On the multiple-access channel, the rate advantage of feedback is due to dependence: the channel input sequences, though initially independent, can be made gradually more dependent by cleverly exploiting the feedback. Therefore, upper bounds can be thought of as limits to this dependence. The standard cut-set bound provides such an upper bound. Ozarow (1984) showed that for two users, this upper bound is achievable via a linear "innovation coding" strategy originally due to Schalkwijk and Kailath. Kramer (2002) extended this strategy to more than two users, but noticed that it no longer attains the cut-set upper bound. We present a new upper bounding technique based on work by Hekstra and Willems (1989) that proves capacity results for the linear "innovation coding" strategy for more than two users, and provides the first non-trivial capacity outer bound for noisy feedback. The new capacity results show that the multiple-access rate gain due to feedback only behaves doubly-logarithmically in the number of users, implying that most of the gain can be harvested even if only a small fraction of the users actually have feedback.
This is joint work with Gerhard Kramer (Bell Labs).
Speaker Bio:
Michael Gastpar
received his Engineering degree from ETH in Zurich (1997),
his MS from the University of Illinois at Urbana-Champaign
(1999), and his Ph.D. from EPFL in Lausanne (2002). He was
also student in engineering and philosophy at the Universities
of Edinburgh and Lausanne, and a summer researcher in the
Mathematics of Communications Department at Bell Labs, Lucent
Technologies, Murray Hill, NJ. He is now an Assistant Professor
at the University of California, Berkeley.
His research interests are in network information theory and
related coding and signal processing techniques, with
applications to sensor networks and neuroscience. He won the
2002 EPFL Best Thesis Award and an NSF CAREER award in 2004.