The Shannon limit for information capacity I is

(1) \(B~lo{g_2}\left( {1 - \frac{S}{N}} \right)\)

(2) \(B~lo{g_2}\left( {1 + \frac{S}{N}} \right)\)

(3) \(B~lo{g_{10}}\left( {1 - \frac{S}{N}} \right)\)

(4) \(B~lo{g_{10}}\left( {1 + \frac{S}{N}} \right)\)

Where:

N = Noise power (W)

B = Bandwidth (Hz)

 S = Signal power (W) 

Shannon–Hartley theorem: 

It states the channel capacity C, meaning the theoretical highest upper bound on the information rate of data that can be communicated at an arbitrarily low error rate using an average received signal power S through an analog communication channel that is subject to additive white Gaussian noise (AWGN) of power N.

Mathematically, it is defined as:

\({\rm{C}} = {\rm{B\;lo}}{{\rm{g}}_2}\left( {{\rm{\;}}1 + \frac{{\rm{S}}}{{\rm{N}}}{\rm{\;}}} \right)\)

C = Channel capacity

B = Bandwidth of the channel

S = Signal power

N = Noise power

∴ It is a measure of capacity on a channel. And it is impossible to transmit information at a faster rate without error.