GATE ECE 2025 | Noise In Digital Communication Question 2 | Communications

GATE ECE 2025

MCQ (Single Correct Answer)

-0.67

A source transmits symbol $S$ that takes values uniformly at random from the set $\{-2,0,2\}$. The receiver obtains $Y=S+N$, where $N$ is a zero-mean Gaussian random variable independent of $S$. The receiver uses the maximum likelihood decoder to estimate the transmitted symbol $S$.

Suppose the probability of symbol estimation error $P_e$ is expressed as follows:

$$ P_e=\alpha P(N>1), $$

where $P(N>1)$ denotes the probability that $N$ exceeds 1 .

What is the value of $\alpha$ ?

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{4}{3}$

GATE ECE 2021

Numerical

-0

Consider a polar non-return to Zero (NRZ) waveform, using +2 V and -2 V for representing binary ' 1 ' and ' 0 ' respectively, is transmitted in the presence of additive zero-mean white Gaussian noise with variance $0.4 \mathrm{~V}^2$. If the a priori probability of transmission of a binary ' 1 ' is 0.4 , the optimum threshold voltage for a maximum a posteriori (MAP) receiver (rounded off to two decimal places) is $\_\_\_\_$ V.

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GATE ECE 2016 Set 1

MCQ (Single Correct Answer)

-0.6

An analog pulse s(t) is transmitted over an additive white Gaussian noise (AWGN) channel. The received signal is r(t) = s(t) + n(t), where n(t) is additive white Gaussian noise with power spectral density $${{{N_0}} \over 2}$$. The received signal is passed through a filter with impulse response h(t). Let $${E_s}$$ and $${E_n}$$ denote the energies of the pulse s(t) and the filter h(t), respectively. When the signal-to-noise ratio (SNR) is maximized at the output of the filter $$\left( {SN{R_{\max }}} \right)$$, which of the following holds?

$${E_s} = \,{E_h};\,\,SN{R_{\max }} = \,{{2{E_s}} \over {{N_0}}}$$

$${E_s} = \,{E_h};\,\,SN{R_{\max }} = \,{{{E_s}} \over {2{N_0}}}$$

$${E_s} > \,\,{E_h};\,\,SN{R_{\max }} > \,\,{{2{E_s}} \over {{N_0}}}$$

$${E_s} < \,\,{E_h};\,\,SN{R_{\max }} = \,\,{{2{E_h}} \over {{N_0}}}$$

GATE ECE 2016 Set 1

Numerical

-0

A digital communication system uses a repetition code for channel encoding/decoding. During transmission, each bit is repeated three times (0 is transmitted as 000, and 1 is transmitted as 111). It is assumed that the source puts out symbols independently and with equal probability. The decoder operates as follows: In a block of three received bits, if the number of zeros exceeds the number of ones, the decoder decides in favor of a 0, and if the number of ones exceeds the number of zeros, the decoder decides in favor of a 1, Assuming a binary symmetric channel with crossover probability p = 0.1, the average probability of error is _______

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