Channels: Pushing Through Noise

A channel carries a message from sender to receiver. Noise corrupts it. The surprising result is that noise does not make reliable communication impossible — it just sets a speed limit with a name: channel capacity.

The trick: add redundancy on purpose

If you want to say a single bit 1 over a noisy line, repeat it: 111. Majority vote recovers the bit — at the cost of sending three bits for one. That is an error-correcting code, and it trades rate for reliability.

Shannon’s noisy-channel theorem says something astonishing: for any noisy channel there is a maximum rate — the capacity — below which you can make errors as small as you like, while above it errors are unavoidable. You do not have to slow to a crawl to be perfect. You have to be just under the ceiling.