concept

Noisy-channel coding theorem

Shannon's central and most beautiful result. It states: as long as you transmit BELOW the channel's capacity, you can - with clever enough coding - drive the error rate as close to zero as you like, even over a noisy channel. Perfect, lossless communication over an imperfect line is genuinely possible. But the instant you try to transmit FASTER than capacity, the promise shatters: errors become not unlikely but mathematically certain. This is a law as firm as the speed of light, not an engineering inconvenience to be designed around.