Lattice Coding for the Two-Way Line Network

Full-duplex allows for the simultaneous flow of information in two directions and, in point-to-point Gaussian two-way channels, doubles capacity. A two-way line network where two sources exchange messages through multiple serial relays is considered. It is shown that when all nodes are full duplex, one may achieve to within a constant gap, independent of the number of relays, of the capacity of two one-way line networks. This shows that, even in the presence of relays that carry information in two directions, full duplex is able to approximately double capacity. A novel lattice coding scheme is developed for the two-way line network with two relays, which may be extended to an arbitrary number of relays and to half-duplex scenarios. The key technical contribution is the achievability strategy, where each relay decodes the sum of several signals (using lattice codes) and then re-encodes it into another lattice codeword. This allows other nodes to again decode sums of codewords. The presented lattice-coding-based scheme ensures that both directions simultaneously fully utilize the relays' powers, even for asymmetric channels. The symmetric rate achieved by the proposed scheme is within 0.5 log 5 bit/Hz/s of the symmetric rate capacity regardless of the number of relays.