Stability of Scheduled Message Communication over Degraded Broadcast Channels

We consider scheduled message communication over a discrete memoryless degraded broadcast channel. The framework we consider here models both the random message arrivals and the subsequent reliable communication by suitably combining techniques from queueing theory and information theory. The channel from the transmitter to each of the receivers is quasi-static, flat, and with independent fades across the receivers. Requests for message transmissions are assumed to arrive according to an i.i.d. arrival process. Then, (i) we derive an outer bound to the region of message arrival vectors achievable by the class of stationary scheduling policies, (ii) we show for any message arrival vector that satisfies the outerbound, that there exists a stationary ``state-independent'' policy that results in a stable system for the corresponding message arrival process, and (iii) under two asymptotic regimes, we show that the stability region of nat arrival rate vectors has information-theoretic capacity region interpretation.Comment: 5 pages, Submitted to 2006 International Symposium on Information Theor

Improved Delay Estimates for a Queueing Model for Random Linear Coding for Unicast

Consider a lossy communication channel for unicast with zero-delay feedback. For this communication scenario, a simple retransmission scheme is optimum with respect to delay. An alternative approach is to use random linear coding in automatic repeat-request (ARQ) mode. We extend the work of Shrader and Ephremides, by deriving an expression for the delay of random linear coding over field of infinite size. Simulation results for various field sizes are also provided.Comment: 5 pages, 3 figures, accepted at the 2009 IEEE International Symposium on Information Theor

Scheduling for Stable and Reliable Communication over Multiaccess Channels and Degraded Broadcast Channels

Information-theoretic arguments focus on modeling the reliability of information transmission, assuming availability of infinite data at sources, thus ignoring randomness in message generation times at the respective sources. However, in information transport networks, not only is reliable transmission important, but also stability, i.e., finiteness of mean delay incurred by messages from the time of generation to the time of successful reception. Usually, delay analysis is done separately using queueing-theoretic arguments, whereas reliable information transmission is studied using information theory. In this thesis, we investigate these two important aspects of data communication jointly by suitably combining models from these two fields. In particular, we model scheduled communication of messages, that arrive in a random process, (i) over multiaccess channels, with either independent decoding or joint decoding, and (ii) over degraded broadcast channels. The scheduling policies proposed permit up to a certain maximum number of messages for simultaneous transmission. In the first part of the thesis, we develop a multi-class discrete-time processor-sharing queueing model, and then investigate the stability of this queue. In particular, we model the queue by a discrete-time Markov chain defined on a countable state space, and then establish (i) a sufficient condition for $c$-regularity of the chain, and hence positive recurrence and finiteness of stationary mean of the function $c$ of the state, and (ii) a sufficient condition for transience of the chain. These stability results form the basis for the conclusions drawn in the thesis.Comment: Ph.D. Thesis submitted to Department of Electrical Communication Engineering at Indian Institute of Science, Bangalore, Indi