Salman Avestimehr answers questions like "How much information can a wireless network transmit?"
Given that Claude Shannon, the father of information theory, established the fundamental limits of point-to-point communication in 1948, one might think this question would have been answered by now, but it hasn't. "People have been trying to generalize what Shannon developed and find the fundamental limits of communication over networks," says Avestimehr. "But it turns out these problems are very complex. You just change the problem a bit by adding one relay to the system and then nobody knows how to solve it. It's been an open problem for 40 years."
Shannon developed and find the fundamental limits of communication over networks," says Avestimehr. "But it turns out these problems are very complex. You just change the problem a bit by adding one relay to the system and then nobody knows how to solve it. It's been an open problem for 40 years."
Rather than trying to prove the limits of wireless networks precisely, Avestimehr created a deterministic model to approximate the maximum amount of data a wireless network could possibly communicate. "Before people were trying to characterize the capacity of wireless networks exactly. But from an engineering perspective you don't need to know it exactly," he says. "So my goal was to build simplified models that can approximate the capacity of wireless networks."
With this information, electrical engineers can determine how close communication protocols—like Bluetooth or WiFi—come to the ideal. "People have their schemes but if you don't know the theoretical limits, you don't know how good it is. Now, with our model, we can say what the capacity is approximately, so whatever scheme you come up with, you can compare it to see how well it's doing."
Using what he learns about the theoretical limits, Avestimehr also designs better wireless network protocols. His work has shed light on how cellular base stations, used to boost reception in buildings, can be improved. "We have found new techniques for relaying information, how you should process the information in a distributed fashion," he says. "You can get a lot of gain over just repeating the signal at a relay."
Avestimehr is in discussions with engineers at Qualcomm and other telecommunication companies about putting these ideas into next generation of wireless networks. "What's really important for us is the link to practice," he says. "It's how you formulate the problems and choose what directions you go in, because in theory it's easy just to do math without wondering what's happening in the real world."
Another area where Avestimehr is using information theory to improve technology is in a new field called compressed sensing. Most sensing applications, like digital cameras and MRI machines, collect a lot of information that ends up getting compressed in the final product. In digital photography the silicon used to make the sensor is inexpensive, but the materials in an infrared sensor are much more costly. And remaining perfectly still for 30 minutes while an MRI gathers all that information is tedious.
"Usually there is a lot of redundancy in the data. The role of information theory has been to see the fundamentals on how many measurements do you need to guarantee that you don't lose anything," says Avestimehr. "It turns out that for these kind of signals there is a threshold on the number of measurements, which is much less that you expect, above which you don't lose anything. So you can get the same compressed output with much less measurement."
When he's not proving information theorems or devising new wireless protocols, Avestimehr enjoys the piano, which he has played since he was 7. He says there are some connections between math and music, but he tries not to think about them. "At the time I play piano I really want to enjoy it," he says. "When you play a piece of music, you follow a sequence of simple or complex patterns that take you to a conclusion. The same is also true for a mathematical proof, so in that sense it's similar."