The Maximum Data Rate of a Channel

Data rate refers to the speed of data transfer through a channel. It is generally computed in bits per second (bps). Higher data rates are expressed as Kbps ("Kilo" bits per second, i.e.1000 bps), Mbps ("Mega" bits per second, i.e.1000 Kbps), Gbps ("Giga" bits per second, i.e. 1000 Mbps) and Tbps ("Tera" bits per second, i.e. 1000 Gbps).

One of the main objectives of data communications is to increase the data rate. There are three factors that determine the data rate of a channel:

• Bandwidth of the channel
• Number of levels of signals that are used
• Noise present in the channel

Data rate can be calculated using two theoretical formulae:

• Nyquist Bit Rate – for noiseless channel
• Shannon’s Capacity – for noisy channel

Nyquist Bit Rate

Nyquist bit rate was developed by Henry Nyquist who proved that the transmission capacity of even a perfect channel with no noise has a maximum limit.

The theoretical formula for the maximum bit rate is:

maximum bit rate = 2 × Bandwidth × log₂V

Here, maximum bit rate is calculated in bps

Bandwidth is the bandwidth of the channel

V is the number of discrete levels in the signal

For example, if there is a noiseless channel with a bandwidth of 4 KHz that is transmitting a signal with 4 discrete levels, then the maximum bit rate will be computed as, maximum bit rate = 2 × 4000 × log₂4 = 16,000 bps = 16 kbps

Shannon's Capacity

Claude Shannon extended Nyquist's work for actual channels that are subject to noise. Noise can be of various types like thermal noise, impulse noise, cross-talks etc. Among all the noise types, thermal noise is unavoidable. The random movement of electrons in the channel creates an extraneous signal not present in the original signal, called the thermal noise. The amount of thermal noise is calculated as the ratio of the signal power to noise power, SNR.

Signal-to-Noise Ratio,SNR = Average Signal Power/Average Noise Power

Since SNR is the ratio of two powers that varies over a very large range, it is often expressed in decibels, called SNR_db and calculated as: SNR_db = 10log₁₀SNR.

Shannon's Capacity gives the theoretical maximum data rate or capacity of a noisy channel. It is expressed as:

Capacity = Bandwidth × log₂( 1+SNR )

Here, Capacity is the maximum data rate of the channel in bps

Bandwidth is the bandwidth of the channel

SNR is the signal – to – noise ratio

For example, if the bandwidth of a noisy channel is 4 KHz, and the signal to noise ratio is 100, then the maximum bit rate can be computed as:

Capacity = 4000 × log₂( 1+100 ) = 26,633 bps = 26.63 kbps