Shannon’s Theorem

Shannon’s theorem gives the capacity of a system in the presence of noise.

$$ C = B\ log_2\ (1 + \frac SR)$$

Where,

C = Channel Capcity (bits/sec)

B = Channel Bandwidth

$\frac SN$ = Signal to Noise Ratio

Channel Capacity in Extremely Noisy Channel -

• Consider an extremely noisy channel in which the value of the signal-to-noise ratio is almost zero.
• In other words, the noise is so strong that the signal is faint.
• For this channel, the capacity C is calculated as:

$$ C = B\ log_2\ (1 + \frac SR)$$

$$ C = B\ log_2\ (1 + 0)$$

$$ C = B\ log_2\ 1$$

$$ C = B \times 0$$

$$ C = 0$$

• This means that the capacity of this channel is zero regardless of the bandwidth.
• In other words, we can not receive any data through this channel.