We consider single-source single-sink (ss-ss) multi-hop relay networks, with slow-fading links and single-antenna half-duplex relay nodes. While two-hop cooperative relay networks have been studied in great detail in terms of the diversity-multiplexing tradeoff (DMT), few results are available for more general networks. In this paper, we identify two families of networks that are multi-hop generalizations of the two-hop network: K-Parallel-Path (KPP) networks and layered networks. KPP networks can be viewed as the union of K node-disjoint parallel relaying paths, each of length greater than one. KPP networks are then generalized to KPP(I) networks, which permit interference between paths and to KPP(D) networks, which possess a direct link from source to sink. We characterize the DMT of these families of networks completely for K > 3. Layered networks are networks comprising of layers of relays with edges existing only between adjacent layers, with more than one relay in each layer. We prove that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4. For multiple-antenna KPP and layered networks, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks. For arbitrary multi-terminal wireless networks with multiple source-sink pairs, the maximum achievable diversity is shown to be equal to the min-cut between the corresponding source and the sink, irrespective of whether the network has half-duplex or full-duplex relays. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable. Along the way, we derive the optimal DMT of a generalized parallel channel and derive lower bounds for the DMT of triangular channel matrices, which are useful in DMT computation of various protocols. All protocols in this paper are explicit and use only amplify-and-forward (AF) relaying. We also construct codes with short block-lengths based on cyclic division algebras that achieve the optimal DMT for all the proposed schemes. Two key implications of the results in the paper are that the half-duplex constraint does not entail any rate loss for a large class of cooperative networks and that simple AF protocols are often sufficient to attain the optimal DMT.

This thesis consists of two parts addressing two different problems in fading channels. The first part deals with asynchronous cooperative relay communication. The assumption of nodes in a cooperative communication relay network operating in synchronous fashion is often unrealistic. In this work we consider two different models of asynchronous operation in cooperative-diversity networks experiencing slow fading and examine the corresponding Diversity-Multiplexing Tradeoffs (DMT). For both models, we propose protocols and distributed space-time codes that asymptotically achieve the transmit diversity bound on DMT for all multiplexing gains and for number of relays N ≥ 2. The distributed space-time codes for all the protocols considered are based on Cyclic Division Algebras (CDA). The second part of the work addresses the DMT analysis of diversity embedded codes for MIMO channels. Diversity embedded codes are high rate codes that are designed so that they have a high diversity code embedded within them. This allows a form of opportunistic communication depending on the channel conditions. The high diversity code ensures that at least a part of the information is received reliably, whereas the embedded high rate code allows additional information to be transferred if the channel is good. This can be thought of coding the data into two streams: high priority and low priority streams so that the high priority stream gets a better reliability than the lower priority stream. We show that superposition based diversity embedded codes in conjunction with naive single stream decoding is sub-optimal in terms of the DM tradeoff. We then construct explicit diversity embedded codes by the superposition of approximately universal space-time codes from CDAs. The relationship between broadcast channels and the diversity embedded setting is then utilized to provide some achievable Diversity Gain Region (DGR) for MIMO broadcast Channels.