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Much of the power of Shannon’s idea lay in its unification of what had been a diverse bunch of technologies. “Until then, communication wasn’t a unified science,” says MIT’s Gallager. “There was one medium for voice transmission, another medium for radio, still others for data. Claude showed that all communication was fundamentally the same-and furthermore, that you could take any source and represent it by digital data.”

That insight alone would have made Shannon’s paper one of the great analyti-cal achievements of the 20th century. But there was more. Suppose you were trying to send, say, a birthday greeting down a telegraph line, or through a wireless link, or even in the U.S. mail. Shannon was able to show that any such communication channel had a speed limit, measured in binary digits per second. The bad news was that above that speed limit, perfect fidelity was impossible: no matter how cleverly you encoded your message and compressed it, you simply could not make it go faster without throwing some information away.

The mind-blowing good news, however, was that below this speed limit, the transmission was potentially perfect. Not just very good: perfect. Shannon gave a mathematical proof that there had to exist codes that would get you right up to the limit without losing any information at all. Moreover, he demonstrated, perfect transmission would be possible no matter how much static and distortion there might be in the communication channel, and no matter how faint the signal might be. Of course, you might need to encode each letter or pixel with a huge number of bits to guarantee that enough of them would get through. And you might have to devise all kinds of fancy error-correcting schemes so that corrupted parts of the message could be reconstructed at the other end. And yes, in practice the codes would eventually get so long and the communication so slow that you would have to give up and let the noise win. But in principle, you could make the probability of error as close to zero as you wanted.

This “fundamental theorem” of information theory, as Shannon called it, had surprised even him when he discovered it. The conquest of noise seemed to violate all common sense. But for his contemporaries in 1948, seeing the theorem for the first time, the effect was electrifying. “To make the chance of error as small as you wish? Nobody had ever thought of that,” marvels MIT’s Robert Fano, who became a leading information theorist himself in the 1950s-and who still has a reverential photograph of Shannon hanging in his office. “How he got that insight, how he even came to believe such a thing, I don’t know. But almost all modern communication engineering is based on that work.”

Shannon’s work “hangs over everything we do,” agrees Robert Lucky, corporate vice president of applied research at Telcordia, the Bell Labs spinoff previously known as Bellcore. Indeed, he notes, Shannon’s fundamental theorem has served as an ideal and a challenge for succeeding generations. “For 50 years, people have worked to get to the channel capacity he said was possible. Only recently have we gotten close. His influence was profound.”

And, Lucky adds, Shannon’s work inspired the development of “all our modern error-correcting codes and data-compression algorithms.” In other words: no Shannon, no Napster.

Shannon’s theorem explains how we can casually toss around compact discs in a way that no one would have dared with long-playing vinyl records: those error-correcting codes allow the CD player to practically eliminate noise due to scratches and fingerprints before we ever hear it. Shannon’s theorem likewise explains how computer modems can transmit compressed data at tens of thousands of bits per second over ordinary, noise-ridden telephone lines. It explains how NASA scientists were able to get imagery of the planet Neptune back to Earth across three billion kilometers of interplanetary space. And it goes a long way toward explaining why the word “digital” has become synonymous with the highest possible standard in data quality.

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