Capacity of an Erasure Queue-Channel Without and With Feedback

Speaker: Krishna Jagannathan

Abstract

A queue-channel is a model that captures waiting time-dependent degradation of information bits—a scenario motivated by quantum communications and delay-sensitive streaming. Recent work has characterized the capacity of the erasure queue-channel, and other noise models encountered in quantum communications . In this talk, we first review the capacity results for an erasure queue-channel without feedback and show that the capacity has a simple form that depends on the Laplace transform of the stationary sojourn time distribution. Next, we study an erasure queue-channel with feedback, and ask after the optimal transmission strategy to minimize waiting-induced erasures. Specifically, we assume that instantaneous feedback of queue-length (or of the queue-channel output) is available at the transmitter, which can modulate the rate of Poisson transmissions into the queue-channel. We pose an optimal control problem using HJB-style equations to maximize the information capacity, when the transmitter can choose from a bounded set of transmission rates. We show (under a numerically verifiable condition) that the optimal transmission policy is a single-threshold policy of the bang-bang type. In other words, transmitting at the maximum (minimum) possible rate when the queue is below (above) a threshold, maximizes the information capacity of the erasure queue-channel with feedback.

Bio

Krishna Jagannathan obtained his B. Tech. in Electrical Engineering from IIT Madras in 2004, and the S.M. and Ph.D. degrees in Electrical Engineering and Computer Science from the Massachusetts Institute of Technology (MIT) in 2006 and 2010 respectively. During 2010-2011, he was a visiting post-doctoral scholar in Computing and Mathematical Sciences at Caltech, and an off-campus post-doctoral fellow at MIT. Since November 2011, he has been with the Department of Electrical Engineering, IIT Madras, where he is currently an associate professor. He worked as a consultant at the Mathematical Sciences Research Center, Bell Laboratories, Murray Hill, NJ in 2005, and as an engineering intern at Qualcomm, Campbell, CA in 2007. His research interests lie in the stochastic modeling and analysis of communication networks, network control, and queuing theory.