Approaching the capacity of two‐pair bidirectional Gaussian relay networks

The authors present an improved achievable rate region for two‐pair bidirectional Gaussian relay networks based on successive compute‐and‐forward method. In these networks, one relay helps in the communication between two pairs of users. In their proposed scheme, the authors use nested lattice codes for encoding the messages at the users, and Gaussian random codes for the encoding at the relay. They use the successive compute‐and‐forward strategy to decode two integer linear combinations of the lattice codewords in the uplink, and successive interference cancellation for decoding the Gaussian codewords in the downlink. The downlink channel can be considered as a broadcast channel with two receiver groups, but within each group, a pair of users is considered as an additive white Gaussian noise channel (instead of a broadcast channel) because each node knows its own transmitted message. It is shown that for all channel gains of downlink channels and all channel gains of symmetric uplink channel pairs, the strategy achieves rates to within constant gaps of 1/2 and 3/4 bit/s/Hz per user of the cut‐set upper bound for restricted and non‐restricted models, respectively. These gaps are tighter than those previously obtained for this network, which have not exploited the successive compute‐and‐forward method.