In those predigital days, communications channels — such as phone lines or radio bands — were particularly susceptible to the electrical or electromagnetic disruptions known as “noise.” Shannon proved the counterintuitive result that no matter how noisy a channel, information could be sent over it error free. All you needed was a way to add enough redundancy to the information so that errors could be corrected. He also demonstrated that there was a hard limit on how efficient those error-correcting codes could be — a minimum amount of extra information that would guarantee near-zero error. Since longer codes take longer to send, a minimum code length implied a maximum transmission rate — the Shannon limit. Finally, Shannon proved that codes approaching that limit must exist. But he didn’t show how to find them.

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