) before sending the next. Frames and ACKs are numbered modulo 2 (0 and 1) to detect duplicates. A timer is started for every transmitted frame.

Timing diagram (described):

Sender                         Receiver
  | --- Frame 0 ----------->  |  (accept, send ACK1)
  | <----------- ACK 1 ------ |
  | --- Frame 1 ----------->  |  (accept, send ACK0)
  | <----------- ACK 0 ------ |

Lost data frame: The receiver gets nothing, so it sends no ACK. The sender's timer expires (timeout) and it retransmits the same frame with the same sequence number.

Lost acknowledgment: The frame arrived but its ACK was lost. The sender times out and resends the frame. The receiver sees a frame with a sequence number it has already accepted, discards the duplicate, and re-sends the ACK, keeping both sides synchronized.

Limitation: Only one frame is outstanding at a time, so link utilization is low on long-delay or high-bandwidth links.

(a) Cyclic Redundancy Check (CRC) (10)

Principle: The sender treats the data word as a binary polynomial. It appends $r$ zero bits (where $r$ = degree of generator $G(x)$) and divides this by $G(x)$ using modulo-2 (XOR) division. The remainder is the CRC; it replaces the appended zeros to form the transmitted code word, which is exactly divisible by $G(x)$. The receiver divides the received word by $G(x)$; a non-zero remainder indicates an error.

Given: Data = 1101011011, $G(x) = x^4 + x + 1 \Rightarrow$ divisor = 10011 (degree $r = 4$).

Append 4 zeros: dividend = 1101011011 0000.

Modulo-2 division (XOR at each step):

1101011011 0000 ÷ 10011

11010 ^ 10011 = 01001
 bring down → 010011
 10011 ^ 10011 = 00000
 bring down bits → 000001 ...continuing the standard XOR long division

Performing the full long division gives:

     1 1 0 0 0 1 0 1 0 0   (quotient)
10011 ) 1101011011 0000
        10011
        -----
        010011
         10011
         -----
         000001 1011
              1 0011
              ------
                 1 1100
                 1 0011
                 ------
                   1111 0
                   1001 1
                   ------
                    110 10
                    100 11
                    ------
                     10 010
                     10 011
                     ------
                        001  → remainder bits

The remainder (last $r=4$ bits) is 1110 (CRC).

Transmitted code word = data + CRC =

$$\texttt{1101011011}\;\texttt{1110} = \texttt{1101011011 1110}$$

Note: the CRC is the 4-bit remainder of the modulo-2 division; dividing the transmitted word 11010110111110 by 10011 gives remainder 0, confirming a valid code word.

(b) Hamming Distance, Error Detection & Correction (5)

The minimum Hamming distance $d_{min}$ of a code is the smallest number of bit positions in which any two valid code words differ.

• To detect up to $s$ errors: $d_{min} \ge s + 1$, so $s = d_{min} - 1$.
• To correct up to $t$ errors: $d_{min} \ge 2t + 1$, so $t = \left\lfloor \dfrac{d_{min}-1}{2} \right\rfloor$.

For $d_{min} = 5$:

$$s = 5 - 1 = 4 \text{ errors detectable}$$ $$t = \left\lfloor \frac{5-1}{2} \right\rfloor = 2 \text{ errors correctable}$$

Result: A code with minimum Hamming distance 5 can detect up to 4-bit errors and correct up to 2-bit errors.

FDM vs TDM

Synchronous TDM

In synchronous TDM, the time axis is divided into frames, and each frame is divided into slots, one fixed slot per input line. A multiplexer scans the inputs in round-robin order and places each input's data into its dedicated slot in every frame, even if that input has no data (the slot is then left empty). The demultiplexer at the receiver, synchronized by framing bits, distributes slot data back to the correct output lines.

Diagram (described): Inputs A, B, C feed a MUX; output stream is A1 B1 C1 | A2 B2 C2 | A3 B3 C3 | ... where each | marks a frame boundary.

Drawback: slots reserved for idle inputs waste bandwidth — solved by statistical (asynchronous) TDM.

Why guard bands in FDM

Real filters are not ideal, so adjacent frequency channels can overlap. Guard bands are unused frequency gaps placed between channels to prevent inter-channel interference (crosstalk) and to allow practical band-pass filters to separate the channels cleanly.

