Lattice strategies for a multi-pair bi-directional relay network

We consider a cellular network inspired channel model which consists of the bi-directional exchange of information between a base-station and M terminal nodes with the help of a relay. The base-station has a message for each of M terminals, and conversely, each terminal node has a message for the base-station. A single relay assists the bi-directional communication endeavor. We assume an AWGN channel model with direct links (omitted in previous studies) between the base-station, relay, and half-duplex nodes. In this scenario, we derive achievable rate regions for two temporal protocols - needed in half-duplex networks - which indicate which users transmit when. These achievable rate regions are based on a novel lattice encoding and decoding strategy which outperforms previously derived regions using random-coding based decode-and-forward strategies under certain channel conditions. The terminal nodes employ nested lattice codes, and the relay decodes a series of codeword combinations - one of the main novelties of our scheme - from which it deduce the sum-codewords of the base-station to terminal node i, which it then broadcasts. This scheme differs markedly from previously considered successive-decoding based lattice strategies and provides a more general framework for the joint decoding of lattice codewords in a MAC. Numerical evaluations of our lattice-based inner bounds are shown to improve upon previous random-coding based schemes under certain channel conditions, and are compared to half-duplex cut-set outer bounds. We further demonstrate a constant sum-rate gap result using this lattice-based scheme for symmetric channels for one of the two protocols.