# What is Shannon Capacity for Noisy Channel

In reality, we cannot have a noiseless channel; the channel is always noisy. In 1944, Claude Shannon introduced a formula, called the Shannon capacity, to determine the theoretical highest data rate for a noisy channel:

## Shannon Capacity for Noisy Channel

**Capacity =bandwidth X log2 (1 +SNR)**

In this formula, bandwidth is the bandwidth of the channel, SNR is the signal-to-noise ratio, and capacity is the capacity of the channel in bits per second.

**Note** that in the Shannon formula there is no indication of the signal level, which means that no matter how many levels we have, we cannot achieve a data rate higher than the capacity of the channel.

In other words, the formula defines a characteristic of the channel, not the method of transmission.