| Wireless communications have gained much currency in the last few decades. In this thesis we present results regarding several wireless communication systems, in particular, wireless networks.; It is known that in an ad hoc network, if the connection strengths between nodes follow a distance-based decay law, the throughput scales like O( n ), where n is the number of nodes. In Chapter 2 we introduce randomness in the connection strengths and examine the effects of this on the throughput. We assume that all the channels are drawn independently from a common distribution and are not governed by a distance-decay law. For certain distributions, a throughput of nlogn d with d > 0 is possible, which is a significant improvement over the O( n ) results. In Chapter 3, we generalize the network model to two-scale networks. This model incorporates the distance-decay law for nodes that are separated by large distances, while maintaining randomness in close neighborhoods of a node.; In Chapter 4, we consider a model of an erasure wireless network, in which nodes broadcast messages to other nodes over erasure links. For such networks and in certain multicast scenarios, we obtain the precise capacity region. This region has a max-flow, min-cut interpretation and can be achieved using linear codes. We require the side-information regarding erasure locations on all links to be available to the destinations. Thus; we have the capacity region for a non-trivial class of wireless networks.; In Chapter 5, we first show that for networks with certain wireless features it suboptimal to separate channel and network coding. Restricting the permitted operations for each node to forwarding and decoding, we propose greedy and decentralized algorithms that determine the optimal operation for each node, such that the rate achievable at the destination is maximized.; In Chapter 6, we consider a point-to-point communication system, involving multiple transmit and receive antennas. Maximum-likelihood decoding of the received message is an integer least-squares problem and is NP-complete. We propose and analyze an algorithm that is a generalization of the sphere decoding algorithm and allows for suboptimal decoding. This algorithm increases efficiency significantly and allows us to tradeoff performance with computational complexity. |
