Shannon capacity formula

Shannon's formula C = 12log(1+P/N) is the emblematic expression for the information capacity of a communication channel.

1. How is Shannon capacity calculated?
2. Why is Shannon capacity calculated?
3. What is the formula for Shannon capacity in bps?
4. What is the Shannon limit for information capacity?

How is Shannon capacity calculated?

If the requirement is to transmit at 5 mbit/s, and a bandwidth of 1 MHz is used, then the minimum S/N required is given by 5000 = 1000 log₂(1+S/N) so C/B = 5 then S/N = 2⁵ −1 = 31, corresponding to an SNR of 14.91 dB (10 x log₁₀(31)).

Why is Shannon capacity calculated?

The Shannon capacity theorem defines the maximum amount of information, or data capacity, which can be sent over any channel or medium (wireless, coax, twister pair, fiber etc.). What this says is that higher the signal-to-noise (SNR) ratio and more the channel bandwidth, the higher the possible data rate.

What is the formula for Shannon capacity in bps?

At a SNR of 0 dB (Signal power = Noise power) the Capacity in bits/s is equal to the bandwidth in hertz. If the SNR is 20 dB, and the bandwidth available is 4 kHz, which is appropriate for telephone communications, then C = 4000 log₂(1 + 100) = 4000 log₂ (101) = 26.63 kbit/s.

What is the Shannon limit for information capacity?

The Shannon limit or Shannon capacity of a communication channel refers to the maximum rate of error-free data that can theoretically be transferred over the channel if the link is subject to random data transmission errors, for a particular noise level.