DATA RATE LIMIT

A very important consideration in the data communication is how fast we can send data, in bits/second, over a channel. Data rate depends on the three factors.

-   The bandwidth available

-   The level of the signal we use

-   The quality of the channel (Level of noise)

Two theoretical formula we developed to calculate the data rate: one by Nyquist for a noise less channels and other one is Shannon for a noisy channel.

Noise less channel: Nyquist bitrate :

For noiseless channel, the Nyquist bit rate formula defined the maximum bit rate                 

In the above formula bandwidth is Bandwidth of the channel, L is the number of signal level use to represent data, and BitRate is the bit rate in bits/second

According to the formula, we might think that, given a specific bandwidth, we can have any bit rate we want to increase the number of signal level. Although Idea is theoretically correct, practically there us a limit. When we increase the number of signal level, we impose the burden on the receiver. If the number signal lever is just two, the receiver easily distinguishes between the bit “1” and “0”. If the level of the signal if 64, then receiver must be very sophisticated to distinguish between 64 different level. In other worlds, increasing the level of a signal reduce the reliability of the system.

Noise channel: Shannon capacity:

In a reality, we can not have the noiseless channel; the channel always noisy. In 1944, Claude Shannon introduce a formula, called the Shannon capacity, to determine the theoretical highest data rate for a noisy channel;

 In the above formula bandwidth is Bandwidth of the channel, SNR is the signal to noise ratio, and capacity is the capacity of the channel in it per second. Note that in the Shannon formula there is no indication of signal level, which means no matter how many levels we have, we can not achieve the   data rate higher than the capacity of the channel. In other worlds, the formula defines a characteristic of the channel, not the method of transmission.

 For Example: -

Consider an extremely noisy channel in which the value of the signal- to -noise ratio is almost “Zero”. In other worlds, the noise is so strong that the signal is faint. For this channel the capacity C is calculated as