GATE ECE topic:information-theory PYQs & Answers

Questions 1–10 of 12. Imported answers require independent review unless marked reviewed.

Let the relevant bandwidth (B) of a digital communication system be 1 MHz and kT = −174 dBm/Hz, where k is Boltzmann’s constant and T is equivalent noise temperature of the receiver. The power (S) of signal received through an additive Gaussian channel is −80 dBm.

Which of the following options is/are TRUE about Shannon capacity (C) of the channel?

Your answerSelect all correct options. You can choose more than one.

C = B

C = 2B

C > 3B

C < B

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Consider an additive white Gaussian noise (AWGN) channel with bandwidth

and noise power spectral density

. Let

denote the average transmit power constraint. Which one of the following plots illustrates the dependence of the channel capacity

on the bandwidth

(keeping

and

fixed)?

Your answerChoose one option.

Diagram for Electronics and Communication Engineering question 15

Diagram for Electronics and Communication Engineering question 15 (figure 2)

Diagram for Electronics and Communication Engineering question 15 (figure 3)

Diagram for Electronics and Communication Engineering question 15 (figure 4)

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The random variable

takes values in

with probabilities

and

, where

. Let

denote the entropy of

(in bits), parameterized by

. Which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

and

are Bernoulli random variables taking values in

. The joint probability mass function of the random variables is given by:

The mutual information

is __________ (rounded off to two decimal places).

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is ______.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The frequency of occurence of 8 symbols (a-h) is shown in the table below. A symbol is chosen and it is determined by asking a series of “yes/no” questions which are assumed to be truthfully answered. The average number of questions when asked in the most efficient sequence, to determine the chosen symbol, is ______ (rounded off to two decimal places).

Symbols	a	b	c	d	e	f	g	h
Frequency of occurence

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

denote the entropy of a discrete random variable

taking

possible distinct real values. Which of the following statements is/are necessarily true?

Your answerSelect all correct options. You can choose more than one.

bits

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition probabilities are as marked.

The parameter

lies in the interval

. The value of

for which the capacity of this channel is maximized, is ________ (rounded off to two decimal places).

Diagram for Electronics and Communication Engineering question 61

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Let

be independent random variables.

has mean 0 and variance 1, while

has mean 1 and variance 4. The mutual information

between

and

in bits is ________.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Which one of the following graphs shows the Shannon capacity (channel capacity) in bits of a memoryless binary symmetric channel with crossover probability

Your answerChoose one option.