Lattice coding for the Two-way Two-relay channel

We develop a novel lattice coding scheme for the Two-way Two-relay Channel: 1 ↔ 2 ↔ 3 ↔ 4, where Node 1 and 4 communicate with each other through two relay nodes 2 and 3. Each node only communicates with its neighboring nodes. The key technical contribution is the lattice-based achievability strategy, where each relay is able to remove the noise while decoding the sum of several signals in a Block Markov strategy and then re-encode the signal into another lattice codeword using the so-called “Re-distribution Transform”. This allows nodes further down the line to again decode sums of lattice codewords. The symmetric rate achieved by the proposed lattice coding scheme is within 1/2 log 3 bit/Hz/s of the symmetric rate capacity.