The Noisy Channel Coding Theorem

The Noisy Channel Coding Theorem states that it's possible to reliably transmit information over a noisy communication channel—where some data may get distorted—by using appropriate error-correcting codes. These codes add extra bits to detect and fix errors introduced during transmission. The theorem tells us that, given sufficient coding complexity, we can approach the maximum data rate (capacity) of the channel with arbitrarily low error probability. In essence, it provides a fundamental limit and methodology for efficient, reliable communication despite interference or noise.