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The data rate limit is nothing but how fast we can send data. Basically, the corresponding range uses bits per second on a channel. This is a very important consideration in data communication. We need fast communication. What does this basically mean? It basically tells the receiver about the data transfer rate between the sender that it should be fast enough. Also, the time requirement should be minimal and that is why we always worry about data transfer rate. The data rate depends on three factors: –

- Bandwidth available
- Bandwidth means the difference between the maximum frequency and the minimum frequency of the respective channel and the level of the signal.

- The level of signal that we use inside the transmission medium
- Channel quality or we can say noise level

Theoretical formulas have been developed to calculate the data rate: –

- The Nyquist theorem will apply for a noiseless channel or we can say that we need it for a noiseless channel.
- Shannon for a noise channel

## Noise Channel: Nyquist Bit Rate

According to this Nyquist theorem we can only detect bitrate if given bandwidth and signal levels. So for a noiseless channel, the Nyquist bit rate formula derives the theoretical maximum bit rate. This means that we need a formula to find the maximum bit rate in the case of a noiseless channel. So, by related formula, we can decide: –

- The bitrate is equal to multiplication of 2, multiplied again with the bandwidth and log L of base 2.

- L is the number of levels used
- When we increase the number of levels, the distance between levels decreases and the error will be greater. Subsequently, this will reduce the reliability of the system.
- Increasing the level of a signal can reduce the reliability of the system, obviously, L must have some upper limit and it will be the above formula to calculate the bit rate in the noiseless channel that we should use.

### Noise Channel: Shannon Capacity

We cannot have a noiseless channel. Claude Shannon seems to have this noisy channel which means Shannon capability. The so-called Schoenens potential that determines the theoretical highest data rate for a noisy channel. So to calculate the Shannon capacity which is a noise channel, the formula is: –

- The capacity is equal to the bandwidth and multiplied with a log (1 + SNR) basis of 2.

This is the expected equation to calculate the channel capacity.

- So this line is very important -> Shannon potential gives us the upper limit while the Nyquist formula tells us how many signal levels we need.