Speaker: Dr. Tolga M. Duman, Bilkent University, Turkey
Title: Upper Bounds on the Capacity of Deletion Channels Using Channel Fragmentation
We study memoryless channels with synchronization errors as defined by a stochastic channel matrix allowing for symbol drop-outs or symbol insertions with particular emphasis on the binary and non-binary deletion channels. We offer a different look at these channels by considering equivalent models by “fragmenting” the input sequence where different subsequences travel through different channels. The resulting output symbols are combined appropriately to come up with an equivalent input-output representation of the original channel, which allows for derivation of new upper bounds on the channel capacity. We consider both random and deterministic types of fragmentation processes applied to binary and non-binary deletion channels. With two specific applications of this idea, a random fragmentation applied to a binary deletion channel and a deterministic fragmentation process applied to a non-binary deletion channel, we prove certain inequality relations among the capacities of the original channels and those of the introduced sub-channels. The resulting inequalities prove useful in deriving tighter capacity upper bounds for 1) independent identically distributed (i.i.d.) deletion channels when the deletion probability exceeds 0.65, and 2) non-binary deletion channels. Some extensions of these results, for instance, to the case of deletion/substitution channels are also explored.
Tolga M. Duman is a Professor of Electrical and Electronics Engineering Department at Bilkent University in Turkey. He received the B.S. degree from the same university in 1993, M.S. and Ph.D. degrees from Northeastern University, Boston, MA, in 1995 and 1998, respectively, all in electrical engineering. Prior to joining Bilkent University in September 2012, he has been with the Electrical Engineering Department of Arizona State University first as an Assistant Professor (1998-2004), then as an Associate Professor (2004-2008), and a Professor (after 2008). Dr. Duman's current research interests are in systems, with particular focus on communications and signal processing, including wireless and mobile communications, coding/modulation, coding for wireless communications, data storage systems and underwater acoustic communications. Dr. Duman is a Fellow of IEEE, a recipient of the National Science Foundation CAREER Award and IEEE Third Millennium medal. He has served as an editor for various journals, and he is currently the coding and information theory area editor of IEEE Trans. on Communications and the Editor-in-Chief of Elsevier's Physical Communication.