Three Causes of Transmission Impairment

1. Attenuation — Loss of signal energy/strength as it travels through the medium, due to resistance/absorption. It increases with distance and frequency; amplifiers or repeaters are used to compensate. Measured in decibels (dB).
2. Distortion — Change in the shape of the signal. In composite signals, different frequency components travel at different speeds and have different delays, so they arrive with shifted phases and the combined waveform is distorted.
3. Noise — Unwanted external energy added to the signal: thermal noise (random electron motion), induced noise (from motors/appliances), crosstalk (coupling between wires), and impulse noise (spikes from lightning/switching).

Attenuation in Decibels

Given the power is reduced to one-half: $P_2 = \tfrac{1}{2}P_1$.

$$\text{dB} = 10 \log_{10}\frac{P_2}{P_1} = 10 \log_{10}\frac{1}{2} = 10 \times (-0.301) = -3.01 \text{ dB}$$

Result: The attenuation is approximately −3 dB (a 3 dB loss), i.e. halving the power corresponds to a 3 dB drop.

Digital-to-Analog Modulation Techniques

Digital-to-analog conversion modulates one parameter of a carrier $A\cos(2\pi f t + \phi)$ according to the data bits.

1. Amplitude Shift Keying (ASK)

The amplitude of the carrier is changed; frequency and phase stay constant. Typically bit 1 = carrier present (high amplitude), bit 0 = no/low carrier. Waveform (described): for 1 0 1 1 → carrier burst, flat (off), carrier burst, carrier burst. Simple but very sensitive to noise.

2. Frequency Shift Keying (FSK)

The frequency is changed; amplitude and phase constant. Bit 1 = frequency $f_1$ (higher), bit 0 = frequency $f_2$ (lower). Waveform (described): for 1 0 1 → fast oscillation, slow oscillation, fast oscillation. More noise-immune than ASK.

3. Phase Shift Keying (PSK)

The phase is changed; amplitude and frequency constant. In BPSK, bit 1 = phase $0°$, bit 0 = phase $180°$. Waveform (described): for 1 0 → carrier, then carrier inverted (180° shift) at the bit boundary. Robust against noise; basis of modern modems.

Why QPSK is preferred over BPSK

QPSK uses four phases ($45°, 135°, 225°, 315°$), so each symbol carries 2 bits instead of 1.

• For the same baud (symbol) rate, QPSK gives double the bit rate of BPSK.
• Equivalently, QPSK achieves the same bit rate as BPSK using half the bandwidth, improving spectral (bandwidth) efficiency — with essentially the same bit-error-rate performance.

Sliding Window Concept

Flow control with a sliding window lets the sender transmit several frames before needing an acknowledgment, instead of one at a time. Both sender and receiver maintain a window (a range of sequence numbers, numbered modulo $2^m$). The sender may send frames while its window is open; as ACKs arrive, the window slides forward, allowing new frames. This keeps the link busy and greatly improves efficiency over Stop-and-Wait.

Go-Back-N ARQ vs Selective Repeat ARQ

Summary: Go-Back-N is simpler but retransmits more frames on error; Selective Repeat is more efficient on noisy links because it retransmits only the lost frames, at the cost of receiver buffering and a smaller window.

Line-Coding Schemes

Line coding converts binary data into a digital signal. (Diagrams described per scheme.)

(a) NRZ-L (Non-Return-to-Zero Level)

The voltage level represents the bit: e.g. high (positive) = 0, low (negative) = 1 (or vice versa). The level stays constant for the whole bit. Signal for 0 1 1 0: high, low, low, high. Problem: long runs of same bit give no transitions → loss of synchronization.

(b) NRZ-I (Non-Return-to-Zero Invert)

The bit is encoded by transition, not level: a 1 causes an inversion at the start of the bit; a 0 means no change. This is differential, so it tolerates polarity reversal. Signal for 0 1 1 0: stay, invert, invert, stay.

(c) Manchester

Mid-bit transition carries data: e.g. 0 = high-to-low transition, 1 = low-to-high transition (IEEE convention). There is always a transition in the middle of every bit, so it is self-synchronizing, but needs double the bandwidth.

(d) Differential Manchester

Always has a mid-bit transition for timing. The bit value is shown by the presence/absence of a transition at the start of the bit: 0 = transition at the beginning, 1 = no transition at the beginning. It is both self-synchronizing and differential (polarity-independent).

