DIGITAL COMMUNICATION – KEC601
Section-wise Important Questions & Ready Answers
SECTION A
(Attempt all – 2 marks each)
(a) Properties of Probability Density Function (PDF)
A probability density function describes how a continuous random variable is distributed. A valid PDF is always non-negative for all values of the random variable. The total area under the PDF curve over the entire range must be equal to one, which represents total probability. Also, the probability that a random variable lies within a certain interval is obtained by integrating the PDF over that interval.
(b) Complete Probability Scheme
The complete probability scheme is used when an event can occur due to several mutually exclusive and exhaustive events. It states that the probability of an event is the sum of the conditional probabilities of that event given each cause, multiplied by the probability of each cause. This scheme is widely used in communication systems for noise and error analysis.
(c) Eye Diagram
An eye diagram is a graphical tool used to analyze digital signals in the time domain. It is formed by overlapping successive bits of a digital signal on an oscilloscope. The openness of the eye indicates signal quality. A wider eye opening means less noise, lower intersymbol interference, and better timing accuracy.
(d) Roll-off Factor in Pulse Shaping
The roll-off factor defines the excess bandwidth used in raised cosine pulse shaping. Its value ranges from 0 to 1. A smaller roll-off factor results in higher spectral efficiency but more intersymbol interference, while a larger value reduces ISI at the cost of increased bandwidth.
(e) Disadvantages of Coherent Demodulation
Coherent demodulation requires accurate carrier phase and frequency synchronization at the receiver. This increases system complexity and cost. Any phase mismatch between transmitter and receiver leads to performance degradation, making coherent systems sensitive to noise and channel variations.
(f) Disadvantages of Non-Coherent FSK
Non-coherent FSK does not require carrier synchronization, but it has poorer error performance compared to coherent schemes. It also requires larger bandwidth and offers lower spectral efficiency, making it unsuitable for bandwidth-limited systems.
(g) Spread Spectrum and Its Advantages
Spread spectrum is a technique in which the signal bandwidth is spread over a wide frequency range. Its main advantages include resistance to interference and jamming, improved security, and better performance in noisy environments. It is widely used in wireless and military communication.
(h) Comparison of ASK, FSK, and PSK (Error Performance)
Among the three modulation schemes, PSK offers the best probability of error performance due to phase-based signaling. FSK performs better than ASK because it is less sensitive to noise. ASK has the worst error performance as it depends directly on signal amplitude, which is easily affected by noise.
(i) Use of Logarithmic Function in Information Measurement
The logarithmic function is used because it converts multiplicative probabilities into additive information measures. This property makes it easier to analyze and combine information from multiple sources. It also aligns with human perception and provides a consistent unit such as bits.
(j) Mutual Information Is Symmetric
Mutual information between two random variables X and Y is symmetric because the information X provides about Y is the same as the information Y provides about X. Mathematically, I(X;Y) = I(Y;X), showing that the shared information is mutual and bidirectional.
SECTION B
(Attempt any three – 10 marks each)
1. Random Process & Strict Sense Stationary (SSS) Process
A random process is a collection of random variables indexed by time. A process is called strict sense stationary if its statistical properties remain unchanged with time shift. This means that all joint probability distributions are invariant under time translation. SSS is a very strong condition and rarely satisfied in practical systems.
2. Duobinary Signaling and Its Advantages
Duobinary signaling is a partial response signaling technique that intentionally introduces controlled intersymbol interference to reduce bandwidth. By correlating adjacent symbols, it achieves better spectral efficiency. Its advantages include reduced bandwidth requirement and improved transmission efficiency compared to binary signaling.
3. ASK Modulation and Demodulation
In Amplitude Shift Keying (ASK), the amplitude of a carrier signal is varied according to the digital data. During demodulation, an envelope detector or coherent detector is used to recover the original data. ASK is simple but highly susceptible to noise, making it less reliable in noisy channels.
4. FHSS with FSK – Transmitter & Receiver
Frequency Hopping Spread Spectrum (FHSS) spreads the signal by rapidly switching carrier frequencies using a pseudo-random sequence. When combined with FSK, data is transmitted by shifting frequencies within each hop. Although FHSS improves security and interference resistance, it increases system complexity and requires precise synchronization.
5. Relations Between Different Entropies
Entropy measures uncertainty in a random variable. Joint entropy represents uncertainty in two variables together, while conditional entropy measures uncertainty of one variable given another. Mutual information represents shared information. These measures help analyze channel capacity and efficiency in communication systems.
SECTION C
(Attempt one from each question)
Q3(a) Mean and Variance of Gaussian PDF
For a Gaussian random variable with mean m and variance σ², the mean is directly equal to m. The variance is σ², representing the spread of the distribution around the mean. Gaussian PDFs are widely used to model noise in communication systems.
Q3(b) Wide Sense Stationary (WSS) Process
A random process is WSS if its mean is constant and its autocorrelation depends only on time difference. For
X(t) = A cos(ωt + Ω), where Ω is uniformly distributed between 0 and 2π, the mean is zero and autocorrelation depends only on time difference. Hence, the process is wide sense stationary.
Q4(a) Scrambling and Its Purpose
Scrambling randomizes data patterns to avoid long sequences of zeros or ones. This helps in clock recovery and reduces spectral lines. Using the given polynomial F = D³ ⊕ D⁵, the scrambled output is obtained by XORing delayed versions of the input data accordingly.
Q4(b) PSD of Polar Line Codes
The Power Spectral Density (PSD) of polar line codes shows how signal power is distributed over frequency. It depends on bit duration and pulse shape. Polar signaling has no DC component, making it suitable for AC-coupled systems.
Q5(a) DPSK Modulation and Demodulation
In Differential PSK, data is encoded as phase difference rather than absolute phase. This eliminates the need for carrier phase synchronization. The receiver compares the phase of consecutive symbols to recover data, making DPSK simpler than coherent PSK.
Q6(a) Matched Filter and Autocorrelation
The output of a matched filter is proportional to a time-shifted autocorrelation of the input signal. This property maximizes the signal-to-noise ratio at the sampling instant, making matched filters optimal for detecting known signals in noise.
Q6(b) Probability of Error for PSK
The probability of error in PSK decreases as signal energy increases. It is derived using Gaussian noise statistics and depends on Eb/N0. PSK offers better error performance compared to ASK and FSK for the same bandwidth.
Q7(a) Huffman Coding Problem
Using the given probabilities, a binary Huffman tree is constructed by combining the least probable symbols. The resulting code minimizes average word length. Efficiency is calculated as the ratio of entropy to average length, while redundancy represents unused coding capacity.
Q7(b) (2,1,2) Convolutional Encoder
A (2,1,2) convolutional encoder has one input, two outputs, and constraint length two. It uses shift registers and modulo-2 adders. This encoder improves error performance by introducing controlled redundancy in transmitted data.
