In the celebrated slotted ALOHA system, multiple users access a shared medium to a base-station in a distributed fashion, leading to collisions and data-loss. We take a slight detour and present an information theoretic re-look, where variable-sized packets arrive independently at N transmitters. The packets carry a strict delay constraint, that it should be delivered within a single time-slot. However, each user is aware only of its own packet arrival process. The following two questions are of interest. 1) Can all the packets be successfully delivered within the delay constraint, without knowing how much data other users may have? 2) If yes, can we find the minimum average power required by the users to deliver all the data to the destination? After reviewing the basics of ALOHA and relevant parts of the Shannon theory of wireless-networks, we will reformulate the ALOHA problem and answer the above questions.
Sibiraj Pillai obtained his PhD in Computer Science and Communications from EPFL in 2007. He was a research fellow at the University of Melbourne from 2007 to April 2009. Since then, he is an Assistant Professor at the Electrical Engineering Department of IIT Bombay. He teaches Information Theory, Wireless Communications, and other basic communication and signal processing courses at IIT Bombay, and researches primarily of Gaussian problems in Network Information Theory. He is currently developing the information systems and radios laboratory at the EE department, which specializes on software radio algorithms for the physical layer. He is the recipient of Australian Early Career Researcher Award in 2009 for excellence in communication theory.