Asymmetric compute-and-forward

This paper generalizes the compute-and-forward framework to allow for unequal (or asymmetric) power allocation across transmitters. Each transmitter's codebook is formed using a fine lattice that is chosen to ensure decodability as well as a coarse lattice that is chosen to enforce the power constraint. The employed lattices are drawn from a nested lattice chain, which makes it possible for the receivers to decode integer-linear combinations of the transmitted codewords. Like the original compute-and-forward framework, this scheme has a natural interpretation in terms of sending linear combinations of messages that are vectors over a finite field. Interestingly, each transmitter's power constraint and noise tolerance can be viewed in terms of restrictions on the available “signal levels”. That is, transmitters with less power must send zeros along higher order levels and transmitters that need to tolerate more noise must send zeros along lower order levels.