Though random codes are shown to be optimal for point-to-point channels, codes with algebraic structure are found to be useful in many network scenarios. This thesis demonstrates the role of structured codes in several network and MIMO settings. In MIMO channels, structured codes can be used to improve receiver design. Traditional receiver architectures decorrelate the mixed data streams and recover each of them individually. Although optimal when the channel matrix is orthogonal, this can be highly sub-optimal when the channel is near singular. To overcome this limitation, a new architecture that recovers linear combinations of the data streams instead of the data streams individually is proposed. The proposed integer-forcing receiver outperforms traditional linear architectures and achieves the optimal diversity-multiplexing tradeoff. In network information theory, it has been shown that structured codes are useful for computation over multiple-access channels. This thesis considers function computation across general relay networks and proposes a scheme that decouples the physical and network layers. By using lattice codes in the physical layer and network codes in the network layer, the proposed scheme achieves the optimal distortion to within a constant factor. Finally, structured codes can be used to efficiently transmit channel state information when global channel state information is absent in networks. It is shown that sending a function of the channel state information is sufficient and can be much more efficient than sending the full information.

In a network, interference between transmitters is usually viewed as highly undesirable and clever algorithms and protocols have been devised to avoid it. Collectively, these strategies transform the physical layer into a set of reliable bit pipes which can then be used seamlessly by higher layers in the protocol stack. Unfortunately, interference avoidance results in sharply decreasing rates as the number of users increases. In this thesis, we develop a new tool, computation coding, that allows receivers to reliably decode equations of transmitted messages by harnessing the interference structure of the channel. Applied to a wireless network, this enables relays to decode linear functions of the transmitted messages with coefficients dictated by the fading realization. Relays can then forward these equations towards the destinations which simply collect enough equations to solve for their desired messages. Structured codes (such as lattices) ensure that these linear combinations can be decoded reliably at the relays, often at far higher rates than the messages individually. Through examples drawn from cooperative communication including cellular uplink, distributed MIMO and wireless network coding, we demonstrate that this compute-and-forward strategy can improve end-to-end throughput in a network. As a consequence, we will see that structured codes can play an important role in approaching the capacity of networks. We also show that our techniques can result in both energy and delay savings for distributed signal processing over a sensor network. Finally, by viewing interference as implicit computation, we provide a new perspective on the interference channel with time-varying fading. We describe a simple interference alignment scheme that enables each user to achieve at least half its interference-free capacity at any signal-to-noise ratio.