Consider a discreet memoryless source with alphabet $$S = \left\{ {{s_0},\,{s_1},\,{s_2},\,{s_3},\,{s_{4......}}} \right\}$$ and respective probabilities of occurrence $$P = \left\{ {{1 \over 2},\,{1 \over 4},\,{1 \over 8},\,{1 \over {16}},\,{1 \over {32}},......} \right\}$$. The entropy of the source (in bits) is__________.

A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of 4.0 kHz and two-sided noise power spectral density $${\eta \over 2} = 2.5\, \times \,{10^{ - 5}}$$ Watt per Hz. If information at the rate of 52 kbps is to be transmitted over this channel with arbitrarily small bit error rate, then the minimum bit energy $${E_b}$$ (in mJ/bit) necessary is ________________

Consider the Z- channel given in the figure. The input is 0 or 1 with equal probability. If the output is 0, the probability that the input is also 0 equals____________________________________

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