# Can channel capcity be explained in simple terms? [closed]

Can channel capacity be explained in simple terms - without mutual information and such probabilistic concepts? In its most general form, what are all the parameters that it depends on? What is its dependence on physical parameters such as the electrical parameters if we talk of information conveying through electrical signals? Can we measure/calculate the channel capacity of any channel given its physical parameters?

• It's probably better if you ask a more pointed question. $$C = B \log_2 \left(1 + \frac{P_s}{P_n}\right)$$ $B$, $P_s$, and $P_n$ are very much physical electrical parameters. – Jason R Mar 18 '16 at 12:47
• There are several bandwidth definitions for example 3 dB bandwidth. What is the bandwidth in this context? Are there any assumptions for this formula? Is this applicable for any channel, any signal waveform any noise distribution and any noise spectrum - white, colored etc? – Seetha Rama Raju Sanapala Mar 18 '16 at 15:40

There is a limit where simplifying a scientific concept starts becoming inaccurate.

However, the capacity of a channel is a really simple idea that is completely illustrated by the following equation:

$C = B\log_2(1+\frac{S}{N})$

The equation says that the maximum amount of information (in bits per second) that can be transmitted in a channel error-free is proportional to the Bandwidth $B$ in Hertz, and is also proportional to the logarithm of base-2 of 1+ the signal to noise ratio.

So let us break this down to two points, the bandwidth and signal to noise ratio.

The bandwidth is the range of frequencies that you use in your channel. Let us take an example where your channel has a really small bandwidth ($B=0$) where you only have one frequency that you can operate on. This translates to a single sinusoid of a certain frequency. Note that you cannot turn it on or off, or even change its phase because that will result in a range of other frequencies. Therefore communication is impossible on this channel.

The signal to noise ratio, is a measure of how strong a signal is to how strong the noise is and can take values between 0 and $\infty$. A signal power equal to 0 or a noise power equal to $\inf$ will make $\log_2(1+S/N)$ go to zero where communication is impossible.

On the other hand, 0 noise power, or an infinite signal power (given the bandwidth is not 0) will mean that you can send as much data as you like through the channel without any errors. Which is also the case for an infinite bandwidth and a non-zero value of $\log_2(1+S/N)$.