Multicast transmission, in which data is sent from a source to multiple destinations, is an important form of data communication in wireless networks. Numerous applications require multicast transmission, including content distribution, conferencing, and military and emergency messages, as well as certain network control mechanisms, such as timing synchronization and route establishment. Finding a means to ensure efficient, reliable multicast communication that can adapt to changing channel conditions and be implemented in a distributed way remains a challenging open problem. In this dissertation, we propose to meet that challenge through the use of random coding of data packets coupled with random access to a shared channel. We present an analysis of both the throughput and delay performance of this scheme.

We first analyze the multicast throughput in a random access network of finitely many nodes, each of which serves as either a source or a destination node. Our work quantifies throughput in terms of both the Shannon capacity region and the stable throughput region and indicates the extent to which a random linear coding scheme can outperform a packet retransmission scheme. Next, we extend these notions to a random access network of general topology in which each node can act as a receiver or a sender for multiple multicast flows. We present schemes for nodes in the network to compute their random access transmission probabilities in such a way as to maximize a weighted proportional fairness objective function of the multicast throughput. In the schemes we propose, each node can compute its transmission probability using information from neighboring nodes up to two hops away.

We then turn our focus to queueing delay performance and propose that random coding of packets be modeled as a bulk-service queueing system, where packets are served and depart the queue in groups. We analyze within this framework two different coding schemes: one with fixed expected coding rate and another with a coding rate that adapts to the traffic load. Finally, we return to the question of multicast throughput and address the effects of packet length, overhead, and the time-varying nature of the wireless channel.