On the Capacity Region of Asymmetric Gaussian Two-Way Line Channel

Lattice codes are known to outperform random codes for certain networks, especially in the Gaussian two-way relay channels (GTWRCs) where lattice codes are able to exploit their linearity. As an extension of the GTWRC, in this paper, we consider the asymmetric Gaussian two-way line network where two nodes exchange their messages through multiple relays. We first investigate the capacity region of the full-duplex two-way two-relay line network. The results can be extended to an arbitrary number of relays and to half-duplex scenarios. This channel consists of four nodes: 1 ↔ 2 ↔ 3 ↔ 4, where nodes 1 and 4 with the help of two full-duplex relays, i.e., nodes 2 and 3, exchange their messages with each other. Using lattice codes, we design a novel scheme that allows the relay nodes to send the data in both directions simultaneously under an asymmetric rate region. In the proposed scheme, each relay decodes the sum of lattice points and then re-encodes it into another lattice codeword (which satisfies the transmit power constraint at the relay). It is shown that the proposed scheme achieves the capacity region of asymmetric two-way line network within 0.5 bit independent of the number of relays.