Shannon’s Noisy Coding Theorem

Suppose that we have some information that we want to transmit over a noisy channel. Nowadays, this happens all the time: when you’re talking on a cell phone, and there is interference from radio waves from other devices; when you’re playing a CD (on a good CD player, CD’s are remarkably scratch-resistant); when you’re downloading stuff from the Internet. You’d like to make sure that the information gets through intact, even though the line is noisy. How can we do this? Here we will discuss a theoretical result on how much information can be transmitted over a noisy channel.