Consider an additive white Gaussian noise (AWGN) channel with bandwidth $W$ and noise power spectral density $\frac{N_o}{2}$. Let $P_{a v}$ denote the average transmit power constraint. Which one of the following plots illustrates the dependence of the channel capacity $C$ on the bandwidth $W$ (keeping $P_{a v}$ and $N_0$ fixed)?

Consider a message signal $m(t)$ which is bandlimited to $[-W, W]$, where $W$ is in Hz . Consider the following two modulation schemes for the message signal:

Double sideband-suppressed carrier (DSB-SC):

$$ f_{\mathrm{DSB}}(t)=A_c m(t) \cos \left(2 \pi f_c t\right) $$

Amplitude modulation (AM):

$$ f_{\mathrm{AM}}(t)=A_c(1+\mu m(t)) \cos \left(2 \pi f_c t\right) $$

Here, $A_c$ and $f_c$ are the amplitude and frequency (in Hz ) of the carrier, respectively. In the case of AM, $\mu$ denotes the modulation index.

Consider the following statements:

(i) An envelope detector can be used for demodulation in the DSB-SC scheme if $m(t)>0$ for all $t$.

(ii) An envelope detector can be used for demodulation in the AM scheme only if $m(t)>0$ for all $t$.

Which of the following options is/are correct?

The generator matrix of a $(6,3)$ binary linear block code is given by

$$ G=\left[\begin{array}{llllll} 1 & 0 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1 & 1 & 0 \end{array}\right] $$

The minimum Hamming distance $d_{\min }$ between codewords equals___________ (answer in integer).

A source transmits symbol $S$ that takes values uniformly at random from the set $\{-2,0,2\}$. The receiver obtains $Y=S+N$, where $N$ is a zero-mean Gaussian random variable independent of $S$. The receiver uses the maximum likelihood decoder to estimate the transmitted symbol $S$.

Suppose the probability of symbol estimation error $P_e$ is expressed as follows:

$$ P_e=\alpha P(N>1), $$

where $P(N>1)$ denotes the probability that $N$ exceeds 1 .

What is the value of $\alpha$ ?