Channel Capacity of a Discrete Memoryless Channel (DMC)# is defined as the maximum average Mutual Information# which is measured in bits per channel use:
$$ C = I(A_X; A_Y) $$
By Shannon’s third theorem, Channel Capacity is defined as:
$$ \begin{align} C &= B \lg (1 + \frac{P}{N_0 B}), \quad \text{or}\\ C &= B \lg (1 + \frac{E_b C}{N_0 B}), \quad \text{or}\\ C &= B \lg (1 + SNR) \end{align} $$
Where:
- \(B\) is the channel bandwidth in Hz
- \(N_0\) is the additive white Gaussian noise of power spectral density
- \(P\) is the average transmitted power which \(P = E_b C\) where \(E\) is the transmitted energy per bit
- \(SNR\) is the average signal-to-noise ratio#
We can get the signal energy-per-bit to noise power spectral density ratio \(\frac{E_b}{N_0}\) by changing the equation:
$$ \frac{E_b}{N_0} = \frac{2^{\frac{C}{B}} - 1}{\frac{C}{B}} $$
It is not possible to transmit at a rate higher than \(C\) bits per second by any encoding system without a definite probability of error. Thus, it defines the fundamental limit on the rate of error-free transmission for a power-limited, band-limited Gaussian channel. (an application of Channel Coding Theorem) From that, we could know the Shannon’s Limit# for an Additive White Gaussian Noise (AWGN) Channel if the bandwidth is infinite. A Bandwidth Efficiency Diagram# could be plotted utilising the equation’s characteristics.