1
GATE ECE 2024
Numerical
+1
-0.33

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

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2
GATE ECE 2024
MCQ (Single Correct Answer)
+2
-1.33

A source transmits a symbol $s$, taken from $\\{-4, 0, 4\\}$ with equal probability, over an additive white Gaussian noise channel. The received noisy symbol $r$ is given by $r = s + w$, where the noise $w$ is zero mean with variance 4 and is independent of $s$.

Using $Q(x) = \frac{1}{\sqrt{2\pi}} \int\limits_{x}^{\infty} e^{-\frac{t^{2}}{2}} dt$, the optimum symbol error probability is _______.

A

$\frac{2}{3} Q(2)$

B

$\frac{4}{3} Q(1)$

C

$\frac{2}{3} Q(1)$

D

$\frac{4}{3} Q(2)$

3
GATE ECE 2024
MCQ (Single Correct Answer)
+2
-1.33

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 generator polynomial is $C(x) = x^4 + x + 1$. The encoded sequence of bits is ____.

A

{1 1 1 0 1 0 1 1 1 0 0}

B

{1 1 1 0 1 0 1 1 1 0 1}

C

{1 1 1 0 1 0 1 1 1 1 0}

D

{1 1 1 0 1 0 1 0 1 0 0}

4
GATE ECE 2024
Numerical
+2
-1.33

Let $X(t) = A\cos(2\pi f_0 t+\theta)$ be a random process, where amplitude $A$ and phase $\theta$ are independent of each other, and are uniformly distributed in the intervals $[-2,2]$ and $[0, 2\pi]$, respectively. $X(t)$ is fed to an 8-bit uniform mid-rise type quantizer.

Given that the autocorrelation of $X(t)$ is $R_X(\tau) = \frac{2}{3} \cos(2\pi f_0 \tau)$, the signal to quantization noise ratio (in dB, rounded off to two decimal places) at the output of the quantizer is _________.

Your input ____
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