Electronic – Calculating maximum data rates

bandwidthcommunicationcomputers

A channel has bandwidth 3 KHz, signal to noise ratio is 40 dB find maximum data rate for 16 level encoding schemes.

There are two ways to find channel capacity. First one is with Nyquist theorem and second one is with shanon capacity. For Nyquist theorem I found 24 kbps and for Shanon capacity I found 39.84 kbps. So which one would be preferable? Is there any other method to do?

Best Answer

The difference between the two formulas arises from the fact that the Nyquist formula uses the number of encoding levels that was explicitly given (16 levels implies 4 bits/baud), while the Shannon formula is the theoretical maximum based on the SNR of the channel (40 dB implies about 6.64 bits/baud).

3000 Hz × 2 baud/cycle × 4 bits/baud = 24000 bits/sec

3000 Hz × 2 baud/cycle × 6.64 bits/baud = 39840 bits/sec