In this project, we use lattice and other structured coding techniques to induce alignment in wireless networks. This effort uses these codes on three different fronts: a.) Interference networks, where we use structured codes to align the interference seen at each receiver. The objective is to determine the capacity of this channel to within a constant gap using these codes. b.) Cognitive networks - where we use lattice codes to mitigate the interference seen by both the licensed and the cognitive radios. We exploit code structure to both (partially) learn the interfering signal at the cognitive radio and then use this knowledge to precode/align our interference signal. c.) Secure wireless networks: again, we utilize the structure of the codebook to determine simple transformations at the source in order to keep eavesdroppers in the network at bay. We employ these codes to detect, and depending on code structure, correct for modification attacks on the codebook.
This project advanced the science in our understanding of mechanisms to handle interference in wireless networks in two respects: in building a greater understanding of the manner in which time variability can be utilized in order to affect alignment (so called ergodic alignment), and well as manner in which networks (wired or wireless) can utilize interference alignment through the notion of network alignment. Both these techniques utilize structure within signaling in a manner that was not considered possible before, and present guarantees for finite SNR/real-world networks. These have direct implications for next generation wireless networks as well as network coded wired/optical networks of the future. Our results guarantee that, for a wide class of networks, close to one half of the point-to-point (also called as single user) channel capacity without the presence of interferers can be achieved in the presence of interferers, using alignment. In one case, the idea is to combine two different instances of the channel into one, in a manner where the interference in one is counteracted in the other. In the second case, an extension of transmission symbol is utilized, in order for multiple unicasts, or multiple groupcasts, to proceed simultaneously together, and a suitable embedding dimension is picked to enable interference alignment.
