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Electronics and Communication Engineering (ECE) Exam  >  Electronics and Communication Engineering (ECE) Test  >  GATE ECE (Electronics) Mock Test Series 2027  >  Test: Information Theory & Coding - Electronics and Communication Engineering (ECE) MCQ

GATE ECE (Electronics) Test: Information Theory & Coding Free Online Test


MCQ Practice Test & Solutions: Test: Information Theory & Coding (10 Questions)

You can prepare effectively for Electronics and Communication Engineering (ECE) GATE ECE (Electronics) Mock Test Series 2027 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Information Theory & Coding". These 10 questions have been designed by the experts with the latest curriculum of Electronics and Communication Engineering (ECE) 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 30 minutes
  • - Number of Questions: 10

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Test: Information Theory & Coding - Question 1
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The probabilities of the five possible outcomes of an experiment are given as:

If there are 16 outcomes per second then the rate of information would be equal to

Detailed Solution: Question 1

The entropy of the system is

or

Now, rate of outcome r= 16 outcomes/sec (Given)

∴ The rate of information R is

Test: Information Theory & Coding - Question 2
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Consider the binary Hamming code of block length 31 and rate equal to (26/31). Its minimum distance is

Detailed Solution: Question 2

Minimum distance in hamming code = 3.
The minimum distance of a Hamming code is always 3. This property allows Hamming codes to detect up to two-bit errors and correct single-bit errors within a block of data. The minimum distance is not directly related to the block length or rate but is a characteristic of the Hamming code's design.

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Test: Information Theory & Coding - Question 3
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Assertion (A): The Shannon-Hartley law shows that we can exchange increased bandwidth for decreased signal power for a system with given capacity C.
Reason (R): The bandwidth and the signal power place a restriction upon the rate of information that can be transmitted by a channel.

Detailed Solution: Question 3

According to Shannon-Hartley faw, the channel capacity is expressed as

Thus, if signal power is more, bandwidth will be less and vice-versa. Thus, assertion is a true statement. Reason is also a true statement because the rate of information that can be transmitted depends on bandwidth and signal to noise power. Thus, both assertion and reason are true but reason is not the correct explanation of assertion.

Test: Information Theory & Coding - Question 4
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A 1200 band data stream is to be sent over a non-redundant frequency hopping system, The maximum bandwidth for the spread spectrum signal is 10 MHz. if no overlap occurs, the number of channels are equal to

Detailed Solution: Question 4

Test: Information Theory & Coding - Question 5
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The differential entropy H(x) of the uniformly distributed random variable* with the following probability density function for a = 1 is

Detailed Solution: Question 5

We know that the differential entropy of x is given by

Using the given probability density function, we have:

for

a = 1, H(x) = log2 1 = 0

Test: Information Theory & Coding - Question 6
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During transmission over a communication channel bit errors occurs independently with probability 1/2 . If a block of 3 bits are transmitted the probability of at least one bit error is equal to

Detailed Solution: Question 6

(1 - p)n + np{ 1 - p)n-1 = Required probability
(Here, n = no. of bits and p = probability) ∴  Required probability

Test: Information Theory & Coding - Question 7
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A channel has a bandwidth of 8 kHz and signal to noise ratio of 31. For same channel capacity, if the signal to noise ratio is increased to 61, then, the new channel bandwidth would be equal to

Detailed Solution: Question 7

We know that channel capacity is

Since channel capacity remains constant, therefore

Test: Information Theory & Coding - Question 8
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A source generates 4 messages. The entropy of the source will be maximum when

Test: Information Theory & Coding - Question 9
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A source delivers symbols m1, m2, m3 and m4 with probabilities  respectively. 

The entropy of the system is

Detailed Solution: Question 9

The entropy of the system is

Test: Information Theory & Coding - Question 10
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A communication channel with AWGN has a BW of 4 kHz and an SNR pf 15. Its channel capacity is

Detailed Solution: Question 10

Channel capacity is

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About this Electronics and Communication Engineering (ECE) Practice Test

This test contains 10 MCQs on Information Theory & Coding with detailed solutions for each question. It is part of the GATE ECE (Electronics) Mock Test Series 2027 course on EduRev, designed to align with the current Electronics and Communication Engineering (ECE) syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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