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The Shannon Limit, and the Codes Nobody Could Find
Shannon’s 1948 proof showed that almost every code is excellent; engineers then needed forty-five years to build one that was.
Noise does not force errors. Every telephone engineer working in 1948 would have called that claim nonsense, and their reasoning was sound: a line that corrupts one symbol in a hundred will corrupt roughly one symbol in a hundred no matter how the message is dressed up, and the only known remedies were to shout louder or to say everything twice. Both cost something, and both run into a limit. And yet the noisy-channel coding theorem, published that year by Claude Shannon at Bell Labs, says that every channel carries a number called its channel capacity, and that at any transmission rate strictly below that number the probability of a wrong bit arriving at the far end can be pushed as close to zero as the customer cares to specify.
The Shannon limit, as that number is now called, is the highest rate in bits per second at which a channel can carry information reliably. It depends on the channel’s bandwidth and its noise, and on nothing that better transmitters or better receivers can be made to do.
The scandal is in how Shannon knew. His proof exhibits no code. It does not describe one or hint at where…
