University at Buffalo - The State University of New York

Published: February 14, 2008

By KEVIN FRYLING
Reporter Staff Writer

It wasn’t a big surprise that Avner Peleg chose to pursue a doctorate after growing up in a family of academics in Jerusalem. What raised a few eyebrows, he says, was his decision to study physics rather than follow in the footsteps of his father, a mathematician who studied under Robert Aumann, winner of the 2005 Nobel Prize in Economics.

Avner Peleg says his background in physics has been valuable in his field of study—fiber-optics communications systems, specifically the mathematical modeling of fiber-optic systems using statistical tools.
PHOTO: NANCY J. PARISI

All this makes it even more fitting that his research has since brought him back to the subject that was also his father’s passion, says Peleg, who joined the UB faculty last fall as an assistant professor in the Department of Mathematics, College of Arts and Sciences. Prior to coming to UB, he served as a postdoctoral research associate at the Los Alamos National Laboratory, and later the University of Arizona.

“The main subject of my research now is fiber-optic communications systems”—specifically the mathematical modeling of fiber-optic systems using statistical tools, says Peleg. “The question I’m trying to answer is how the interplay of randomness in the bit pattern and non-linear phenomena contribute to error generation,” he says.

Since information in a fiber-optic network travels as a series of pulses of light—with each pulse representing a specific bit of data in a long stream of information—Peleg says it’s crucial to learn more about the combined impact of these phenomena, as it can contribute to serious interruptions in the flow of information and form a significant hurdle in the race toward the future of high-speed optical communication, including video-on-demand and ultra-broadband Internet. Peleg explains that non-linear phenomena refer to interactions between the light pulses and the fiber-optic cable—interactions that distort the shape of the waves and degrade transmission—and randomness to the fact that at any given time there is an equal chance of having a 1-bit and a 0-bit in the bit string, and this is reflected in the pulse sequence.

The challenges of fiber-optic transmission are complicated even further in the case of multichannel transmission—in which the same fiber-optic cable transports multiple series of light pulses using different frequencies—because each new channel compounds the chance of detrimental interaction between information streams inside the cable, he says.

“One of the non-linear phenomena that is important in multichannel transmission is called Raman scattering. In this case, the more information you transmit, the more important the energy exchange in pulse collisions becomes,” Peleg says. “If you have a fiber-optic network system with just a few channels, then this effect is completely negligible. But the magnitude of the effect grows by the square of the number of channels.”

Currently, Peleg says typical high-speed broadband connections exploit as many as 10 channels capable of carrying information at a total rate of about 100 gigabytes per second. “Obviously in the future,” he says, “you want to do more than this.” To illustrate the sheer magnitude of information that communication companies are looking to transmit, he points to a 2003 study by Lucent Technologies (now Alcatel-Lucent) in which researchers used a fiber-optic cable carrying 109 channels to send information along a transoceanic distance at a staggering rate of 1.09 terabytes per second.

“What is the probability for an error? How does the probability for an error in the receiver depend on the number of channels? How does it depend on the propagation distance?” Peleg asks. “What we’re trying to do is make the best mathematical models to answer these types of questions. The next step, once we understand how strong or how severe the phenomenon is, is to find ways to reduce it.”

The recipient of master’s and doctoral degrees in physics from the University of Jerusalem, as well as a bachelor’s degree in physics from the Israel Institute of Technology, Peleg says his background in physics has given him a great advantage when it comes to tackling the mathematical puzzles that fascinate him. His own investigations as part of a team of scientists at Los Alamos have even been cited as helping establish a new field of inquiry—the statistical physics of optical communication.

“It’s important to understand the underlying physics because otherwise the mathematical model would be artificial,” he says. “Being resourceful in mathematics is extremely helpful, but I’m still using many of the skills I learned during my Ph.D.”

UB faculty members working on topics related to his research are found not only in the Department of Mathematics, but also in the School of Engineering and Applied Sciences, says Peleg, who is cultivating relationships with colleagues who share his interests and eyeing future collaborations. In addition to fiber optics, Peleg says several colleagues in the math department’s applied mathematics group, of which he is a member, are performing research on materials science—a subject related to his doctoral thesis. His academic activities—both this semester and last fall—also include teaching an undergraduate math course on differential equations.

“One of the things that surprised me, in a good way, is that the level of students that I have encountered in this course has been better than the level of students at the University of Arizona,” Peleg says. “Maybe it’s representative of the university, maybe it just depends on the course, but I’ve been very pleased by the level of students here.”

Although his family remains overseas—his brother, Gadi, a physicist, works in Israel and sister, Orit, an archaeologist, is performing postdoctoral research at Oxford—Peleg, who resides in Williamsville, says the professional opportunities available to him in the United States and at UB provide “an ideal place to work in science.”

“This is a large department,” he adds. “And the fact the university’s growing also makes it attractive. I felt that at Los Alamos they were trying to bring in the best people that they could—both from within the U.S., but also from abroad—and I feel that here they have this same attitude. Usually when a place is growing it means good things are happening.”