Combinatorial design theory is rooted in recreational mathematics and studies the arrangement of finite-set elements into subsets subject to certain "nice" properties. These designs often relate to various areas within communications. In the first part of the talk, regenerating code construction from combinatorial designs will be discussed. Regenerating codes have been proposed as a mechanism for dealing with data-reliability in large distributed storage systems, with additional requirements on repair. When nodes fail, the system needs to be repaired in a speedy manner, by consuming as few resources (such as drives accessed or energy) as possible. We will demonstrate that our constructions based on combinatorial designs are a natural fit for this problem. Following this, I will overview our work that relates combinatorial designs with network coding based function computation. I will demonstrate that an appropriate interpretation of designs can construct a family of directed acyclic networks that have several interesting properties. Our work shows that the computation rate of acyclic networks depends significantly on the source alphabets, which is in contrast with multiple unicast networks where the rate is independent of the source alphabet.
Aditya Ramamoorthy is an Associate Professor of Electrical and Computer Engineering at Iowa State University. He received his BTech degree in Electrical Engineering from the IIT Delhi in 1999, and the MS and PhD degrees from the University of California, Los Angeles in 2002 and 2005 respectively. From 2005 to 2006 he was with the data storage signal processing group at Marvell Semiconductor Inc. He served as an associate editor for the IEEE Transactions on Communications from 2011-2014. He is the recipient of the 2012 Iowa State University's Early Career Engineering Faculty Research Award, the 2012 NSF CAREER award, and the Harpole-Pentair professorship in 2009 and 2010. His research interests are in the areas of network information theory, channel coding and signal processing for nanotechnology and bioinformatics.