Advantage of Self-Synchronizing Schemes

Schemes like Manchester and Differential Manchester guarantee a transition in every bit period, so the receiver can extract the clock directly from the data stream and stay synchronized even during long runs of 0s or 1s — no separate clock line is needed.

Shannon Capacity Formula

For a noisy channel, the maximum theoretical data rate is

$$C = B \log_2\!\left(1 + \frac{S}{N}\right) \text{ bps}$$

where $B$ = bandwidth (Hz) and $S/N$ = signal-to-noise power ratio (not in dB). It gives an upper bound independent of the number of signal levels and accounts for noise.

Nyquist Bit-Rate Formula

For a noiseless channel,

$$C = 2B \log_2 L \text{ bps}$$

where $L$ = number of discrete signal levels. It shows how many levels are needed but ignores noise; in practice the Shannon limit caps how large $L$ can usefully be.

Numerical — Shannon Capacity

Given: $B = 3000$ Hz, $S/N = 3162$ (≈ 35 dB).

$$C = 3000 \times \log_2(1 + 3162) = 3000 \times \log_2(3163)$$ $$\log_2(3163) = \frac{\ln 3163}{\ln 2} = \frac{8.059}{0.693} \approx 11.63$$ $$C = 3000 \times 11.63 \approx 34{,}900 \text{ bps} \approx 35 \text{ kbps}$$

Result: The maximum theoretical capacity is approximately 34.9 kbps (≈ 35 kbps). (A handy check: at 35 dB SNR, $C \approx B \times \text{SNR(dB)}/3 = 3000 \times 35/3 \approx 35$ kbps.)

Simple Parity Check

A single parity bit is appended so the total number of 1s is even (even parity) or odd (odd parity). The receiver recomputes parity; a mismatch signals an error. It detects any odd number of bit errors but misses all even-number errors, and cannot correct errors.

Two-Dimensional (2-D) Parity Check

Data is arranged as a table of rows. A parity bit is computed for each row and for each column, giving a row-parity column and a column-parity row. This detects more errors and can pinpoint and correct a single-bit error by intersection.

Example (even parity)

Data block (3 rows × 4 bits) with row parity (P_row) and column parity (P_col):

Now suppose bit at Row2, b3 flips during transmission (1 → 0). At the receiver:

• Row2 parity fails (its 1-count parity is now wrong).
• Column b3 parity fails.

The error lies at the intersection of the failing row and failing column = Row2, b3. The receiver flips that bit back to correct it.

Capability: A single-bit error causes exactly one row and one column parity to fail, uniquely locating and correcting it; two errors in the same row or column can be detected but not always corrected.

Short Notes (any TWO)

(a) Spread Spectrum Techniques (FHSS & DSSS)

Spread spectrum spreads a signal over a bandwidth much larger than required, improving resistance to jamming, interception, and interference.

• FHSS (Frequency Hopping Spread Spectrum): The carrier hops among many frequencies in a pseudo-random sequence known to both transmitter and receiver. A different frequency is used for each short time interval, so interference on one frequency affects only a fraction of the transmission. Used in Bluetooth.
• DSSS (Direct Sequence Spread Spectrum): Each data bit is XORed with a high-rate pseudo-random chip code (spreading code), multiplying the signal bandwidth by the spreading factor. The receiver uses the same code to de-spread. It offers a processing gain that rejects narrowband noise. Used in early Wi-Fi (802.11b) and CDMA.

(b) Wavelength Division Multiplexing (WDM)

WDM is FDM applied to optical fiber: several optical signals at different wavelengths (colours) of light are combined onto one fiber. A multiplexer (prism/grating-based combiner) merges the wavelengths at the sending end and a demultiplexer separates them at the receiving end. It hugely increases fiber capacity. DWDM (Dense WDM) packs many closely-spaced wavelengths for very high-capacity long-haul links.

(c) Unguided Media: Radio, Microwave, Infrared

• Radio waves (3 kHz–1 GHz): Omnidirectional, can penetrate walls, propagate long distances (including via the ionosphere). Used for AM/FM radio, TV, cordless phones.
• Microwaves (1–300 GHz): Line-of-sight, highly directional (parabolic dishes); need tower-to-tower alignment. Used in terrestrial point-to-point links, cellular, and satellite communication.
• Infrared (300 GHz–400 THz): Very high frequency, short range, cannot pass through walls (good for confined, secure communication). Used in TV remotes and short-range device links.