GATE Communications: Information Theory – Previous Year Questions
20 GATE previous year questions on Information Theory (Communications, Electronics and Communication Engineering) with answers and explanations, from every paper.
- GATE 2017 EC Q31 – Let (X 1, X 2) be independent random variables. X 1 has mean 0 and variance 1, while X 2 has mean 1 and variance 4. The mutual information I(X 1; X 2)…
- GATE 2015 EC Q59 – The input X to the Binary Symmetric Channel (BSC) shown in the figure is '1' with probability 0.8. The cross-over probability is 1/7. If the received…
- GATE 2016 EC Q58 – Consider a discrete memoryless source with alphabet S = \s 0, s 1, s 2, s 3, s 4, \ and respective probabilities of occurrence P = \12, 14, 18, 116,…
- GATE 2018 EC Q26 – Consider a binary channel code in which each codeword has a fixed length of 5 bits. The Hamming distance between any pair of distinct codewords in…
- GATE 2019 EC Q17 – A linear Hamming code is used to map 4-bit messages to 7-bit codewords. The encoder mapping is linear. If the message 0001 is mapped to the codeword…
- GATE 2020 EC Q32 – A binary random variable X takes the value +2 or -2. The probability P(X=+2)=. The value of (rounded off to one decimal place), for which the entropy…
- GATE 2021 EC Q33 – A speech signal, band limited to 4 kHz, is sampled at 1.25 times the Nyquist rate. The speech samples, assumed to be statistically independent and…
- GATE 2021 EC Q44 – A digital transmission system uses a (7,4) systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-codeword…
- GATE 2021 EC Q61 – In a high school having equal number of boy students and girl students, 75% of the students study Science and the remaining 25% students study…
- GATE 2022 EC Q29 – Let H(X) denote the entropy of a discrete random variable X taking K possible distinct real values. Which of the following statements is/are…
- GATE 2022 EC Q61 – The transition diagram of a discrete memoryless channel with three input symbols and three output symbols is shown in the figure. The transition…
- GATE 2022 EC Q62 – Consider communication over a memoryless binary symmetric channel using a (7, 4) Hamming code. Each transmitted bit is received correctly with…
- GATE 2023 EC Q65 – The frequency of occurrence 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”…
- GATE 2024 EC Q34 – A source transmits symbols from an alphabet of size 16. The value of maximum achievable entropy (in bits) is .
- GATE 2024 EC Q47 – The information bit sequence \1\ 1\ 1\ 0\ 1\ 0\ 1\ 0\ 1\ is to be transmitted by encoding with Cyclic Redundancy Check 4 (CRC-4) code, for which the…
- GATE 2025 EC Q15 – Consider an additive white Gaussian noise (AWGN) channel with bandwidth W and noise power spectral density N 02. Let P av denote the average transmit…
- GATE 2025 EC Q33 – The generator matrix of a (6,3) binary linear block code is given by G=bmatrix1&0&0&1&0&1\\0&1&0&0&1&1\\0&0&1&1&1&0bmatrix. The minimum Hamming…
- GATE 2025 EC Q54 – The random variable X takes values in \-1,0,1\ with probabilities P(X=-1)=P(X=1)= and P(X=0)=1-2, where 0<<12. Let g() denote the entropy of X (in…
- GATE 2025 EC Q60 – X and Y are Bernoulli random variables taking values in \0,1\. The joint probability mass function of the random variables is given by:…
- GATE 2026 EC Q55 – 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…