Shannon introduced the concept of channel capacity, the limit at which data can be transmitted through a medium. The errors in the transmission medium depend on the energy of the signal, the energy of the noise, and the bandwidth of the channel. Conceptually, if the bandwidth is high, we can pump more data in the channel. If the signal energy is high, the effect of noise is reduced. According to Shannon, the bandwidth of the channel and signal energy and noise energy are related by the formula

C = W log₂(1+S/N)

where,

C is channel capacity in bits per second (bps)

W is bandwidth of the channel in Hz

S/N is the signal-to-noise power ratio (SNR). SNR generally is measured in dB using the formula

(S/N) dB = 10 log (Signal Power / Noise Power)

The value of the channel capacity obtained using this formula is the theoretical maximum. As an example, consider a voice-grade line for which W = 3100Hz, SNR = 30dB (i.e., the signal-to-noise ratio is 1000:1)

C = 3100 log₂(1 + 1000) = 30,894 bps.

So, we cannot transmit data at a rate faster than this value in a voice-grade line.

An important point to be noted is that in the above formula, Shannon assumes only thermal noise.

To increase C, can we increase W? No, because increasing W increases noise as well, and SNR will be reduced. To increase C, can we increase SNR? No, that results in more noise, called intermodulation noise.

The entropy of information source and channel capacity are two important concepts, based on which Shannon proposed his theorems.

He also defined channel capacity, which is related to the bandwidth and signal-to-noise ratio. Based on these two measures, he formulated the source coding theorem and channel coding theorem.

Source coding theorem states that "the number of bits required to uniquely describe an information source can be approximated to the information content as closely as desired."

Channel coding theorem states that "the error rate of data transmitted over a bandwidth limited noisy channel can be reduced to an arbitrary small amount if the information rate is lower than the channel capacity."