Data rate governs the speed of data transmission. A very important consideration in data communication is how fast we can send data, in bits per second, over a channel. Data rate depends upon 3 factors:

- The bandwidth available
- Number of levels in digital signal
- The quality of the channel – level of noise

Two theoretical formulas were developed to calculate the data rate : one by Nyquist for a noiseless channel, another by Shannon for a noisy channel.

**Noiseless Channel : Nyquist Bit Rate –**

For a noiseless channel, the Nyquist bit rate formula defines the theoretical maximum bit rateBitRate = 2 * Bandwidth * log2(L)

In the above equation, bandwidth is the bandwidth of the channel, L is the number of signal levels used to represent data, and BitRate is the bit rate in bits per second.

Bandwidth is a fixed quantity, so it cannot be changed. Hence, the data rate is directly proportional to the number of signal levels.

**Note –**Increasing the levels of a signal may reduce the reliability of the system.**Examples:**

**Input1 :**Consider a noiseless channel with a bandwidth of 3000 Hz transmitting a signal with two signal levels. What can be the maximum bit rate?

**Output1 :**BitRate = 2 * 3000 * log2(2) = 6000bps**Input2 :**We need to send 265 kbps over a noiseless channel with a bandwidth of 20 kHz. How many signal levels do we need?

**Output2 :**265000 = 2 * 20000 * log2(L)

log2(L) = 6.625

L = 2^6.625 = 98.7 levels**Noisy Channel : Shannon Capacity –**

In reality, we cannot have a noiseless channel; the channel is always noisy. Shannon capacity is

used, to determine the theoretical highest data rate for a noisy channel:Capacity = bandwidth * log2(1 + SNR)

In the above equation, 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.

Bandwidth is a fixed quantity, so it cannot be changed. Hence, the channel capacity is directly proportional to the power of the signal, as SNR = Power of signal / power of noise.

The signal-to-noise ratio (S/N) is usually expressed in decibels (dB) given by the formula:10 * log10(S/N)

so for example a signal-to-noise ratio of 1000 is commonly expressed as:

10 * log10(1000) = 30 dB.

**Examples:****Input1 :**A telephone line normally has a bandwidth of 3000 Hz (300 to 3300 Hz) assigned for data communication. The SNR is usually 3162. What will be the capacity for this channel?

**Output1 :**C = 3000 * log2(1 + SNR) = 3000 * 11.62 = 34860 bps**Input2 :**The SNR is often given in decibels. Assume that SNR(dB) is 36 and the channel bandwidth is 2 MHz. Calculate the theoretical channel capacity.

**Output2 :**SNR(dB) = 10*log10(SNR)

SNR = 10^(SNR(dB)/10)

SNR = 10^3.6 = 3981Hence, C = 2 * 10^6 * log2(3982) = 24 MHz

**Reference:**

Data Communications and Networking – Book

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