2071 Chaitra(Q)Explain the Shannon channel capacity theorem. Write down the theoretical limitations of this theorem.

The bandwidth and the noise power limit the rate of information that can be transmitted by a channel. It says that a channel that is disturbed by white Gaussian noise, can transmit information at a rate of C bits per second.

C = channel capacity

Mathematically,

C = Bandwith * log₂ (1+SNR)

C= B*log₂ (1+S/N)

in this expression,

B=Bandwidth of this channel in Hz

S=Signal Power

N=Noise power

Theoretical limitations:

1. For noiseless channels N=0 then the value of SNR is infinite and the channel capacity is infinite. But practically N is finite and Hence, C is finite.
2. This is true even if the bandwidth B is infinite. The noise signal is a white noise with a uniform power density spectrum over the entire frequency range. Therefore, as the bandwidth B is increased, N also increases, and Hence the channel capacity remains finite even if B=infinite.