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# Computer Networks : Data Rate Limits

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on The data rate limit is nothing but how fast we can send data. Basically, the respective limit uses bits per second over a channel. This is a very important consideration in data communications. We require to have faster communication. What does this basically mean? This basically states about the data transfer rate between the sender to the receiver should be fast enough. Moreover, the time requires should be minimal enough and that’s why we always have the concern for the data transfer rate. Data rate depends on three factors:-

• The 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 the signals what we use inside the transmission medium
• The channel quality or we can say the noise level

To calculate the data rate theoretical formulas has been developed:-

• The Nyquist theorem will be applicable for a noiseless channel or we can say we require it for the noiseless channel.
• Shannon’s for a noisy channel

## Noiseless Channel: Nyquist Bit Rate

According to this Nyquist theorem if the bandwidth and the signal level are given we can simply find the bitrate. So for a noiseless channel, the Nyquist bit rate formula derives the theoretical maximum bit rate. That means in the case of the noiseless channel to find the maximum bit rate we need a formula. So, by the respective formula, we can decide:-

• Bitrate is equal to the multiplication of 2, bandwidth and again multiplied with log L of base 2.
• L is the number of levels used
• When we increase the number of levels, the distance between the levels gets decrease and error will be more. Henceforth, it will reduce the reliability of the system.
• Increasing the level of a signal may reduce the reliability of the system so obviously, the L should have some upper bound and to calculate the bit rate in the noiseless channel it will be the above formula which we must use.

### Noisy Channel: Shannon Capacity

We cannot have a noiseless channel. Claude Shannon finds this noisy channel that means the Shannon Capacity. So-called the Shannons capacity which determines the theoretical highest data rate for a noise channel. So to calculate the Shannon Capacity which is a noisy channel, the formula is:-

• Capacity is equal to the bandwidth and multiplied with log (1 +SNR) base of 2.

This is the expected equation to calculate the capacity of the channel.

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

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