Structured lattice codes in network communication
As we can see in our work on approximate characterization of wireless relay network capacity, the quantize-map-forward strategy that achieved approximate optimality was based on random Gaussian codebooks. In order to explore lower complexity structures, we have explored the role of lattice codes in wireless relay network information flow. We show that the approximation result can be established by using lattices for transmission and quantization along with structured mappings at the relays. This also extended the original scalar quantizer analysis to vector quantizers and obtained a slightly better approximation constant. In this case, the lattices achieve a similar performance to random Gaussian codes.
We also examine the role of lattice codes in (approximately) achieving the rate-region for a class of wireless relay-interference networks. We study this in the context of a two-stage Gaussian relay-interference networks where there are weak cross-links, causing the networks to behave like a chain of Z Gaussian channels. Our main result is an approximate characterization of the capacity region for such networks. We propose a new interference management scheme, termed interference neutralization, which is implemented using structured lattice codes. This scheme allows for over-the-air interference removal, without the transmitters having complete access the interfering signals. In this case, we do not know of a random Gaussian coding strategy that can achieve the same performance as the lattice codes, which implement interference neutralization.
Finally, we have designed asymmetric multiple description lattice quantizers, which covers the entire range of the distortion profile, from symmetric to successive refinement. We present a solution to the labeling problem, which is an important part of the construction. We show that this construction is optimal in the high-rate regime, by comparing it to the information-theoretic bounds.