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)?

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

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 uniformly distributed in the range -5 V to +5 V , are subsequently quantized in an $8-$ bit uniform quantizer and then transmitted over a voice - grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is 26 dB , the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is $\_\_\_\_$ kHz .