Noise has a speed limit

A channel with a given bandwidth and a given noise has a highest rate at which information can be sent with arbitrarily few errors. Shannon proved it in 1948. Modern links run close to it.

The argument is abstract and the result is a number. Capacity grows with bandwidth and with how loud the signal is relative to the noise. It does not grow because an engineer is clever, past that number. What cleverness buys is getting near the number with a code a machine can actually run. For decades the gap was wide. Turbo codes, low-density parity checks, and polar codes closed it. The radio in a phone, and the link from a space probe, are designed against this ceiling.

Close is a technical word. It means long messages, a noise model that matches the real channel, and a tolerance for delay. A single beep, a burst of interference, or a channel that changes faster than the code expects will not hit the textbook number. The theorem tells you when you are done inventing modulation. It does not tell you the weather.