Capacity theorems for relay networks and wireless Ad Hoc networks

Abstract

Relaying has received great attention in both academia and industry in being able to enhance the network throughput performance. Nevertheless, the optimal relaying strategies are known only for some limited cases. In the first part of this dissertation, we characterize the capacity of two new classes of three-node relay channels and the multicast capacity of a new class of multicast relay networks. In the first two classes of relay channels, which we call more capable and less noisy relay channels, the channel seen by the relay is stronger than that seen by the destination in a certain sense, which resembles the conditions for the more capable and less noisy broadcast channels. In more capable relay channels, decode-and-forward (DF) is shown to be optimal. The more capable relay channel includes as special cases several examples in the literature where DF is shown to be optimal. In less noisy relay channels, partial decode-and-forward (PDF) is shown to achieve the capacity. This is the third class of relay channels where PDF is shown to be optimal, where two previously known classes are the semideterministic relay channel and the relay channel with orthogonal components at the source. By using the definition of less noisy relay channel, we can easily construct many examples where DF is strictly suboptimal but PDF is capacity achieving. Next, we characterize the multicast capacity of a class of multicast relay networks with a tree topology. This class of multicast tree networks includes the class of diamond networks studied by Kang and Ulukus as a special case, where they showed that the capacity can be strictly lower than the cut-set bound. For achievablity, a novel coding scheme is constructed where some relays employ a combination of DF and compress-and-forward (CF) and the other relays perform a random binning such that codebook constructions and relay operations are independent for each node and do not depend on the network topology. For converse, a new t...