## Define shannon and Nyquist channel capacity. Or Discuss Nyquist bit rate and also explain the shannon theorem for capacity.

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** Ans.** A very important consideration in data communications how fast

we can send data. in bits per second, over a channel. Data rate depends on

three factors –

(i) The band width available

(ii) The level of the signals we use

(iii) The quality of the channel (the level noise).

*Two* theoretical formulas were developed to calculate the data rate- one by Nyquist for a no1seless 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 rate

r = 2 X B X log2 L

In this formula, B is the bandwidth of the channel, L is the number of signal levels used to represent data, and r is the bit rate in bits per second.

According to the formula, we might think that, given a specific bandwidth, we can have any bit rate we want by increasing the number of signal levels.

Although the idea is theoretically correct, practically there is a limit. When we increase the number of signal levels, we impose a burden on the receiver. If the number of levels in a signal is just 2, the receiver can easily distinguish between a 0 and a 1. If the level of a signal is 64, the receiver must be very sophisticated to distinguish between 64 different levels. In other words, increasing the levels of a signal reduces the reliability of the system.

**Noisy Channel : Shannon Capacity ****– **In reality, we can not have a

noiseless channel; the channel is always noisy. In 1944, Cloude-shannon

introduced a formula called the shannon capac1fy, to determine the theoretical

highest data rate for a noisy Channel.

C = B *x *Iog2(1 + SNR)

In this formula B is the bandwidth of the channel, SNR is the signal-to noise ratio, and C is the capacity of the channel in bits per second. Note that the Shannon formula there is no indication of the signal level, which means that no matter how many levels we have. We cannot achieve a data rate higher than the capacity of the channel. in other words, the formula defines a characteristic of the channel, not the method of transmission.

In conclusion, we can say for channel capacity that the Shannon capacity gives us the’ upper limit while the Nyquist formula tells us how many signal levels we need.