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Abstract

This thesis addresses issues of design and performance analysis in cellular communication networks. We investigate topics relevant to both uplink and downlink. For the uplink part, we address the stability region of the slotted Aloha protocol under the collision channel model, for the case of a finite number of independent users. The stability region (i.e., the set of arrival rate vectors such that the whole queuing system can be made stable) is in general unknown when the number of users is more than three. We seek to characterize the set of stabilizable rate vectors, whereas most existing works only provide bounds on the region of stabilized rate vectors under a given control (i.e., vector of contention probabilities). We choose a natural and important inner bound on the Aloha stability region. The results we obtain include equivalent forms of and alternate membership testing for this set, as well as other properties such as various geometrically intuitive and simple inner and outer bounds, and generalized convexity properties of the associated "excess rate" functions.

For the downlink part, we seek to characterize the delay when broadcasting random linear combinations of the information packets over independent erasure channels to a finite number of users. Of interest is the random delay until all the receivers recover all the packets initially queued at the base station (i.e., the sender). This falls into the study of certain order statistic of random variables. We obtain tight lower and upper bounds, exact expressions and finite-step computational procedures (recurrence) for the moment(s) of the random delay. We also investigate the dependence of the delay on the code blocklength (under random linear combinations of packets as the scheme employed in random linear network coding), and on the number of receivers, respectively.