The capacity of band-limited additive white Gaussian noise (AWGN) channel is given by $$C = \,W\,\,{\log _2}\left( {1 + {P \over {{\sigma ^2}\,W}}} \right)$$ 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 $${{P \over {{\sigma ^2}\,}} = 1000}$$, the channel capacity (in kbps) with infinite band width $$(W \to \infty )$$ is approximately

A communication channel with AWGN operating at a signal to noise ratio SNR > > 1 and band width B has capacity $${{C_1}}$$ . If the SNR is doubled keeping B constant, the resulting capacity $${{C_2}}$$ is given

A memory less source emits n symbols each with a probability p. The entropy of the source as a function of n

A source generates three symbols with probabilities 0.25, 0.25, 0.50 at a rate of 3000 symbols per second. Assuming independent generation of symbols, the most efficient source encoder would have average bit rate as