Still, Shannon did not foresee the success of Gallager’s codes. “My recollection is he thought they were interesting, but I didn’t have the sense that he was excited by them,” Gallager says. He understands why. Gallager’s codes approached channel capacity as they got longer; but as they got longer, the decoding process also grew more complex–far too complex for the computers of the time. Coding researchers knew, of course, that computers would improve. But no one knew whose codes those improvements would favor.
Nonetheless, MIT immediately hired Gallager as a faculty member on the strength of his thesis. In the ensuing years, while his own coding scheme languished in obscurity, he taught and mentored a wave of brilliant students–including Massey, Forney, and Berlekamp–whose contributions to coding theory had more immediate practical implications than his own.
Gallager, however, seems as unruffled by the long neglect of his codes as he does by their recent revival–perhaps because he always took the long view. “He has a knack of inventing things that lie dormant for tens of years until people suddenly realize it’s pretty good stuff,” says Vincent Chan ‘71, MS ‘71, EE ‘72, PhD ‘74, a professor of electrical engineering who still displays by his desk the doorplate from the office he once shared with Shannon. Chan recalls a recent visit to the labs of a major software company, where a researcher was boasting of a new compression technique that would enable video files to take up only a hundredth as much memory as they do now. Chan felt obliged to point out that Gallager had introduced the technique in 1974. “Many of these ideas take quite a bit of time to think through,” he says, “and at the time that you’re thinking them through, there are many, many options. And you really have to think very carefully and maybe over a long period of time before you figure out which one is the right one. Bob does that a lot.”
Muriel Médard ‘89, ‘90, MS ‘91, ScD ‘95, an information theorist in the Research Lab of Electronics, agrees. “Bob wasn’t running around trying to publish and make sure he wasn’t getting scooped,” she says. For instance, Médard recalls a conversation between Gallager and a prominent younger information theorist, who in describing his own work cited a recently proved theorem that it relied upon. “Bob starts rummaging through stuff, the way he does,” Médard says. Eventually he produced a tattered copy of one of his own papers. “He had this teensy-weensy little proof,” Médard says. “And it was like a footnote. A thick footnote, but a footnote. ‘They named that?’ ‘Yeah, Bob, it’s a major theorem now.’ ”
Today, Gallager’s codes underlie the approaches that come closest to the maximum data rate for a given communication channel–closer even than turbo codes. In addition to their applications in telecommunications, they’re beginning to replace the older codes used to protect data in disk drives and other storage devices.
To people like Forney, who were at MIT during what he calls the “golden age” of coding theory, the fact that the challenge issued by Shannon’s 1948 paper has been met is somewhat bittersweet. “Those of us who know and love coding are reluctant to say that the problem has been completely solved,” says Forney. “But it’s true that most people have moved on to other things.”
“From 1950 to 1965, MIT was the hotbed of information theory,” says Joel West. “It really was a golden age.”