GATE EC 2014 Set 2 Q22 — Probability and Statistics

The capacity of a band-limited additive white Gaussian noise (AWGN) channel is given by $C = W \log_{2}\left ( 1+\frac{p} {\sigma ^{2}w} \right )$ bits per second (bps), where $W$ is the channel bandwidth, $P$ is the average power received and $\sigma ^{2}$ is the one-sided power spectral density of the AWGN. For a fixed $\frac{p}{\sigma ^{2}}=1000$, the channel capacity (in kbps) with infinite bandwidth $(W\rightarrow \infty )$ is approximately