A QPSK modulated signal from an additive white Gaussian noise (AWGN) channel is received with an $E_b / N_o=8.4 \mathrm{~dB}$ at the input of a coherent QPSK demodulator. A maximum-likelihood reception method is used in the demodulator.

Assume the complimentary error function

$$ \operatorname{erfc}(u) \cong\left[\frac{1}{(u \sqrt{\pi})}\right] \exp \left(-u^2\right) $$

Which is the nearest bit error rate (BER) at the output of the demodulator?

Let the relevant bandwidth $(B)$ of a digital communication system be 1 MHz and $k T=-174 \mathrm{dBm} / \mathrm{Hz}$, 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?

Consider a real, narrowband signal $x(t)=A(t) \cos \left[2 \pi f_c t+\theta(t)\right]$ where the maximum frequency components of $A(t)$ and $\theta(t)$ are $f_M$ and $f_C\left(=1000 f_M\right)$, respectively. Which of the following statements is/are correct for $-\infty

The average bit error rate at the input of a $(7,4,1)$ Hamming decoder is 0.10 . The probability that the decoder will fail to decode a received word correctly is $\_\_\_\_$ . (rounded off to two decimal places)